(original) (raw)

%!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: paper.dvi %%Pages: 35 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: Times-Bold Times-Roman Times-Italic Courier %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -f paper.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2002.07.31:1722 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: 8r.enc % @@psencodingfile@{ % author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry", % version = "0.6", % date = "1 July 1998", % filename = "8r.enc", % email = "tex-fonts@@tug.org", % docstring = "Encoding for TrueType or Type 1 fonts % to be used with TeX." % @} % % Idea is to have all the characters normally included in Type 1 fonts % available for typesetting. This is effectively the characters in Adobe % Standard Encoding + ISO Latin 1 + extra characters from Lucida. % % Character code assignments were made as follows: % % (1) the Windows ANSI characters are almost all in their Windows ANSI % positions, because some Windows users cannot easily reencode the % fonts, and it makes no difference on other systems. The only Windows % ANSI characters not available are those that make no sense for % typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen % (173). quotesingle and grave are moved just because it's such an % irritation not having them in TeX positions. % % (2) Remaining characters are assigned arbitrarily to the lower part % of the range, avoiding 0, 10 and 13 in case we meet dumb software. % % (3) Y&Y Lucida Bright includes some extra text characters; in the % hopes that other PostScript fonts, perhaps created for public % consumption, will include them, they are included starting at 0x12. % % (4) Remaining positions left undefined are for use in (hopefully) % upward-compatible revisions, if someday more characters are generally % available. % % (5) hyphen appears twice for compatibility with both % ASCII and Windows. % /TeXBase1Encoding [ % 0x00 (encoded characters from Adobe Standard not in Windows 3.1) /.notdef /dotaccent /fi /fl /fraction /hungarumlaut /Lslash /lslash /ogonek /ring /.notdef /breve /minus /.notdef % These are the only two remaining unencoded characters, so may as % well include them. /Zcaron /zcaron % 0x10 /caron /dotlessi % (unusual TeX characters available in, e.g., Lucida Bright) /dotlessj /ff /ffi /ffl /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef % very contentious; it's so painful not having quoteleft and quoteright % at 96 and 145 that we move the things normally found there to here. /grave /quotesingle % 0x20 (ASCII begins) /space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash % 0x30 /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /less /equal /greater /question % 0x40 /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O % 0x50 /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore % 0x60 /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o % 0x70 /p /q /r /s /t /u /v /w /x /y /z /braceleft /bar /braceright /asciitilde /.notdef % rubout; ASCII ends % 0x80 /.notdef /.notdef /quotesinglbase /florin /quotedblbase /ellipsis /dagger /daggerdbl /circumflex /perthousand /Scaron /guilsinglleft /OE /.notdef /.notdef /.notdef % 0x90 /.notdef /.notdef /.notdef /quotedblleft /quotedblright /bullet /endash /emdash /tilde /trademark /scaron /guilsinglright /oe /.notdef /.notdef /Ydieresis % 0xA0 /.notdef % nobreakspace /exclamdown /cent /sterling /currency /yen /brokenbar /section /dieresis /copyright /ordfeminine /guillemotleft /logicalnot /hyphen % Y&Y (also at 45); Windows' softhyphen /registered /macron % 0xD0 /degree /plusminus /twosuperior /threesuperior /acute /mu /paragraph /periodcentered /cedilla /onesuperior /ordmasculine /guillemotright /onequarter /onehalf /threequarters /questiondown % 0xC0 /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla /Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis % 0xD0 /Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply /Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls % 0xE0 /agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla /egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis % 0xF0 /eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide /oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis ] def %%EndProcSet %%BeginProcSet: texps.pro %! TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{ dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def} if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def} def end %%EndProcSet %%BeginProcSet: special.pro %! TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N /vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N /rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N /@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ /hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B /@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ /urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known {userdict/md get type/dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup length 20 add dict copy def}if end md begin /letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{ itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack} if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{ noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{ Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale }if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState save N userdict maxlength dict begin/magscale true def normalscale currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts /psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR/showpage{}N/erasepage{}N/copypage{}N/p 3 def @MacSetUp}N/doclip{ psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath moveto}N/endTexFig{end psf$SavedState restore}N/@beginspecial{SDict begin/SpecialSave save N gsave normalscale currentpoint TR @SpecialDefaults count/ocount X/dcount countdictstack N}N/@setspecial{ CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR }{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury lineto closepath clip}if/showpage{}N/erasepage{}N/copypage{}N newpath}N /@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{end} repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N /@fedspecial{end}B/li{lineto}B/rl{rlineto}B/rc{rcurveto}B/np{/SaveX currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X /yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end %%EndProcSet TeXDict begin 40258431 52099146 1000 600 600 (paper.dvi) @start %DVIPSBitmapFont: Fa cmr5 5 4 /Fa 4 51 df<14E0B0B712C0A3C700E0C7FCB022237C9B2B>43 D48 D<1360EA01E0120F12FF12F1 1201B3A3387FFF80A2111C7B9B1C>II E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fb cmmi5 5 3 /Fb 3 84 df<0003B512C0000F14E05A4814C0397030600038C070E0EA0060A213E0A2EA 01C0A21203497E120780EB0078000613701B127D9123>25 D<3803FFFC5CD8003EC7FCA4 5BA45BA4485AA3150C48481318A2153815304848137015F0EC01E0140FB612C0A21E1C7C 9B28>76 D<903807F02090381FFC609038780EE09038E003C03801C001EA0380A2D80700 1380A26DC7FCA27FEA03FC3801FFC06C13F0EB3FF8EB01FCEB003E141E140EA21230A200 705BA25C00785B38FE01E038C7FF80D881FEC7FC1B1E7B9C24>83 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fc cmsy7 7 4 /Fc 4 50 df0 D<176017F01770A217781738173C171C171E83 717E717E717EEF00F8BAFC19801900CB12F8EF01E04D5A4D5A4DC7FC171E171C173C1738 17781770A217F01760391F7C9D42>33 D<13E0EA01F0EA03F8A3EA07F0A313E0A2120F13 C0A3EA1F80A21300A25A123EA35AA3127812F8A25A12100D1E7D9F13>48 D<017F157F2601FFE0903803FFC0000701F890380FF1F0260F83FC90381F0038261E00FF 013C7F001890263F8078130C4890261FC0E07F007090260FE1C07F0060EB07E3913803F7 80486DB4C7EA01806E5A157E157F81824B7E0060DAF7E0EB0300913801E3F0DBC3F85B6C 90260381FC13066C90260F00FE5B001C011E90387F803C6C017C90381FE0F82607C7F86D B45A2601FFE0010313C06C6CC86CC7FC391B7C9942>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fd cmr12 12 6 /Fd 6 62 df<14FF010713E090381F81F890383E007C01FC133F4848EB1F8049130F4848 EB07C04848EB03E0A2000F15F0491301001F15F8A2003F15FCA390C8FC4815FEA54815FF B3A46C15FEA56D1301003F15FCA3001F15F8A26C6CEB03F0A36C6CEB07E0000315C06D13 0F6C6CEB1F806C6CEB3F00013E137C90381F81F8903807FFE0010090C7FC28447CC131> 48 D<143014F013011303131F13FFB5FC13E713071200B3B3B0497E497E007FB6FCA320 4278C131>II<000615C0D807C01307 01FCEB7F8090B612005D5D5D15E0158026063FFCC7FC90C9FCAE14FF010713C090381F01 F090383800FC01F0137ED807C07F49EB1F8016C090C7120F000615E0C8EA07F0A316F815 03A216FCA5123E127F487EA416F890C712075A006015F0A20070140F003015E00038EC1F C07E001EEC3F806CEC7F006C6C13FE6C6C485A3901F807F039007FFFE0011F90C7FCEB07 F826447BC131>53 D<14FF010713E0011F13F890387F00FE01FC133FD801F0EB1F804848 EB0FC049EB07E00007EC03F048481301A290C713F8481400A47FA26D130116F07F6C6CEB 03E013FC6C6CEB07C09039FF800F806C9038C01F006CEBF03EECF87839007FFEF090383F FFC07F01077F6D13F8497F90381E7FFFD97C1F1380496C13C02601E00313E048486C13F0 00079038007FF84848EB3FFC48C7120F003EEC07FE150148140016FF167F48153FA2161F A56C151E007C153EA2007E153C003E157C6C15F86DEB01F06C6CEB03E06C6CEB07C0D803 F8EB1F80C6B4EBFF0090383FFFFC010F13F00101138028447CC131>56 D<007FBAFCBB1280A3CEFCB0BB1280A36C190041187BA44C>61 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fe cmmi12 12 2 /Fe 2 59 df26 D<121EEA7F80A2EAFFC0A4EA7F80A2EA1E000A0A78891B>58 D E %EndDVIPSBitmapFont /Ff 157[72 64 55[48 48 40[{TeXBase1Encoding ReEncodeFont}4 143.462 /Times-Roman rf /Fg 138[60 60 1[60 3[60 1[60 6[60 3[60 13[60 1[60 13[60 21[60 45[{TeXBase1Encoding ReEncodeFont}11 99.6264 /Courier rf /Fh 138[50 50 1[50 3[50 1[50 6[50 3[50 13[50 1[50 13[50 21[50 45[{TeXBase1Encoding ReEncodeFont}11 83.022 /Courier rf %DVIPSBitmapFont: Fi cmr7 7 14 /Fi 14 127 df1 D<1306130C13181330136013E0EA01C0EA0380A2EA 07005A120E121EA2121C123CA35AA512F85AAB7E1278A57EA3121C121EA2120E120F7EEA 0380A2EA01C0EA00E0136013301318130C13060F3B7AAB1A>40 D<12C012607E7E7E120E 7EEA0380A2EA01C013E0120013F0A213701378A3133CA5133E131EAB133E133CA51378A3 137013F0A213E0120113C0EA0380A2EA0700120E120C5A5A5A5A0F3B7DAB1A>I<140EB3 A2B812E0A3C7000EC8FCB3A22B2B7DA333>43 D48 D<13381378EA01F8121F 12FE12E01200B3AB487EB512F8A215267BA521>I<13FF000313E0380E03F0381800F848 137C48137E00787F12FC6CEB1F80A4127CC7FC15005C143E147E147C5C495A495A5C495A 010EC7FC5B5B903870018013E0EA0180390300030012065A001FB5FC5A485BB5FCA21926 7DA521>I<13FF000313E0380F01F8381C007C0030137E003C133E007E133FA4123CC712 3E147E147C5C495AEB07E03801FF8091C7FC380001E06D7E147C80143F801580A2123812 7C12FEA21500485B0078133E00705B6C5B381F01F03807FFC0C690C7FC19277DA521>I< 1438A2147814F81301A2130313071306130C131C131813301370136013C012011380EA03 005A120E120C121C5A12305A12E0B612E0A2C7EAF800A7497E90383FFFE0A21B277EA621 >I<0018130C001F137CEBFFF85C5C1480D819FCC7FC0018C8FCA7137F3819FFE0381F81 F0381E0078001C7F0018133EC7FC80A21580A21230127C12FCA3150012F00060133E1270 00305B001C5B380F03E03803FFC0C648C7FC19277DA521>I<007FB712C0B812E0A2CBFC ABB812E0A26C16C02B117D9633>61 D91 D93 D<380F8010381FF038383FFFF048 13E038E07FC038400F8015067BA621>126 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fj cmr10 10 26 /Fj 26 127 df<1506150FA24B7EA24B7EA24B7EA2EDDFF0A29138018FF8A291380307FC A291380603FEA291380E01FF140CDA1C007F141802386D7E143002706D7E146002E06D7E 5C01016E7E5C01036E7E91C7FC496E7E1306010E6E7E130C011C6E7F131801386F7E1330 01706F7E136001E06F7E5B170F484882170748C97F17030006831701488383481880001F B9FC4818C0A24818E0A2BA12F0A23C3C7CBB45>1 D<146014E0EB01C0EB0380EB070013 0E131E5B5BA25B485AA2485AA212075B120F90C7FCA25A121EA2123EA35AA65AB2127CA6 7EA3121EA2121F7EA27F12077F1203A26C7EA26C7E1378A27F7F130E7FEB0380EB01C0EB 00E01460135278BD20>40 D<12C07E12707E7E7E120F6C7E6C7EA26C7E6C7EA21378A213 7C133C133E131EA2131F7FA21480A3EB07C0A6EB03E0B2EB07C0A6EB0F80A31400A25B13 1EA2133E133C137C1378A25BA2485A485AA2485A48C7FC120E5A5A5A5A5A13527CBD20> I<15301578B3A6007FB812F8B912FCA26C17F8C80078C8FCB3A6153036367BAF41>43 D48 DIII<121C127FEA FF80A5EA7F00121CC7FCB2121C127F5A1380A4127F121D1201A412031300A25A1206A212 0E5A121812385A1260093479A317>59 D<007FB812F8B912FCA3CCFCAEB912FCA36C17F8 36167B9F41>61 D80 D91 D93 D97 DI104 DI108 D<2703F00FF0EB1FE000FFD93FFCEB7FF8913AF03F01E07E903BF1C01F8380 3F3D0FF3800FC7001F802603F70013CE01FE14DC49D907F8EB0FC0A2495CA3495CB3A348 6C496CEB1FE0B500C1B50083B5FCA340257EA445>I111 D<3903F01FE000FFEB7FF89038F1E07E9039F3801F803A07F7000FC0D803FEEB07E049EB 03F04914F849130116FC150016FEA3167FAA16FEA3ED01FCA26DEB03F816F06D13076DEB 0FE001F614C09039F7803F009038F1E07E9038F0FFF8EC1FC091C8FCAB487EB512C0A328 357EA42E>I<3807E01F00FFEB7FC09038E1E3E09038E387F0380FE707EA03E613EE9038 EC03E09038FC0080491300A45BB3A2487EB512F0A31C257EA421>114 D<1318A51338A31378A313F8120112031207001FB5FCB6FCA2D801F8C7FCB215C0A93800 FC011580EB7C03017E13006D5AEB0FFEEB01F81A347FB220>116 D119 D121 D126 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fk cmmi7 7 16 /Fk 16 121 df15 D21 D<48B61280000715C0481580481500263C0C06C7FC127012C0EB1C0EEA0018A21338A2EB 701EA313F013E01201141F120313C0000780A2380F800FA26C486CC7FC221A7D9827>25 D<14FCEB03FF903807878090381E03C0EB3C01017813E0A213F0000114F013E01203A239 07C003E0A4390F8007C0A21580EC0F00EA1F00141E6D5A6D5A383EE1F0EB7FC0011FC7FC 90C8FC5AA45AA45A5A1C267D9922>I<1238127C12FE12FFA2127F123B1203A31206A312 0C121812381270122008127A8614>59 D<013FB612FCA2903901FC00014AEB007C173C01 03153817185CA21307A24A13C0A2010F010113005E14C01503011F130F91B5C7FCA2EC80 0F013F7F15061400A249010E13E0030C13C0017E90C7FC160101FEEC0380A249EC0700A2 0001150E161E495C16FC0003EC07F8B7FC5E2E287DA731>69 D<90383FFFF8A2D901FCC7 FC5CA21303A25CA21307A25CA2130FA25CA2131FA25CA2133FA291C8FCA249141C161813 7E163801FE1430167049146016E000011401ED03C0491307ED0F800003147FB7FC160026 287DA72E>76 D78 D<4AB4FC021F13E091387E01F8903901F8007ED907E0131FD90F80EB0F8049C7EA07C013 7E49EC03E0485A4915F0484814011207485A4915F8121F90C8FC5A17F0007E1503A4007C ED07E012FC17C0160F1780161F007C1600163E007E157E003E017C5BD901FE5B3A1F0387 01F09039070387C03A0F86018F80D807C6019FC7FCD803F613FC3900FF03F090393FFFC0 06EB07FDD90001130E6F5A163C6F5AEDFFF85E6E5B5E6F5A033EC7FC2D347DA834>81 D<91381FE0089138FFFC18903903E01E3890390780077090390E0003F049130149130001 7814E0137013F0A2000115C0A216007F7F6CB47E14F86DB47E6D13F06D7F01077F01007F 1407EC00FF153F81A3001880A20038141E12300038141C153C00781438007C5C007E5C00 77EB03C026E3E00FC7FC38C0FFFE38801FF0252A7CA829>83 D87 D<903B3FFFE00FFFC0A2010190390001FC 006D4814F017C0027F495A4CC7FC6E130E6F5A021F5B6F5A5E91380FE1C0EDE380DA07F7 C8FC15FE6E5A5D6E7EA2811403EC077F140E4A7E02187FEC301F02607F14C049486C7EEB 030001066D7E5B01386D7E5B01F06D7E485AD80FF0497ED8FFFC90381FFFE0A232287DA7 36>I<15F8141FA2EC01F0A21403A215E0A21407A215C0A2140FEB1F8F90387FCF80EBF0 EF3803C03FEA0780390F001F00A2001E5B123E003C133E127C147E5A147CA214FC5AECF8 30A3903801F060A2EA7803010E13C0393C1CF980381FF07F3907C01E001D297CA723> 100 D115 D<131C133EA25BA45BA4485AB512E0A23801 F000485AA4485AA4485AA448C7FC1460A214C0123EEB0180EB0300EA1E06EA1F1CEA0FF8 EA03E013267EA419>I<90387C03C03901FF0FF03907079C30390E03B078000CEBF0F800 1813E1123015F0396007C0E015001200A2495AA449C7FC15301238007C1460EAFC3E15C0 EAF87E39F06F03803970C70700383F83FE381F01F81D1B7D9926>120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fl cmmi10 10 25 /Fl 25 121 df15 D<133F14C0EB07F06D7E801301A26D7E A3147FA36E7EA36E7EA36E7EA36E7EA36E7EA36E7EA26E7EA214014A7E5C4A7E91381E3F 80143C14784A6C7E1301EB03E049486C7EEB0F80EB1F00496D7E137E5B48486D7E485A48 5A000F6E7E485A485A48C87E12FE167F4816800070151F293B7CB930>21 DI<013FB612E090B712F05A120717E0270F807006C7FC391E00600E48140C003813 E04813C048141CEAC0011200148001035BA213071400A25B1578011E137CA3133E133C13 7C157E13FC5B1201157F1203497FA3D801C0131C2C257EA32F>25 D<15FE913803FF8091380F83E091383E01F091387C00F85C494813FC0103147C4948137E 5C130F495AA249C7FC16FE5B137EA2150113FE4914FCA20001140316F85BED07F01203ED 0FE04914C0151F000715806DEB3F00157E6D5B390FEE01F09038E707E09038C3FF80D9C0 FCC7FC001F90C8FCA25BA2123FA290C9FCA25AA2127EA212FEA25AA2127027377EA42B> I<121C127FEAFF80A5EA7F00121C0909798817>58 D<121C127FEAFF80A213C0A3127F12 1C1200A412011380A2120313005A1206120E5A5A5A12600A19798817>II<1760177017F01601A21603A21607 160FA24C7EA216331673166316C3A2ED0183A2ED0303150683150C160115181530A21560 A215C014011580DA03007FA202061300140E140C5C021FB5FC5CA20260C7FC5C83495A83 49C8FC1306A25BA25B13385B01F01680487E000716FFB56C013F13FF5EA2383C7DBB3E> 65 D<0103B77E4916F018FC903B0007F80003FE4BEB00FFF07F80020FED3FC0181F4B15 E0A2141FA25DA2143F19C04B143F1980027F157F190092C812FE4D5A4A4A5AEF0FF04AEC 1FC005FFC7FC49B612FC5F02FCC7B4FCEF3FC00103ED0FE0717E5C717E1307844A1401A2 130F17035CA2131F4D5A5C4D5A133F4D5A4A4A5A4D5A017F4BC7FC4C5A91C7EA07FC49EC 3FF0B812C094C8FC16F83B397DB83F>I<0103B812F05BA290260007F8C7123F4B1407F0 03E0020F150118005DA2141FA25D19C0143FA24B1330A2027F1470190092C7126017E05C 16014A495A160F49B6FCA25F9138FC000F01031407A24A6DC8FCA201075C18034A130660 010F160693C7FC4A150E180C011F161C18184A1538A2013F5E18F04A4A5AA2017F15074D 5A91C8123F49913803FF80B9FCA295C7FC3C397DB83D>69 D<902603FFF891381FFFF849 6D5CA2D90007030113006FEC007C02061678DA0EFF157081020C6D1460A2DA1C3F15E070 5CEC181F82023815016F6C5C1430150702706D1303030392C7FC02607FA2DAE0015C7013 06ECC0008201016E130EEF800C5C163F0103EDC01C041F131891C713E0160F49EDF03818 300106140717F8010E02031370EFFC60130CEE01FE011C16E004005B011815FF177F1338 600130153FA20170151F95C8FC01F081EA07FCB512E01706A245397DB843>78 D<4BB4FC031F13F09238FE01FC913903F0007EDA07C0EB1F80DA1F80EB0FC0023EC7EA07 E002FCEC03F0495A4948EC01F8495A4948EC00FC495A49C912FE49167E13FE49167F1201 485AA2485AA2120F5B001F17FFA2485AA34848ED01FEA400FFEE03FC90C9FCA2EF07F8A2 EF0FF0A218E0171F18C0EF3F806C167F180017FE4C5A6C6C5D1603001F4B5A6D4A5A000F ED1F806C6C4AC7FC6D147E0003EC01F8D801FC495AD8007EEB0FC090263F807FC8FC9038 07FFF801001380383D7CBA3F>I<0003B812FEA25A903AF8003FC00101C0913880007E48 48163C90C7007F141C121E001C92C7FCA2485CA200305C007017180060130112E0485CA2 1403C716005DA21407A25DA2140FA25DA2141FA25DA2143FA25DA2147FA292C9FCA25CA2 5CA21301A25CA21303A25CEB0FFC003FB6FC5AA237397EB831>84 D<277FFFFC01B500F890B51280B5FC60000390C7D807FCC7380FF80001FC4BEC03E00001 6204035E98C7FC621A0604075DA2040F5DA2041B5D6216336D02735D1663000003C34A5A 83DB01834AC8FC04815CDB0301140603075D1506030C5DA203185D197003301560611560 6D01E04A5A15C090267F01804AC9FC17FEDA030014060400130E0206150C020E5D140C4A 5DA24A5D18E04A5D715A5C4A92CAFCA26DC85AA2013E157C1778133C1770133801301560 513B7CB84E>87 D<49B500F890387FFFF095B5FC1AE0D90003018090380FFC004BC713E0 0201ED07804EC7FC6E6C140E606F5C705B606F6C485A4D5A031F91C8FCEEE0065F6F6C5A 5F03075B705A16F96FB45A94C9FC6F5AA36F7EA34B7FED037F9238063FC0150E4B6C7E15 38ED700F03E07F15C04A486C7EEC0300020613034A805C4A6D7E14704A1300494880495A 49C86C7E130E011E153F017E4B7ED803FF4B7E007F01E0011FEBFFC0B5FC6144397EB845 >I<163FED1FFFA3ED007F167EA216FEA216FCA21501A216F8A21503A216F0A21507A202 7E13E0903803FF8790380FC1CF90381F00EF017EEB7FC049133F485A4848131F00071580 5B000F143F485A1600485A5D127F90C7127EA215FE5A485CA21401A248ECF80CA2140316 1CEDF0181407007C1538007E010F1330003E131F027B13706C01E113E03A0F83C0F9C03A 03FF007F80D800FCEB1F00283B7DB92B>100 DI<16F8ED03FEED0F8792381F0F 80ED3E3F167F157CA215FC1700161C4A48C7FCA414035DA414075DA20107B512F0A39026 000FE0C7FC5DA4141F5DA4143F92C8FCA45C147EA514FE5CA413015CA4495AA45C1307A2 5C121E123F387F8F80A200FF90C9FC131E12FEEA7C3CEA7878EA1FF0EA07C0294C7CBA29 >III111 D<14FF010313C090380F80F090383E00380178131C153C4913FC0001130113E0A33903F0 00F06D13007F3801FFE014FC14FF6C14806D13C0011F13E013039038003FF01407140300 1E1301127FA24814E0A348EB03C012F800E0EB07800070EB0F006C133E001E13F83807FF E0000190C7FC1E267CA427>115 DI<903907E001F090391FF807FC9039783E0E0F9039E01F1C1FD801C09038383F 803A03800FF07F0100EBE0FF5A000E4A1300000C157E021F133C001C4AC7FC1218A2C712 3FA292C8FCA25CA2147EA214FEA24A130CA20101141C001E1518003F5BD87F8114380183 5C00FF1560010714E03AFE0E7C01C0D87C1C495A2778383E0FC7FC391FF00FFC3907C003 F029267EA42F>120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fm cmsy10 10 10 /Fm 10 107 df<007FB81280B912C0A26C17803204799641>0 D<121C127FEAFF80A5EA 7F00121C0909799917>I<007FB812F8B912FCA26C17F8CCFCAD007FB812F8B912FCA26C 17F8CCFCAD007FB812F8B912FCA26C17F836267BA741>17 D20 D<127012FCB4FCEA7FC0EA1FF0EA07FCEA01FF38007FC0EB1FF0EB07FCEB01FF9038007F C0EC1FF0EC07FCEC01FF9138007FC0ED1FF0ED07FCED01FF9238007FC0EE1FF0EE07FCEE 01FF9338007FC0171F177F933801FF80933807FC00EE1FF0EE7FC04B48C7FCED07FCED1F F0ED7FC04A48C8FCEC07FCEC1FF0EC7FC04948C9FCEB07FCEB1FF0EB7FC04848CAFCEA07 FCEA1FF0EA7FC048CBFC12FC1270CCFCAD007FB81280B912C0A26C1780324279B441>I< 181EA4181F84A285180785727EA2727E727E85197E85F11F80F10FC0F107F0007FBA12FC BCFCA26C19FCCCEA07F0F10FC0F11F80F13F00197E61614E5A4E5AA24E5A61180F96C7FC A260181EA4482C7BAA53>33 D49 D102 D<12FCEAFFC0EA07F0EA01FCEA007E7F80131F 80130FB3A7801307806D7E6D7EEB007EEC1FF0EC07F8EC1FF0EC7E00495A495A495A5C13 0F5CB3A7131F5C133F91C7FC137E485AEA07F0EAFFC000FCC8FC1D537ABD2A>I<126012 F0B3B3B3B3A91260045377BD17>106 D E %EndDVIPSBitmapFont /Fn 186[55 69[{TeXBase1Encoding ReEncodeFont}1 83.022 /Times-Bold rf /Fo 134[50 1[72 50 55 33 39 44 1[55 50 55 83 28 55 33 28 55 50 33 44 55 44 55 50 10[72 8[94 6[61 1[72 13[50 1[50 50 50 50 2[25 4[33 33 40[{ TeXBase1Encoding ReEncodeFont}35 99.6264 /Times-Bold rf %DVIPSBitmapFont: Fp cmsy8 8 4 /Fp 4 104 df0 D49 D<141F14FFEB03F0EB0FC0EB1F8014005B133EB3A2137E137C13FC485A485AEA7FC048C7 FCEA7FC0EA03F06C7E6C7E137C137E133EB3A2133F7F1480EB0FC0EB03F0EB00FF141F18 437BB123>102 D<12FCB47EEA0FE0EA01F0EA00FC137C137E133EB3A37F1480130FEB07 E0EB01FEEB007FEB01FEEB07E0EB0F80131F1400133EB3A3137E137C13FCEA01F0EA0FE0 EAFF8000FCC7FC18437BB123>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fq cmex10 10 25 /Fq 25 113 df<1538EC01F8EC07E0EC1F80EC7E005CEB03F85C495AA2495AB3AB131F5C A249C7FC137E5BEA03F8EA07E0EA3F8000FCC8FCA2EA3F80EA07E0EA03F8C67E137E7F6D 7EA280130FB3AB6D7EA26D7E80EB00FC147EEC1F80EC07E0EC01F8EC00381D62778230> 8 D<12E012FCEA3F80EA07E0EA03F8C67E137E7F6D7EA280130FB3AB6D7EA26D7E80EB00 FC147EEC1F80EC07E0EC01F8A2EC07E0EC1F80EC7E005CEB03F85C495AA2495AB3AB131F 5CA249C7FC137E5BEA03F8EA07E0EA3F8000FCC8FC12E01D62778230>I<12F0B3B3B204 3674811C>12 D<151E153E157C15F8EC01F0EC03E01407EC0FC0EC1F8015005C147E5CA2 495A495AA2495AA2495AA2495AA249C7FCA2137EA213FE5B12015BA212035BA21207A25B 120FA35B121FA45B123FA548C8FCA912FEB3A8127FA96C7EA5121F7FA4120F7FA312077F A21203A27F1201A27F12007F137EA27FA26D7EA26D7EA26D7EA26D7EA26D7E6D7EA2147E 80801580EC0FC0EC07E01403EC01F0EC00F8157C153E151E1F94718232>16 D<12F07E127C7E7E6C7E7F6C7E6C7E12017F6C7E137EA27F6D7EA26D7EA26D7EA26D7EA2 6D7EA26D7EA280147E147F80A21580141FA215C0A2140F15E0A3140715F0A4140315F8A5 EC01FCA9EC00FEB3A8EC01FCA9EC03F8A515F01407A415E0140FA315C0141FA21580A214 3F1500A25C147E14FE5CA2495AA2495AA2495AA2495AA2495AA249C7FC137EA25B485A5B 1203485A485A5B48C8FC123E5A5A5A1F947D8232>I<160F161F163E167C16F8ED01F0ED 03E0ED07C0150FED1F801600153E157E5D4A5A5D14034A5A5D140F4A5AA24AC7FC143E14 7E5CA2495AA2495AA2495AA2130F5CA2495AA2133F91C8FCA25B137E13FEA25B1201A25B 1203A35B1207A35B120FA35BA2121FA45B123FA690C9FC5AAA12FEB3AC127FAA7E7FA612 1F7FA4120FA27FA312077FA312037FA312017FA212007FA2137E137F7FA280131FA26D7E A2801307A26D7EA26D7EA26D7EA2147E143E143F6E7EA26E7E1407816E7E1401816E7E15 7E153E811680ED0FC01507ED03E0ED01F0ED00F8167C163E161F160F28C66E823D>I<12 F07E127C7E7E6C7E6C7E6C7E7F6C7E1200137C137E7F6D7E130F806D7E1303806D7EA26D 7E147C147E80A26E7EA26E7EA26E7EA2811403A26E7EA2811400A281157E157FA2811680 A2151F16C0A3150F16E0A3150716F0A31503A216F8A4150116FCA6150016FEAA167FB3AC 16FEAA16FC1501A616F81503A416F0A21507A316E0150FA316C0151FA31680153FA21600 5DA2157E15FE5DA214015DA24A5AA214075DA24A5AA24A5AA24AC7FCA2147E147C14FC49 5AA2495A5C1307495A5C131F49C8FC137E137C5B1201485A5B485A485A48C9FC123E5A5A 5A28C67E823D>I<161E167EED01FE1507ED0FF8ED3FE0ED7FC0EDFF80913801FE004A5A 4A5A5D140F4A5A5D143F5D147F92C7FCA25C5CB3B3B3A313015CA3495AA213075C495AA2 495A495A137F49C8FC485A485AEA07F0EA1FE0485AB4C9FC12FCA2B4FCEA3FC06C7EEA07 F0EA03FC6C7E6C7E6D7E133F6D7E6D7EA26D7E801303A26D7EA3801300B3B3B3A38080A2 81143F81141F816E7E1407816E7E6E7E913800FF80ED7FC0ED3FE0ED0FF8ED07FE1501ED 007E161E27C675823E>26 D<177C17FCEE01F8A2EE03F0EE07E0EE0FC0A2EE1F80EE3F00 5E167E5E15015E15034B5A5E150F5E151F4B5AA24BC7FCA215FEA24A5AA24A5AA24A5AA2 140F5D141F5D143F5DA2147F92C8FC5CA25C13015C1303A25C1307A3495AA3495AA3133F 5CA3137F5CA313FF91C9FCA35A5BA31203A25BA31207A35BA3120FA45BA2121FA65BA212 3FA85BA2127FAE5B12FFB3A62E95688149>48 D<12F87E127EA27E6C7E6C7EA26C7E6C7E 7F12016C7E7F137E137F6D7E131F80130F806D7EA26D7EA26D7EA26D7EA2147FA26E7EA2 81141F81140F811407A281140381A2140181140081A28182A36F7EA36F7EA382150FA382 1507A3821503A3821501A382A281A31780A3167FA317C0A4163FA217E0A6161FA217F0A8 160FA217F8AE160717FCB3A62E957E8149>I56 D58 D60 D62 D64 DIII80 D90 D101 D<93263FFF801906031FB500F8193E0203B76CEF03F891273FFE000301F0EF1FC0902601 FF809026003FFC933801FE00D91FF0C82603FF80ED1FF001FFCAD87FF8DA03FFC7FCD807 F094261FFF80EBFFF8D83F80050390B6128000F8CC003F02F0C8FC00C0070301F8C9FC77 0B80BD78>103 D110 D<12F012FE6C7E13E0EA3FF0EA0FFCEA03FE6C7E6C6C7E6D 7E6D7EA26D7E1307A2801303B3B3A76D7EA28013008080816E7E6E7E6E7E6E7EEC01FC6E B4FCED3FC0150FA2153FEDFF00EC01FCEC07F84A5A4A5A4A5A4A5A92C7FC5C5C13015CA2 495AB3B3A713075CA2130F495AA2495A495A4848C8FC485AEA0FFCEA3FF0B45A138048C9 FC12F02294768237>I<1B301B781BF8A2F201F0A2F203E0A2F207C0A2F20F80A2F21F00 A21A3EA262A262A24F5AA24F5AA24F5AA262190FA24FC7FCA2193EA261A261A24E5AA24E 5AA24E5AA24E5AA24EC8FCA2183EA260131001305E13F800014C5A1203D80FFC4B5A121D D838FE4B5A12F0D8407F4B5A12004DC9FC6D7E173E6D7E5F6D7E5FA26D6C495AA26D6C49 5AA26D6C5C1607A26D6C495AA2027F49CAFCA291383F803EA25EEC1FC05EEC0FE0EDE1F0 EC07F1EDF3E0A26EB45AA26E5BA26E90CBFCA25D157E157C15384D64788353>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fr cmsy10 10.95 10 /Fr 10 104 df<007FB812FEBAFCA26C17FE3804799847>0 D<121EEA7F80A2EAFFC0A4 EA7F80A2EA1E000A0A799B19>I15 D<127012FCB4FCEA7FC0EA1FF0EA07FCEA01FF38007FC0EB1FF8EB07FE 903801FF809038007FE0EC0FF8EC03FE913800FF80ED3FE0ED0FFCED03FF030013C0EE3F F0EE07FCEE01FF9338007FC0EF1FF0EF07FCEF01FFEF007FEF01FFEF07FEEF1FF0EF7FC0 933801FF00EE07FCEE3FF0EEFFC0030390C7FCED0FFCED3FE0EDFF80DA03FEC8FCEC0FF8 EC7FE0903801FF80D907FEC9FCEB1FF8EB7FC04848CAFCEA07FCEA1FF0EA7FC048CBFC12 FC1270CCFCAE007FB812FEBAFCA26C17FE384779B947>21 D24 D<19301978A2197C193CA2193E191EA2191F737EA2737E737EA2737E737E1A7C1A7EF21F 80F20FC0F207F0007FBB12FCBDFCA26C1AFCCDEA07F0F20FC0F21F80F27E001A7C624F5A 4F5AA24F5A4F5AA24FC7FC191EA2193E193CA2197C1978A2193050307BAE5B>33 D40 DI<153FEC03FFEC0FE0EC 3F80EC7E00495A5C495AA2495AB3AA130F5C131F495A91C7FC13FEEA03F8EA7FE048C8FC EA7FE0EA03F8EA00FE133F806D7E130F801307B3AA6D7EA26D7E80EB007EEC3F80EC0FE0 EC03FFEC003F205B7AC32D>102 D<12FCEAFFC0EA07F0EA01FCEA007E6D7E131F6D7EA2 6D7EB3AA801303806D7E1300147FEC1FC0EC07FEEC00FFEC07FEEC1FC0EC7F0014FC1301 495A5C13075CB3AA495AA2495A133F017EC7FC485AEA07F0EAFFC000FCC8FC205B7AC32D >I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fs cmr10 10.95 24 /Fs 24 127 df<16E04B7EA24B7EA24B7EA24B7EA2ED1DFFA203387FA29238787FC01570 9238F03FE015E002016D7E15C002036D7E158002076D7E15004A6D7E140E021E6D7E141C 023C6D7F143802786E7E147002F06E7E5C01016F7E5C01036F7E5C01076F7E91C8FC496F 7E130E011E6F7E131C013C6F7F13380178707E137001F0707E5B0001717E5B0003717E5B 0007717E90CAFC48717E120E001E717E001FBAFC481980A24819C0A2BB12E0A243417CC0 4C>1 D<013F4C7ED9FFC04B7E2601E0E015072607C070150F48486C4B5A023E4BC7FC48 486C5D48D90FC0EB01FE003ED90EF0EB07FCDA0F3F133E007E903A070FFFF8F8007C0200 EBC1F0EE000300FC6D6C495A604D5A171F95C8FC173E177E177C5F16015F007C4948485A 1607007E5E003E49495A020E131F003F93C9FC6C49133E260F803C137E0238137C6C6C48 5B3901E0E0016CB448485AD93F0049133F90C74848EBFFC0030F903801E0E093398007C0 704B4848487E4B153C033E90381F001C4B497F03FC133E4B150F4A48017E7F0203147C5D 4A4801FCEB0380140F5D4AC7FC5C143E5C14FC5C495A13034948027CEB07005C4948147E 011F033E5B91C8140E013E153F017E6F5B017C92380F803C4917380001706C5A49923801 E0E0496FB45A6C48043FC7FC41497BC34C>37 D<1430147014E0EB01C0EB03801307EB0F 00131E133E133C5B13F85B12015B1203A2485AA2120F5BA2121F90C7FCA25AA3123E127E A6127C12FCB2127C127EA6123E123FA37EA27F120FA27F1207A26C7EA212017F12007F13 787F133E131E7FEB07801303EB01C0EB00E014701430145A77C323>40 D<12C07E12707E7E121E7E6C7E7F12036C7E7F12007F1378137CA27FA2133F7FA2148013 0FA214C0A3130714E0A6130314F0B214E01307A614C0130FA31480A2131F1400A25B133E A25BA2137813F85B12015B485A12075B48C7FC121E121C5A5A5A5A145A7BC323>I<1506 150FB3A9007FB912E0BA12F0A26C18E0C8000FC9FCB3A915063C3C7BB447>43 D48 DIII<150E151E153EA2157EA215FE1401A21403EC077E140614 0E141CA214381470A214E0EB01C0A2EB0380EB0700A2130E5BA25B5BA25B5B1201485A90 C7FC5A120E120C121C5AA25A5AB8FCA3C8EAFE00AC4A7E49B6FCA3283E7EBD2D>I<0006 1403D80780131F01F813FE90B5FC5D5D5D15C092C7FC14FCEB3FE090C9FCACEB01FE9038 0FFF8090383E03E090387001F8496C7E49137E497F90C713800006141FC813C0A216E015 0FA316F0A3120C127F7F12FFA416E090C7121F12FC007015C012780038EC3F80123C6CEC 7F00001F14FE6C6C485A6C6C485A3903F80FE0C6B55A013F90C7FCEB07F8243F7CBC2D> II56 DI<121EEA7F80A2EAFFC0A4EA7F80A2EA1E00C7FCB3121E127FEAFF80A213C0A4127F121E 1200A412011380A3120313005A1206120E120C121C5A1230A20A3979A619>59 D<007FB912E0BA12F0A26C18E0CDFCAE007FB912E0BA12F0A26C18E03C167BA147>61 D80 D91 D93 D105 D<2701F801FE14FF00FF902707FFC00313E0913B1E07E00F 03F0913B7803F03C01F80007903BE001F87000FC2603F9C06D487F000101805C01FBD900 FF147F91C75B13FF4992C7FCA2495CB3A6486C496CECFF80B5D8F87FD9FC3F13FEA34728 7DA74C>109 D<3901F801FE00FF903807FFC091381E07E091387803F000079038E001F8 2603F9C07F0001138001FB6D7E91C7FC13FF5BA25BB3A6486C497EB5D8F87F13FCA32E28 7DA733>I<3901F807E000FFEB1FF8EC787CECE1FE3807F9C100031381EA01FB1401EC00 FC01FF1330491300A35BB3A5487EB512FEA31F287EA724>114 D<01F01308D803FC131C 48B4133848EB8070391F3FF3E0393807FFC0486C138048C613000040133C1E0979BC2D> 126 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ft cmmi8 8 20 /Ft 20 118 df<15C0140114031580A214071500A25C140EA2141E141CA2143C14381478 1470A214F05CA213015CA213035C130791C7FCA25B130EA2131E131CA2133C1338A21378 137013F05BA212015BA212035BA2120790C8FC5A120EA2121E121CA2123C1238A2127812 70A212F05AA21A437CB123>61 D<013FB71280A2D900FEC7127F170F4A1407A201011503 18005CA21303A25C16300107147094C7FC4A136016E0130F15019138C007C091B5FC5BEC C0074A6C5AA2133FA20200EB000CA249151C92C71218017E1538173001FE15705F5B4C5A 000115034C5A49140F161F00034AB4C7FCB8FC5E312D7DAC34>69 D<92387FC003913903FFF80791391FC03E0F91397E00071FD901F8EB03BF4948EB01FED9 0FC013004948147E49C8FC017E157C49153C485A120348481538485AA2485A1730484815 00A2127F90CAFCA35A5AA292381FFFFCA29238003FC0EE1F80163F1700A2127E5E167E7E A26C6C14FE000F4A5A6C7E6C6C1307D801F8EB1E3CD8007EEBFC3890391FFFE018010390 C8FC302F7CAD37>71 D<90383FFFFEA2010090C8FC5C5CA21301A25CA21303A25CA21307 A25CA2130FA25CA2131FA25CA2133FA291C7EA0180A24914031700017E5C160601FE140E A2495C163C12015E49EB01F84B5A0003141FB7FC5E292D7DAC30>76 DII81 D<913807F00691383FFE0E9138F80F9E903903E001FE90 3807800049C7127C131E49143CA2491438A313F81630A26D1400A27FEB7F8014F86DB47E 15F06D13FC01077F01007F141F02011380EC003F151F150FA215071218A3150F00381500 A2151EA2007C5C007E5C007F5C397B8003E039F1F00F8026E07FFEC7FC38C00FF0272F7C AD2B>83 D<90260FFFFCEB7FFFA29026007FC0EB0FF06E48148018006E6C131E1718020F 5C6F5B02075C6F485A020349C7FCEDF8065E6E6C5A5E6E6C5A5EED7F8093C8FC6F7EA26F 7E153F156FEDCFE0EC018791380307F0EC0703020E7F141C4A6C7E14704A6C7E495A4948 137F49C7FC010E6E7E5B496E7E5BD801F081D807F8143FD8FFFE0103B5FCA2382D7EAC3A >88 D96 D<151FEC03FFA2EC003FA2153EA2157EA2157CA215 FCA215F8A21401EB07E190381FF9F0EB7C1DEBF80FEA01F03903E007E0EA07C0120FEA1F 8015C0EA3F00140F5A007E1480A2141F12FE481400A2EC3F021506143E5AEC7E0E007CEB FE0C14FC0101131C393E07BE18391F0E1E38390FFC0FF03903F003C0202F7DAD24>100 DI<157C4AB4FC9138 07C380EC0F87150FEC1F1FA391383E0E0092C7FCA3147E147CA414FC90383FFFF8A2D900 F8C7FCA313015CA413035CA413075CA5130F5CA4131F91C8FCA4133EA3EA383C12FC5BA2 5B12F0EAE1E0EA7FC0001FC9FC213D7CAE22>I<131FEA03FFA2EA003FA2133EA2137EA2 137CA213FCA25BA21201143F9038F1FFC09038F3C1F03803FF0001FC7F5BA2485A5BA25B 000F13015D1380A2001F13035D1300140748ECC04016C0003E130F1580007E148191381F 0180007C1403ED070000FCEB0F06151E48EB07F80070EB01E0222F7DAD29>104 D<1307EB0F80EB1FC0A2EB0F80EB070090C7FCA9EA01E0EA07F8EA0E3CEA1C3E12381230 1270EA607EEAE07C12C013FC485A120012015B12035BA21207EBC04014C0120F13801381 381F01801303EB0700EA0F06131EEA07F8EA01F0122E7EAC18>I<137CEA0FFCA21200A2 13F8A21201A213F0A21203A213E0A21207A213C0A2120FA21380A2121FA21300A25AA212 3EA2127EA2127CA2EAFC08131812F8A21338133012F01370EAF860EA78E0EA3FC0EA0F00 0E2F7DAD15>108 D<90387C01F89038FE07FE3901CF8E0F3A03879C0780D907B813C000 0713F000069038E003E0EB0FC0000E1380120CA2D8081F130712001400A249130F16C013 3EA2017EEB1F80A2017C14005D01FC133E5D15FC6D485A3901FF03E09038FB87C0D9F1FF C7FCEBF0FC000390C8FCA25BA21207A25BA2120FA2EAFFFCA2232B829D24>112 D115 D<130E131FA25BA2133EA2 137EA2137CA213FCA2B512F8A23801F800A25BA21203A25BA21207A25BA2120FA25BA200 1F1310143013001470146014E0381E01C0EB0380381F0700EA0F0EEA07FCEA01F0152B7E A919>II E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fu cmmi10 10.95 34 /Fu 34 121 df<133F14E0EB07F0EB03FC13016D7EA3147FA26E7EA36E7EA36E7EA36E7E A36E7EA26E7EA36E7EA3157FA36F7E157F15FF4A7F5C913807CFE0EC0F8FEC1F0F91383E 07F0147C14FC49486C7EEB03F0EB07E049486C7EEB1F80EB3F00496D7E13FE4848147F48 5A485A4848EC3F80485A123F4848EC1FC048C8FC4816E048150F48ED07F0007015032C40 7BBE35>21 DI<011FB612FE017F15FF48B8FC5A4816FE3B 0FC03801C000EA1F00003E1403003C01785B4813705AECF0075AC712E0010191C7FCA25D EB03C0A313071480A2010F5BA2EB1F0082A2133EA2137E825B150F0001815B120315075B C648EB038030287DA634>25 DI<121EEA7F80A2EAFFC0A4EA7F80A2EA 1E000A0A798919>58 D<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413E013C0A3 12011380120313005A120E5A1218123812300B1C798919>I<180E183F18FFEF03FEEF0F F8EF3FE0EFFF80933803FE00EE0FF8EE3FE0EEFF80DB03FEC7FCED1FF8ED7FE0913801FF 80DA07FEC8FCEC1FF0EC7FC04948C9FCEB07FCEB1FF0EB7FC04848CAFCEA07FCEA1FF0EA 7FC048CBFCA2EA7FC0EA1FF0EA07FCEA01FF38007FC0EB1FF0EB07FCEB01FF9038007FC0 EC1FF0EC07FE913801FF809138007FE0ED1FF8ED03FE923800FF80EE3FE0EE0FF8EE03FE 933800FF80EF3FE0EF0FF8EF03FEEF00FF183F180E383679B147>II<127012FCB4 FCEA7FC0EA1FF0EA07FCEA01FF38007FC0EB1FF0EB07FCEB01FF9038007FC0EC1FF8EC07 FE913801FF809138007FE0ED0FF8ED03FE923800FF80EE3FE0EE0FF8EE03FE933800FF80 EF3FE0EF0FF8EF03FEEF00FFA2EF03FEEF0FF8EF3FE0EFFF80933803FE00EE0FF8EE3FE0 EEFF80DB03FEC7FCED0FF8ED7FE0913801FF80DA07FEC8FCEC1FF8EC7FC04948C9FCEB07 FCEB1FF0EB7FC04848CAFCEA07FCEA1FF0EA7FC048CBFC12FC1270383679B147>I<1707 5F84171FA2173F177FA217FFA25E5EA24C6C7EA2EE0E3F161E161C1638A21670A216E0ED 01C084ED0380171FED07005D150E5DA25D157815705D844A5A170F4A5A4AC7FC92B6FC5C A2021CC7120F143C14384A81A24A140713015C495AA249C8FC5B130E131E4982137C13FE D807FFED1FFEB500F00107B512FCA219F83E417DC044>65 D<49B712F818FF19E0902600 01FEC7EA3FF0F007F84B6E7E727E850203815D1A80A20207167F4B15FFA3020F17004B5C 611803021F5E4B4A5A180FF01FE0023F4B5A4B4A5ADD01FEC7FCEF07F8027FEC7FE092B6 C8FC18E092C7EA07F84AEC01FE4A6E7E727E727E13014A82181FA213034A82A301075F4A 153FA261010F167F4A5E18FF4D90C7FC011F5E4A14034D5A013FED1FF04D5A4AECFFC001 7F020790C8FCB812FC17F094C9FC413E7DBD45>II<49B912C0A3D9000190C71201F0003F4B151F190F1A80020316075DA3 14075D1A00A2140F4BEB0380A205075B021FED000E4B92C7FC5FA2023F141E5D173EEE01 FE4AB55AA3ED800102FF6D5A92C71278A34915705C191C05F0133C01034B13384A167894 C71270A2010717F04A5E180161010F16034A4B5AA2180F011F4CC7FC4A5D187E013F16FE 4D5A4A140F017F15FFB95AA260423E7DBD43>69 D<49B612F0A3D900010180C7FC93C8FC 5DA314035DA314075DA3140F5DA3141F5DA3143F5DA3147F5DA314FF92C9FCA35B5C180C 181E0103161C5C183C183813074A1578187018F0130F4AEC01E0A21703011FED07C04A14 0F171F013FED3F8017FF4A1303017F021F1300B9FCA25F373E7DBD3E>76 D<49B56C49B512F81BF0A290C76D9039000FFE004AEE03F0705D735A03DF150302037F03 8F5E82190791380787FC030793C7FC1503705C140F91260E01FF140EA26F151E021E8002 1C017F141C83193C023C6D7E02381638161F711378147802706D6C1370A2040714F002F0 804A01035C8318010101EC01FF4A5E82188313034A91387FC380A2EF3FC7010716E791C8 001F90C8FC18F718FF4981010E5E1707A2131E011C6F5AA2013C1501137C01FE6F5AEA03 FFB512FC187818704D3E7DBD49>78 D81 D83 D<48B912FCA25A913A0003FE000F01F84A13 01D807E0EE00F8491307491778000F5D90C7FC001E140FA2001C4B1470123C0038141FA2 00785D1270033F15F000F018E0485DC81600157FA25EA215FFA293C9FCA25CA25DA21403 A25DA21407A25DA2140FA25DA2141FA25DA2143FA25DA2147FA214FF497F001FB612FCA2 5E3E3D7FBC35>I<007FB500F090387FFFFE19FC5D26007FE0C7000313804A913800FC00 4A5D187001FF16F0A291C95AA2481601605BA200031603605BA20007160795C7FC5BA200 0F5E170E5BA2001F161E171C5BA2003F163C17385BA2007F1678A2491570A200FF16F0A2 90C95AA216015F5A16035F16074CC8FC160E161E5E007F5D5E6C4A5A6D495A6C6C495A6C 6C011FC9FC6C6C137E3903FC03F8C6B512E0013F1380D907FCCAFC3F407ABD3E>I87 D<027FB5D88007B512C091B6FCA2020101F8C7EBF80091 26007FE0EC7F804C92C7FC033F157C701478616F6C495A4E5A6F6C495A4EC8FC180E6F6C 5B606F6C5B6017016F6C485A4D5A6F018FC9FC179E17BCEE7FF85F705AA3707EA283163F 167FEEF7FCED01E7EEC3FEED0383ED070392380E01FF151E4B6C7F5D5D4A486D7E4A5A4A 486D7E92C7FC140E4A6E7E5C4A6E7E14F0495A49486E7E1307D91F806E7ED97FC0140726 03FFE0EC1FFF007F01FC49B512FEB55CA24A3E7EBD4B>I97 D99 DII<163EEEFFC0923803E1E0923807C0F0ED0F811687ED1F8F160F153FA217E0 92387E038093C7FCA45DA514015DA30103B512FCA390260003F0C7FCA314075DA4140F5D A5141F5DA4143F92C8FCA45C147EA414FE5CA413015CA4495AA35CEA1E07127F5C12FF49 5AA200FE90C9FCEAF81EEA703EEA7878EA1FF0EA07C02C537CBF2D>I<143C14FEA21301 A314FCEB00701400AD137E3801FF803803C7C0EA0703000F13E0120E121C13071238A2EA 780F007013C0A2EAF01F14801200133F14005B137EA213FE5BA212015B0003130E13F0A2 0007131EEBE01CA2143CEBC0381478147014E013C13803E3C03801FF00EA007C173E7EBC 1F>105 DI109 DI112 D115 D<147014FC1301A25CA21303A25CA213 07A25CA2130FA25CA2007FB512F0B6FC15E039001F8000133FA291C7FCA25BA2137EA213 FEA25BA21201A25BA21203A25BA21207EC01C013E01403000F1480A2EBC0071500140E14 1E5C000713385C3803E1E03801FF80D8003EC7FC1C3A7EB821>I120 D E %EndDVIPSBitmapFont /Fv 133[32 37 37 55 37 42 23 32 32 42 42 42 42 60 23 37 23 23 42 42 23 37 42 37 42 42 3[32 1[32 6[46 42 1[60 51 1[55 1[46 5[51 51 2[51 51 6[28 42 6[42 42 2[21 28 21 2[28 28 28 36[42 2[{TeXBase1Encoding ReEncodeFont}49 83.022 /Times-Italic rf /Fw 133[37 42 42 60 42 42 23 32 28 42 42 42 42 65 23 1[23 23 42 42 28 37 42 37 42 37 3[28 1[28 2[60 78 1[60 51 46 55 1[46 1[60 74 51 1[32 28 60 1[46 51 60 55 55 60 5[23 23 42 42 42 42 42 42 42 42 42 42 1[21 28 21 2[28 28 28 36[46 2[{TeXBase1Encoding ReEncodeFont} 65 83.022 /Times-Roman rf /Fx 138[55 55 55 55 55 55 55 55 55 55 55 1[55 55 55 1[55 55 55 55 55 9[55 2[55 55 55 55 3[55 55 1[55 55 1[55 55 1[55 55 1[55 14[55 2[55 1[55 45[{TeXBase1Encoding ReEncodeFont}36 90.9091 /Courier rf /Fy 105[45 27[35 40 40 61 40 45 25 35 35 45 45 45 45 66 25 40 25 25 45 45 25 40 45 40 45 45 9[76 56 1[51 45 56 66 56 66 61 76 51 1[40 30 66 66 56 56 66 61 56 56 7[45 1[45 45 45 45 45 45 45 1[25 23 30 23 2[30 30 30 36[45 2[{TeXBase1Encoding ReEncodeFont}64 90.9091 /Times-Italic rf /Fz 134[37 1[54 37 37 21 29 25 1[37 37 37 58 21 37 1[21 37 37 25 33 37 33 37 33 7[54 1[71 1[54 46 42 50 1[42 1[54 66 2[29 25 54 54 42 46 54 50 50 54 69 5[21 37 37 37 37 37 1[37 1[37 37 1[19 25 19 44[{TeXBase1Encoding ReEncodeFont}54 74.7198 /Times-Roman rf %DVIPSBitmapFont: FA cmr6 6 5 /FA 5 54 df<13E01201120712FF12F91201B3A7487EB512C0A212217AA01E>49 DI<13FF000313C0380F03E0381C00F014F800 3E13FC147CA2001E13FC120CC712F8A2EB01F0EB03E0EB0FC03801FF00A2380003E0EB00 F01478147C143E143F1230127812FCA2143E48137E0060137C003813F8381E03F0380FFF C00001130018227DA01E>I<14E01301A213031307A2130D131D13391331136113E113C1 EA01811203EA07011206120C121C12181230127012E0B6FCA2380001E0A6EB03F0EB3FFF A218227DA11E>I<00101330381E01F0381FFFE014C01480EBFE00EA1BF00018C7FCA513 FE381BFF80381F03C0381C01E0381800F014F8C71278A2147CA21230127812F8A2147848 13F8006013F0387001E01238381E07803807FF00EA01F816227CA01E>I E %EndDVIPSBitmapFont /FB 134[45 45 66 45 51 30 35 40 1[51 45 51 76 25 51 30 25 51 45 30 40 51 40 51 45 10[66 1[61 51 66 71 56 71 1[86 61 71 1[35 71 1[56 61 66 66 1[66 6[30 5[45 45 45 45 2[23 30 23 2[30 30 37[51 2[{TeXBase1Encoding ReEncodeFont}52 90.9091 /Times-Bold rf /FC 105[45 1[40 40 24[40 45 45 66 45 45 25 35 30 45 45 45 45 71 25 45 25 25 45 45 30 40 45 40 45 40 3[30 1[30 56 66 66 86 66 66 56 51 61 66 51 66 66 81 56 66 35 30 66 66 51 56 66 61 61 66 5[25 25 45 45 45 45 45 45 45 45 45 45 25 23 30 23 2[30 30 30 1[76 33[51 51 2[{TeXBase1Encoding ReEncodeFont}79 90.9091 /Times-Roman rf %DVIPSBitmapFont: FE cmr8 8 13 /FE 13 115 df<13031307130E131C1338137013F0EA01E013C01203EA0780A2EA0F00A2 121EA35AA45AA512F8A25AAB7EA21278A57EA47EA37EA2EA0780A2EA03C0120113E0EA00 F013701338131C130E1307130310437AB11B>40 D<12C07E12707E7E7E120FEA07801203 13C0EA01E0A2EA00F0A21378A3133CA4131EA5131FA2130FAB131FA2131EA5133CA41378 A313F0A2EA01E0A2EA03C013801207EA0F00120E5A5A5A5A5A10437CB11B>I43 D48 D<130C133C137CEA03FC12FFEAFC7C1200B3B113FE387FFFFEA2172C7AAB23>III<140EA2141E143EA2147E14FEA2EB01BE1303143E13 06130E130C131813381330136013E013C0EA0180120313001206120E120C5A123812305A 12E0B612FCA2C7EA3E00A9147F90381FFFFCA21E2D7EAC23>I<000CEB0180380FC01F90 B512005C5C14F014C0D80C7EC7FC90C8FCA8EB1FC0EB7FF8380DE07C380F801F01001380 000E130F000CEB07C0C713E0A2140315F0A4127812FCA448EB07E012E0006014C0007013 0F6C14806CEB1F006C133E380780F83801FFE038007F801C2D7DAB23>II<007FB712F8B812FCA2CBFCADB812FCA26C16F82E137C 9937>61 D80 D<380781F838FF87FEEB8E3FEA0F9CEA07B813B0EBF01EEBE000A45BB0487EB5FCA2 181E7E9D1C>114 D E %EndDVIPSBitmapFont /FF 105[50 28[50 1[72 1[50 28 39 33 50 50 50 50 78 28 50 1[28 50 50 33 44 50 44 1[44 9[94 72 1[61 55 1[72 55 72 1[89 61 1[39 33 72 3[72 66 66 72 12[50 50 50 50 50 1[25 33 25 44[{TeXBase1Encoding ReEncodeFont}46 99.6264 /Times-Roman rf /FG 134[60 60 86 1[66 40 47 53 1[66 60 66 100 33 66 1[33 66 60 40 53 66 53 66 60 10[86 1[80 66 86 93 2[86 4[47 4[86 86 1[86 7[60 60 60 60 60 60 60 60 60 3[40 45[{TeXBase1Encoding ReEncodeFont}42 119.552 /Times-Bold rf end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: Letter %%EndSetup %%Page: 0 1 0 0 bop 698 1072 a FG(Analysis)30 b(of)g(T)-11 b(ask)29 b(Assignment)h(with)g(Cycle)h(Stealing)643 1361 y FF(Mor)25 b(Harchol-Balter)1437 1325 y FE(1)1693 1361 y FF(Cuihong)f(Li)2150 1325 y FE(2)2405 1361 y FF(T)-8 b(akayuki)24 b(Osogami)3159 1325 y FE(3)982 1477 y FF(Alan)h(Scheller)n(-W)-8 b(olf)1755 1441 y FE(4)2068 1477 y FF(Mark)25 b(S.)g(Squillante)2819 1441 y FE(5)1725 1619 y FF(July)f(2002)1574 1756 y FC(C)t(M)t(U)t(-)t (C)t(S)t(-)t(0)t(2)t(-)t(1)5 b(5)g(8)1399 2497 y(School)24 b(of)f(Computer)i(Science)1412 2610 y(Carne)o(gie)g(Mellon)f(Uni)n(v)o (ersity)1533 2723 y(Pittsb)n(ur)n(gh,)i(P)-8 b(A)22 b(15213)1751 3171 y FB(Abstract)120 3384 y FC(The)28 b(problem)h(of)f(task)g (assignment)j(in)d(a)f(distrib)n(uted)k(serv)o(er)e(system)g(is)f (considered,)k(where)c(short)h(jobs)g(are)120 3497 y(separated)37 b(from)d(long)h(jobs,)j(b)n(ut)d(short)g(jobs)h(may)e(be)g(run)h(in)f (the)h(long)g(job)g(partition)i(if)d(it)g(is)g(idle)h(\(c)o(ycle)120 3609 y(stealing\).)c(Jobs)22 b(are)h(assumed)g(to)f(be)g (non-preemptible.)33 b(Ne)n(w)20 b(techniques)26 b(are)c(presented)j (for)d(analyzing)j(this)120 3722 y(problem,)h(both)f(in)g(the)g(case)g (of)g(immediate)h(dispatch)h(of)d(jobs)i(to)e(hosts)i(and)f(in)g(the)g (case)g(of)g(a)f(central)i(queue.)120 3835 y(The)d(analysis)j(is)e (approximate,)j(b)n(ut)d(can)g(be)g(made)g(as)g(close)h(to)f(e)o(xact)g (as)g(desired.)32 b(Analysis)25 b(is)f(v)n(alidated)i(via)120 3948 y(simulation.)k(Results)22 b(of)f(the)h(analysis)h(sho)n(w)e(that) h(c)o(ycle)g(stealing)h(can)f(reduce)h(mean)e(response)j(time)d(for)g (short)120 4061 y(jobs)j(by)g(orders)h(of)e(magnitude,)j(while)d(long)i (jobs)f(are)g(only)g(slightly)i(penalized.)220 4429 y FA(1)254 4461 y Fz(Carne)o(gie)19 b(Mellon)f(Uni)n(v)o(ersity)-5 b(,)18 b(Computer)h(Science)f(Department.)23 b(Email:)f (harchol@cs.cmu.edu.)i(This)18 b(w)o(ork)g(w)o(as)g(supported)120 4552 y(by)f(NSF)e(Career)i(Grant)f(CCR-0133077,)i(by)f(NSF)f(ITR)f (Grant)i(99-167)h(ANI-0081396)g(and)f(by)g(Spinnak)o(er)h(Netw)o(orks)f (via)g(Pittsb)o(ur)o(gh)120 4643 y(Digital)h(Greenhouse)j(Grant)e (01-1.)220 4703 y FA(2)254 4735 y Fz(Carne)o(gie)h(Mellon)f(Uni)n(v)o (ersity)-5 b(,)19 b(GSIA.)f(Email:)k(cuihong@cs.cmu.edu)220 4794 y FA(3)254 4826 y Fz(Carne)o(gie)e(Mellon)f(Uni)n(v)o(ersity)-5 b(,)19 b(CSD.)f(Email:)k(osogami@cs.cmu.edu)220 4886 y FA(4)254 4917 y Fz(Carne)o(gie)e(Mellon)f(Uni)n(v)o(ersity)-5 b(,)19 b(GSIA.)f(Email:)k(a)o(w)o(olf@andre)n(w)-5 b(.cmu.edu)220 4977 y FA(5)254 5009 y Fz(IBM)57 b(Research)h(Di)n(vision,)67 b(Thomas)57 b(J.)g(W)-6 b(atson)57 b(Research)h(Center)m(,)66 b(Y)-8 b(orkto)n(wn)58 b(Heights,)66 b(NY)57 b(10598,)68 b(Email:)120 5100 y(mss@w)o(atson.ibm.com)p eop %%Page: 1 2 1 1 bop 261 4854 a FB(K)n(eyw)o(ords:)46 b FC(c)o(ycle)32 b(stealing,)j(task)d(assignment,)k(serv)o(er)d(f)o(arm,)g(distrib)n (uted)i(system,)f(unf)o(airness,)i(star)n(-)120 4967 y(v)n(ation,)28 b(load)g(sharing,)g(supercomputing,)k(matrix-geometric) d(methods,)g(b)n(usy)f(periods,)g(multi-class)h(queue,)120 5080 y(multiserv)o(er)c(queue.)p eop %%Page: 1 3 1 2 bop 120 91 a FG(1)119 b(Intr)n(oduction)120 298 y FB(Distrib)n(uted)23 b(ser)o(v)o(er)j(model)120 473 y FC(In)k(recent)h(years,)i(distrib)n(uted)g(serv)o(ers)e(ha)n(v)o(e)g (become)g(increasingly)i(common)e(because)h(the)o(y)e(allo)n(w)g(for)g (in-)120 586 y(creased)37 b(computing)g(po)n(wer)e(while)g(being)h (cost-ef)n(fecti)n(v)o(e)i(and)d(easily)i(scalable.)65 b(In)35 b(a)f(distrib)n(uted)k(serv)o(er)120 698 y(system,)25 b(jobs)g(\(tasks\))i(arri)n(v)o(e)e(and)g(must)f(each)h(be)g (dispatched)i(to)e(e)o(xactly)h(one)f(of)f(se)n(v)o(eral)i(host)f (machines)h(for)120 811 y(processing.)49 b(The)29 b(rule)h(for)g (assigning)i(jobs)e(to)f(host)h(machines)h(is)f(kno)n(wn)f(as)h(the)f Fy(task)h(assignment)i(policy)p FC(.)120 924 y(The)27 b(choice)j(of)e(the)g(task)g(assignment)i(polic)o(y)f(has)g(a)e (signi\002cant)j(ef)n(fect)f(on)f(the)g(performance)i(percei)n(v)o(ed)g (by)120 1037 y(users.)f(Designing)c(a)d(distrib)n(uted)k(serv)o(er)d (system)h(thus)f(often)g(comes)g(do)n(wn)g(to)f(choosing)j(the)e (\223best\224)h(possible)120 1150 y(task)i(assignment)h(polic)o(y)g (for)e(the)h(gi)n(v)o(en)f(model)h(and)g(user)g(requirements.)36 b(While)26 b(de)n(vising)h(up)f(ne)n(w)e(task)i(as-)120 1263 y(signment)g(policies)g(is)e(easy)-6 b(,)25 b(analyzing)i(e)n(v)o (en)d(the)h(simplest)g(policies)i(can)d(pro)o(v)o(e)h(to)f(be)g(v)o (ery)h(dif)n(\002cult:)31 b(Man)o(y)120 1376 y(of)h(the)g (long-standing)k(open)d(questions)i(in)d(queueing)i(theory)g(in)l(v)n (olv)o(e)g(the)e(performance)j(analysis)f(of)e(task)120 1489 y(assignment)26 b(policies.)261 1602 y(In)g(this)g(paper)h(we)e (consider)j(the)e Fy(particular)j(model)d FC(of)g(a)f(distrib)n(uted)k (serv)o(er)e(system)f(in)g(which)g(the)g(e)o(x)o(e-)120 1715 y(cution)c(of)f(jobs)g(is)g Fy(non-pr)m(eemptive)j FC(\(run-to-completion\),)i(i.e.,)21 b(the)g(e)o(x)o(ecution)h(of)f(a)f (job)h(can')n(t)h(be)f(interrupted)120 1828 y(and)j(subsequently)k (resumed.)i(W)-7 b(e)23 b(consider)j(both)f(the)f(case)g(where)g(jobs)h (are)e Fy(dispatc)o(hed)k(immediately)e FC(upon)120 1940 y(arri)n(v)n(al)33 b(to)e(one)i(of)e(the)h(host)h(machines)g(for)f (processing,)k(and)d(the)f(case)g(where)g(jobs)g(are)g(held)h(in)f(a)f Fy(centr)o(al)120 2053 y(queue)25 b FC(until)f(requested)i(by)e(a)f (host)h(machine.)120 2299 y FB(Related)g(applications)120 2473 y FC(The)c(model)h(assumptions)j(abo)o(v)o(e)d(are)f(consistent)k (with)c(those)i(of)f(v)n(alidated)h(stochastic)i(models)d(used)g(to)g (study)120 2586 y(a)26 b(wide)h(range)g(of)g(high-v)n(olume)i(W)-7 b(eb)26 b(sites)i([13)q(,)e(25].)38 b(These)27 b(papers)h(analyze)g (the)f(performance)i(of)e(special)120 2699 y(e)n(v)o(ent)j(W)-7 b(eb)29 b(sites)h(\(1998)h(W)l(inter)f(Olympics\))h(go)o(v)o(erned)g (by)f(IBM')-5 b(s)29 b(Netw)o(ork)g(Dispatcher)j(product)f([12)r(],)f (a)120 2812 y(high-speed)37 b(router)e(which)f(immediately)i(routes)f (each)g(incoming)g(W)-7 b(eb)34 b(requests)i(to)d(one)i(of)f(se)n(v)o (eral)g(host)120 2925 y(serv)o(ers.)c(Immediate)25 b(dispatching)i(of)c (jobs)i(is)e(important)j(in)d(this)h(setting)i(for)d(scalability)k(and) d(ef)n(\002cienc)o(y;)h(the)120 3038 y(router)g(must)e(not)h(become)h (a)e(bottleneck.)261 3151 y(Our)34 b(model)g(is)g(also)g(moti)n(v)n (ated)i(by)e(serv)o(ers)h(for)f(high-performance)k(parallel)e (computing.)62 b(F)o(or)33 b(these)120 3264 y(distrib)n(uted)24 b(serv)o(ers,)e(each)f(host)g(machine)g(is)f(usually)i(a)e (multi-processor)k(machine)e(\(e.g.,)e(an)h(eight-processor)120 3377 y(Cray)g(J90\))h(with)f(a)g(single)i(memory)-6 b(,)21 b(and)h(each)g(job)g(submitted)h(is)e(a)g(parallel)i(job,)e(intended)j (to)d(run)h(on)f(a)g(single)120 3490 y(host.)28 b(T)-7 b(ypically)h(,)23 b(in)d(the)h(case)g(of)g(batch)h(jobs,)f Fy(one)g FC(job)g(at)g(a)f(time)g(\(or)h(a)f(small)h(number)g(of)g (jobs\))h(occupies)g(each)120 3603 y(host)h(machine.)29 b(Jobs)23 b(may)f(be)g(held)h(in)f(a)g(central)h(queue)h(until)f(a)e (host)i(is)f(ready)h(for)g(the)f(job,)h(or)f(the)g(jobs)h(might)120 3715 y(be)k(dispatched)j(to)d(hosts)h(and)g(queued)h(at)e(the)g(hosts.) 41 b(In)27 b(such)g(settings)j(it)c(is)h(typical)i(for)e(users)h(to)f (submit)h(an)120 3828 y(upper)d(bound)g(on)e(their)i(job')-5 b(s)24 b(CPU)e(requirement)k(in)e(seconds;)h(the)f(job)g(is)g(killed)g (if)g(it)f(e)o(xceeds)i(this)f(estimate.)120 3941 y(Examples)g(of)g (distrib)n(uted)j(serv)o(er)d(systems)h(that)f(\002t)e(our)i(model)g (are)g(gi)n(v)o(en)g(in)f(T)-7 b(able)24 b(1.)261 4054 y(Our)f(model)h(has)g(also)g(been)g(used)g(for)f(other)i(applications)i (requiring)f(scalable)f(systems,)f(such)g(as)g(depart-)120 4167 y(mental)32 b(computers)h(within)f(an)f(or)n(ganization)k([22)q(]) c(or)g(telecommunication)k(systems)e(with)e(heterogeneous)120 4280 y(serv)o(ers)25 b([5)q(].)j(It)23 b(has)h(also)g(been)g(studied)i (simply)e(as)g(a)f(purely)i(theoretical)h(model)e([24)q(].)120 4526 y FB(Pr)n(e)o(vious)g(w)o(ork)f(on)g(T)-8 b(ask)22 b(Assignment)120 4700 y FC(The)29 b(analysis)i(of)e(task)h(assignment)i (policies)f(has)f(been)g(the)f(topic)h(of)g(man)o(y)f(papers.)47 b(Belo)n(w)28 b(we)h(pro)o(vide)i(a)120 4813 y(brief)24 b(o)o(v)o(ervie)n(w)-6 b(.)30 b(W)-7 b(e)22 b(limit)i(our)g(discussion) i(to)e(task)g(assignment)i(in)d Fy(non-pr)m(eemptive)k FC(systems.)261 4926 y(By)37 b(f)o(ar)g(the)g(most)g(common)h(task)f (assignment)j(polic)o(y)e(used)g(is)f Fx(Round-Robin)31 b FC([13)q(,)36 b(25)q(,)g(7)q(].)69 b(The)120 5039 y(pre)n(v)n(alence) 32 b(for)e(this)h(polic)o(y)g(stems)f(from)g(RR-DNS,)d([6])j(whereby)h (the)f(task)g(assignment)j(at)c(a)h(W)-7 b(eb)29 b(site)h(is)1897 5349 y(1)p eop %%Page: 2 4 2 3 bop 120 3 3880 4 v 118 103 4 100 v 170 73 a Fw(Name)p 1071 103 V 753 w(Location)p 2320 103 V 953 w(No.)24 b(Hosts)p 2757 103 V 100 w(Host)d(Machine)p 3998 103 V 120 106 3880 4 v 118 206 4 100 v 170 176 a(Xolas)f([18)o(])p 1071 206 V 599 w(MIT)g(Lab)g(for)f(Computer)g(Science)p 2320 206 V 345 w(8)p 2757 206 V 247 w(8-processor)f(Ultra)j(HPC)g(5000) e(SMP)p 3998 206 V 120 209 3880 4 v 118 309 4 100 v 170 279 a(Pleiades)h([17)o(])p 1071 309 V 516 w(MIT)g(Lab)g(for)f(Computer) g(Science)p 2320 309 V 345 w(7)p 2757 309 V 247 w(4-processor)f(Alpha)i (21164)e(machine)p 3998 309 V 120 312 3880 4 v 118 412 4 100 v 170 382 a(J90)i(distrib)n(uted)f(serv)o(er)p 1071 412 V 239 w(N)m(ASA)i(Ames)f(Research)g(Lab)p 2320 412 V 484 w(4)p 2757 412 V 247 w(8-processor)e(Cray)i(J90)g(machine)p 3998 412 V 120 415 3880 4 v 118 515 4 100 v 170 485 a(J90)g(distrib)n (uted)f(serv)o(er)g([1])p 1071 515 V 122 w(Pittsb)n(ur)o(gh)g (Supercomputing)e(Center)p 2320 515 V 246 w(2)p 2757 515 V 247 w(8-processor)h(Cray)i(J90)g(machine)p 3998 515 V 120 518 3880 4 v 118 618 4 100 v 170 588 a(C90)g(distrib)n(uted)f (serv)o(er)h([2)o(])p 1071 618 V 99 w(N)m(ASA)h(Ames)f(Research)g(Lab)p 2320 618 V 484 w(2)p 2757 618 V 247 w(16-processor)e(Cray)i(C90)g (machine)p 3998 618 V 120 621 3880 4 v 120 774 a FC(T)-7 b(able)25 b(1:)31 b Fv(Examples)20 b(of)i(distrib)n(uted)f(server)o(s)h (described)f(by)g(the)g(ar)m(c)o(hitectur)o(al)f(model)h(of)g(this)h (paper)-9 b(.)27 b(The)21 b(sc)o(heduler)o(s)120 874 y(used)i(ar)m(e)g(Load-Le)o(veler)-9 b(,)22 b(LSF)-11 b(,)22 b(PBS,)g(or)i(NQS.)f(These)g(sc)o(heduler)o(s)f(typically)h (only)f(support)h(run-to-completion)c(\(non-)120 974 y(pr)m(eemptive\))29 b(for)h(se)o(ver)o(al)g(r)m(easons:)44 b(F)l(ir)o(st,)34 b(the)c(memory)g(r)m(equir)m(ements)f(of)i(jobs)e (tend)h(to)g(be)g(hug)o(e)o(,)h(making)e(it)i(very)120 1073 y(e)n(xpensive)24 b(to)h(swap)g(out)f(a)h(job')m(s)f(memory)g ([9].)39 b(Thus)25 b(timesharing)f(between)g(jobs)h(only)f(mak)o(es)h (sense)g(if)g(all)g(the)g(jobs)120 1173 y(being)j(timeshar)m(ed)g (\002t)i(within)f(the)g(memory)g(of)g(the)g(host,)i(whic)o(h)e(is)h (unlik)o(ely)-5 b(.)51 b(Also,)31 b(many)d(oper)o(ating)g(systems)i (that)120 1272 y(enable)g(timesharing)h(for)g(single-pr)l(ocessor)g (jobs)g(do)g(not)g(facilitate)g(pr)m(eemption)e(among)h(se)o(ver)o(al)h (pr)l(ocessor)o(s)h(in)f(a)120 1372 y(coor)m(dinated)18 b(fashion)h([21)o(].)120 1647 y FC(done)24 b(based)g(on)f(the)h(IP)e (addresses)j(chosen)g(by)e(the)g(Domain)g(Name)g(Serv)o(er)-5 b(.)28 b(The)23 b Fx(Round-Robin)17 b FC(polic)o(y)24 b(is)120 1760 y(simple,)g(b)n(ut)g(it)f(neither)i(maximizes)g (utilization)i(of)c(the)h(hosts,)g(nor)g(minimizes)h(response)g(times.) 261 1872 y(In)i(the)f(case)h(where)g(the)g(size)g(of)f(jobs)i(are)e (not)h(kno)n(wn)g(and)g(we)e(require)k(immediate)e(dispatch)i(of)d (jobs)h(to)120 1985 y(hosts,)c(then)f(the)g Fx(Shortest-Queue)14 b FC(task)23 b(assignment)g(polic)o(y)g(\226)e(where)h(incoming)h(jobs) g(are)e(immediately)120 2098 y(dispatched)27 b(to)c(the)h(host)g(with)g (the)g(fe)n(west)f(number)i(of)f(jobs)g(\226)f(has)h(been)h(sho)n(wn)e (to)h(be)g(optimal)g(when)g(the)g(job)120 2211 y(size)30 b(distrib)n(ution)j(is)c Fy(e)n(xponential)j FC(and)e(the)f(arri)n(v)n (al)i(process)g(is)e(Poisson)h([28)q(].)45 b(Here)29 b(optimality)i(is)e(de\002ned)120 2324 y(as)k(maximizing)h(the)f (discounted)j(number)e(of)f(jobs)g(that)h(complete)g(by)f(some)g(\002x) o(ed)g(time)f Fu(t)p FC(.)56 b(Ephremides,)120 2437 y(V)-10 b(araiya,)27 b(and)f(W)-7 b(alrand)27 b([8])f(sho)n(wed)g(that)g Fx(Shortest-Queue)19 b FC(also)26 b(minimizes)h(the)f(e)o(xpected)i (total)e(time)120 2550 y(for)19 b(the)f(completion)j(of)d(all)g(jobs)i (arri)n(ving)g(by)e(some)g(\002x)o(ed)g(time)h Fu(t)p FC(,)f(under)h(an)g(e)o(xponential)i(job)e(size)g(distrib)n(ution)120 2663 y(and)24 b(arbitrary)i(arri)n(v)n(al)e(process.)261 2776 y(When)i(a)f(centralized)k(queue)d(is)g(allo)n(wed)g(at)f(the)h (dispatcher)l(,)j(the)d Fx(M/G/k)c FC(polic)o(y)27 b(been)f(pro)o(v)o (en)h(to)e(mini-)120 2889 y(mize)c(mean)h(response)i(time)d(when)g(job) h(processing)j(requirements)f(come)e(from)f(an)g(e)o(xponential)k (distrib)n(ution,)120 3002 y(or)j(one)g(with)g(Increasing)j(F)o(ailure) d(Rate)f([29)r(].)41 b(\(Note:)d(throughout)31 b(this)e(paper)f(we)g (will)f(use)h(the)g(terms)h Fy(pr)l(o-)120 3114 y(cessing)22 b(r)m(equir)m(ement)p FC(,)h Fy(service)f(demand)p FC(,)g(and)f Fy(size)f FC(interchangeably)-6 b(.\))33 b(The)20 b Fx(M/G/k)e FC(polic)o(y)j(holds)h(all)e(jobs)h(at)120 3227 y(the)i(dispatcher)i (unit)e(in)f(a)g(single)i(FCFS)c(queue,)k(and)e(only)i(when)e(a)g(host) h(is)g(free)f(does)i(it)e(recei)n(v)o(e)h(the)g(ne)o(xt)g(job)l(.)120 3340 y(This)e(polic)o(y)i(maximizes)g(utilization)h(of)e(the)g(host)g (machines,)h(thereby)h(helping)f(to)f(minimize)g(mean)g(response)120 3453 y(time.)53 b(The)31 b Fx(M/G/k)e FC(polic)o(y)k(is)e(pro)o(v)n (ably)j(identical)g(to)d(the)h Fx(Least-Work-Rema)o(in)o(ing)24 b FC(polic)o(y)33 b(which)120 3566 y(sends)25 b(each)f(job)g(to)f(the)h (host)g(with)g(the)g(least)g(total)g(remaining)i(w)o(ork)d([10)r(].)261 3679 y(While)30 b(policies)h(lik)o(e)f Fx(M/G/k)d FC(and)j Fx(Shortest-Queue)22 b FC(perform)30 b(well)f(under)i Fy(e)n(xponential)i FC(job)d(size)120 3792 y(distrib)n(utions,)23 b(the)o(y)c(perform)h(poorly)g(when)e(the)h(job)g(size)g(distrib)n (ution)j(has)d(higher)h(v)n(ariability)-6 b(.)30 b(In)18 b(such)h(cases,)120 3905 y(it)24 b(has)g(been)h(sho)n(wn)f(that)g(the)g Fx(Dedicated)c FC(polic)o(y)25 b(f)o(ar)f(outperforms)i(all)e(these)h (other)g(policies)h(with)e(respect)120 4018 y(to)30 b(minimizing)i (mean)e(response)j(time.)48 b(In)30 b(the)h Fx(Dedicated)25 b FC(polic)o(y)-6 b(,)33 b(for)d(e)o(xample,)j(some)d(hosts)h(may)f(be) 120 4131 y(designated)24 b(as)d(the)g(\223short)h(hosts\224)h(and)e (others)h(as)f(the)g(\223long)h(hosts.)-6 b(\224)29 b(Short)21 b(jobs)h(are)f(al)o(w)o(ays)h(sent)f(to)g(the)g(short)120 4244 y(hosts)29 b(and)g(long)g(jobs)g(to)f(the)h(long)g(hosts.)44 b(The)27 b(superiority)32 b(of)c(the)g Fx(Dedicated)c FC(polic)o(y)29 b(is)f(demonstrated)120 4356 y(analytically)g(in)c([11) r(],)g(and)h(sho)n(wn)g(empirically)i(on)d(se)n(v)o(eral)i(traces)g(of) e(supercomputing)29 b(w)o(orkloads)d(in)f([23)q(].)120 4469 y(The)k Fx(Dedicated)c FC(polic)o(y)31 b(is)f(also)h(popular)h(in) d(practice)j(\(e.g.)48 b(Cornell)31 b(Theory)f(Center\))h(where)f(dif)n (ferent)120 4582 y(host)20 b(machines)h(ha)n(v)o(e)f(dif)n(ferent)h (duration)h(limitations:)29 b(0\2261/2)21 b(hour)l(,)g(1/2)e(\226)g(2)g (hours,)i(2)e(\226)g(4)g(hours,)i(4)e(\226)g(8)g(hours,)120 4695 y(etc.,)29 b(and)g(users)g(must)f(specify)i(an)e(estimated)i (required)h(service)e(requirement)i(for)e(each)g(job)l(.)43 b(The)28 b(intuition)120 4808 y(behind)34 b(the)e Fx(Dedicated)27 b FC(polic)o(y)33 b(is)f(that)h(for)f(the)g(case)h(of)f(high-v)n (ariability)37 b(job)32 b(size)h(distrib)n(utions,)38 b(it)31 b(is)120 4921 y(important)25 b(to)f(isolate)h(short)f(jobs)h (from)e(the)h(long)g(jobs,)g(as)g(w)o(aiting)g(behind)h(the)f(long)h (jobs)f(is)f(v)o(ery)h(costly)-6 b(.)261 5034 y(Ev)o(en)32 b(when)h(the)g(job)g(size)g(is)g(not)g(kno)n(wn,)i(it)d(has)h(been)h (demonstrated)i(that)d(a)f(polic)o(y)i(v)o(ery)f(similar)g(to)1897 5349 y(2)p eop %%Page: 3 5 3 4 bop 120 91 a Fx(Dedicated)p FC(,)15 b(kno)n(wn)20 b(as)g(the)g Fx(TAGS)d FC(polic)o(y)j(\(T)-7 b(ask)20 b(Assignment)h(by)f(Guessing)h(Size\))f(w)o(orks)g(almost)g(as)f(well) 120 204 y(when)j(job)h(sizes)g(ha)n(v)o(e)g(high)g(v)n(ariability)-6 b(.)31 b(Lik)o(e)22 b Fx(Dedicated)p FC(,)17 b(the)23 b Fx(TAGS)c FC(polic)o(y)24 b(signi\002cantly)h(outperforms)120 317 y(other)g(policies)g(that)f(do)g(not)g(se)o(gre)o(gate)h(jobs)f(by) f(size)i([10)q(].)120 563 y FB(Moti)o(v)o(ation)g(f)n(or)f(Cycle)g (Stealing)120 737 y FC(While)f Fx(Dedicated)17 b FC(assignment)24 b(may)e(be)g(preferable)j(to)d(the)h Fx(M/G/k)c FC(and)j Fx(Shortest-Queue)15 b FC(policies)120 850 y(for)30 b(highly)h(v)n (ariable)g(job)f(sizes,)i(it)e(is)f(clearly)i Fy(not)f FC(optimal.)48 b(One)29 b(problem)i(is)f(that)g Fx(Dedicated)25 b FC(leads)30 b(to)120 963 y(situations)c(where)e(the)g(serv)o(ers)h (are)f(not)g(fully)h(utilized.)31 b(F)o(or)23 b(e)o(xample,)h(there)h (may)e(be)h(\002)n(v)o(e)f(consecuti)n(v)o(e)j(short)120 1076 y(jobs,)f(with)e(no)i(long)f(job,)h(resulting)h(in)e(an)g(idle)h (long)g(host.)30 b(This)24 b(is)g(especially)j(lik)o(ely)e(in)f(common) h(computer)120 1189 y(w)o(orkloads,)31 b(where)d(there)g(are)g(man)o(y) g(short)g(jobs)h(and)f(just)g(a)g(fe)n(w)f(v)o(ery)h(long)g(jobs,)i (resulting)g(in)d(longer)j(idle)120 1302 y(periods)25 b(between)g(the)f(arri)n(v)n(als)h(of)e(long)h(jobs.)261 1415 y(Ideally)e(one)f(w)o(ould)f(lik)o(e)h(a)f(polic)o(y)h(which)g (combines)g(the)g(v)n(ariance-cutting)k(bene\002t)c(of)f(the)g Fx(Dedicated)120 1528 y FC(polic)o(y)34 b(with)g(the)f (high-utilization)38 b(property)e(of)d Fx(M/G/k)d FC(and)k Fx(Shortest-Queue)p FC(.)51 b(W)-7 b(e)32 b(w)o(ould)i(lik)o(e)g(to)120 1641 y(se)o(gre)o(gate)j(jobs)g(by)f(size)h(\(short)g(jobs)g(go)f(to)g (short)h(host,)j(long)d(jobs)g(go)f(to)g(long)h(host\))g(so)f(as)g(to)g (pro)o(vide)120 1753 y(isolation)25 b(for)d(short)h(jobs.)29 b(Ho)n(we)n(v)o(er)22 b(during)h(times)g(when)f(the)g(long)h(job)g (host)g(is)f(free,)g(we)g(w)o(ould)g(lik)o(e)h(to)f Fy(steal)120 1866 y FC(the)29 b(long)h(host')-5 b(s)31 b(idle)e(c)o(ycles)i(and)e (use)h(those)g(to)f(serv)o(e)h(e)o(xcess)g(short)g(jobs.)46 b(This)29 b(w)o(ould)h(mak)o(e)f(our)g(system)120 1979 y(more)g(ef)n(\002cient)g(not)g(only)h(by)e(decreasing)k(the)d(mean)g (response)i(time)d(of)h(short)h(jobs,)g(b)n(ut)f(also)h(by)e(enlar)n (ging)120 2092 y(the)j Fy(stability)i(r)m(e)l(gion)f FC(of)f(the)g(o)o(v)o(erall)g(system.)51 b(Speci\002cally)-6 b(,)34 b(for)d(highly)h(unbalanced)i(systems,)f(where)e(the)120 2205 y(short)23 b(host)f(is)g(more)g(hea)n(vily)i(loaded,)f(granting)h (the)e(short)h(jobs)f(limited)h(access)g(to)f(the)g(long)h(partition)h (may)d(be)120 2318 y(the)29 b(dif)n(ference)h(between)g(an)e(o)o(v)o (erloaded)j(system)e(and)g(a)f(well-beha)n(v)o(ed)j(one.)44 b(\(W)-7 b(e)28 b(discuss)i(this)f(in)g(greater)120 2431 y(detail)24 b(in)g(Section)g(5.\))k(Importantly)-6 b(,)26 b(the)d(short)i(jobs)f(should)h(only)f(use)f(the)h(long)g(host)g(when)f (that)h(host)g(is)f Fy(fr)m(ee)p FC(,)120 2544 y(so)g(that)h(we)e(don') n(t)i Fy(starve)h FC(the)e(long)h(jobs,)f(or)g(cause)h(them)f(undue)i (delay)-6 b(.)30 b(Because)24 b(jobs)f(are)h(not)f(preemptible,)120 2657 y(there)29 b(will)g(still)g(be)f(some)h(penalty)h(to)f(the)g(long) g(jobs,)h(because)h(a)d(long)h(job)g(may)f(arri)n(v)o(e)i(to)e(\002nd)g (a)g(short)i(job)120 2770 y(serving)25 b(at)f(the)g(long)g(host,)g (causing)h(the)f(long)h(job)e(to)h(ha)n(v)o(e)g(to)g(w)o(ait)f(behind)i (that)f(short)h(job)l(.)120 3016 y FB(T)-7 b(w)o(o)23 b(cycle)h(stealing)h(algorithms)120 3190 y FC(W)-7 b(e)23 b(propose)i(tw)o(o)e(c)o(ycle)i(stealing)g(algorithms:)120 3377 y FB(Cycle)f(stealing)h(with)d(Immediate)i(Dispatch)f(\()p Fx(CS-Immediate-Di)o(spa)o(tc)o(h)p FB(\):)40 b FC(In)27 b(this)h(algorithm,)i(all)347 3490 y(jobs)f(are)e(immediately)j (dispatched)g(to)e(a)f(host)h(upon)h(arri)n(v)n(al.)42 b(There)28 b(is)f(a)g(designated)k(short)d(job)g(host)347 3603 y(and)33 b(a)f(designated)j(long)e(job)g(host.)55 b(An)32 b(arri)n(ving)i(long)f(job)g(is)f(al)o(w)o(ays)h(dispatched)i (to)d(the)h(long)g(job)347 3716 y(host.)d(An)22 b(arri)n(ving)j(short)f (job)f(\002rst)g(checks)h(to)f(see)h(if)f(the)g(long)h(job)f(host)h(is) f(idle.)29 b(If)23 b(so,)g(the)g(short)h(job)f(is)347 3829 y(dispatched)29 b(to)d(the)g(long)h(job)f(host.)36 b(If,)26 b(ho)n(we)n(v)o(er)l(,)h(the)f(long)g(job)h(host)f(is)g(not)g (idle)g(\(either)i(it')-5 b(s)26 b(w)o(orking)347 3942 y(on)k(a)e(long)j(job)e(or)g(a)g(short)h(job\),)h(then)f(the)g(arri)n (ving)h(short)f(job)g(is)f(dispatched)j(to)d(the)h(short)g(job)g(host.) 347 4055 y(Jobs)f(at)g(a)f(host)h(are)f(serviced)j(in)d(FCFS)e(order)-5 b(.)44 b(The)28 b Fx(CS-Immediate-Di)o(sp)o(atc)o(h)21 b FC(algorithm)30 b(is)347 4168 y(sho)n(wn)24 b(in)g(Figure)g(1.)347 4318 y(The)31 b Fx(CS-Immediate-Di)o(sp)o(at)o(ch)24 b FC(algorithm)33 b(is)e(an)g(impro)o(v)o(ement)h(o)o(v)o(er)f Fx(Dedicated)p FC(,)d(since)347 4431 y(a)33 b(fraction)h(of)f(the)g (arri)n(v)n(al)g(stream)h(of)e(short)i(jobs)f(can)g(be)g(of)n (\003oaded)h(to)f(the)g(long)g(host,)i(while)e(only)347 4544 y(slightly)28 b(penalizing)g(long)e(jobs.)35 b(Ho)n(we)n(v)o(er)l (,)26 b(only)g(those)h(short)f(jobs)g(arri)n(ving)i(after)e(the)f(long) i(host)f(has)347 4657 y(entered)j(an)f(idle)g(period)h(can)e(obtain)i (this)f(bene\002t.)41 b(If)27 b(a)g(short)i(job)e(arri)n(v)o(es)i(just) f(before)h(the)e(long)h(host)347 4770 y(enters)d(an)f(idle)g(period,)h (the)f(short)g(job)g(is)g(not)g(eligible)h(for)f(running)i(during)f (the)f(idle)g(partition.)31 b(This)23 b(is)347 4883 y(the)h(moti)n(v)n (ation)h(behind)g(our)f(ne)o(xt)g(c)o(ycle)g(stealing)i(algorithm.)1897 5349 y(3)p eop %%Page: 4 6 4 5 bop 120 91 a FB(Cycle)24 b(stealing)h(with)d(Central)i(Queue)e(\()p Fx(CS-Central-Queu)o(e)p FB(\):)40 b FC(In)25 b(this)h(algorithm,)h (all)e(jobs)h(are)f(held)347 204 y(in)d(a)g(central)i(queue.)30 b(Whene)n(v)o(er)23 b(the)f(short)i(job)e(host)h(becomes)h(idle,)e(it)g (picks)i(the)e(\002rst)g(short)h(job)g(in)f(the)347 317 y(central)g(queue)f(to)f(run.)27 b(Whene)n(v)o(er)21 b(the)g(long)f(job)g(host)h(becomes)g(idle,)g(it)f(picks)h(the)f (\002rst)f(long)i(job)f(in)g(the)347 430 y(central)k(queue)g(to)f(run.) 29 b(Ho)n(we)n(v)o(er)l(,)22 b(if)g(there)i(is)e(no)h(long)g(job,)g (the)g(long)h(host)f(picks)h(the)e(\002rst)h(short)g(job)g(in)347 543 y(the)k(central)g(queue.)38 b(A)25 b(minor)i(point:)35 b(Whereas)28 b(in)e Fx(CS-Immediate-Di)o(sp)o(at)o(ch)o FC(,)20 b(the)27 b(short)g(and)347 656 y(long)e(hosts)g(are)g (designated)i(in)d(adv)n(ance,)i(in)e Fx(CS-Central-Queu)o(e)17 b FC(we)23 b(allo)n(w)h(renaming)i(of)e(hosts)347 769 y(\226)e(i.e.,)f(if)g(the)h(long)h(host)f(is)g(w)o(orking)h(on)f(a)f (short)i(job,)f(and)g(the)g(short)h(host)g(is)e(idle,)i(then)f(the)g (long)h(host)f(is)347 882 y(renamed)29 b(the)g(short)g(host)g(and)f (vice)h(v)o(ersa.)43 b(Thus)28 b(in)g Fx(CS-Immediate-D)o(is)o(pa)o(tc) o(h)p FC(,)22 b(there)29 b(could)347 995 y(be)22 b(one)h(short)g(in)f (front)h(of)f(one)h(long)g(job)g(in)f(the)g(system)h(with)f(an)g(idle)h (\(short\))h(serv)o(er)l(,)f(while)f(this)h(could)347 1108 y(not)28 b(happen)i(under)e Fx(CS-Central-Queue)o FC(.)34 b(The)28 b Fx(CS-Central-Que)o(ue)20 b FC(algorithm)29 b(is)f(sho)n(wn)347 1220 y(in)c(Figure)g(2.)678 1414 y 19608221 9472573 0 0 44731596 21576417 startTexFig 678 1414 a %%BeginDocument: ../figures/algid.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: algid.eps %%Creator: fig2dev Version 3.2 Patchlevel 3d %%CreationDate: Thu Jul 11 01:02:06 2002 %%For: harchol@mor.sp.cs.cmu.edu (Mor Harchol-Balter) %%BoundingBox: 0 0 680 328 %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def F2psDictbeginF2psDict begin F2psDictbeginF2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 328 moveto 0 0 lineto 680 0 lineto 680 328 lineto closepath clip newpath -33.5 366.3 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def F2psBegin10setmiterlimit0.060000.06000scF2psBegin 10 setmiterlimit 0.06000 0.06000 sc % % Fig objects follow % % Polyline 7.500 slw n 570 3600 m 1703 3600 l gs col0 s gr % Polyline n 1514 2845 m 1891 3316 l gs col0 s gr % Polyline n 1609 3884 m 1891 3316 l gs col0 s gr % Polyline n 570 3128 m 1703 3128 l gs col0 s gr % Polyline n 5314 1190 m 5314 2315 l gs col0 s gr % Polyline n 4520 2315 m 6306 2315 l gs col0 s gr % Polyline n 4520 1190 m 6306 1190 l gs col0 s gr % Polyline n 4983 1190 m 4983 2315 l gs col0 s gr % Polyline n 5643 1190 m 5643 2315 l gs col0 s gr % Polyline n 5975 1190 m 5975 2315 l gs col0 s gr % Polyline n 6306 1190 m 6306 2315 l gs col0 s gr % Polyline n 5219 4968 m 5219 6093 l gs col0 s gr % Polyline n 4425 6093 m 6213 6093 l gs col0 s gr % Polyline n 4425 4968 m 6213 4968 l gs col0 s gr % Polyline n 4888 4968 m 4888 6093 l gs col0 s gr % Polyline n 5550 4968 m 5550 6093 l gs col0 s gr % Polyline n 5881 4968 m 5881 6093 l gs col0 s gr % Polyline n 6213 4968 m 6213 6093 l gs col0 s gr % Ellipse n 6952 1795 584 584 0 360 DrawEllipse gs col0 s gr % Ellipse n 6862 5458 584 584 0 360 DrawEllipse gs col0 s gr % Polyline gs clippath 4751 1861 m 4751 1710 l 4401 1710 l 4704 1786 l 4401 1861 l cp eoclip n 2941 3297 m 3886 1786 l 4736 1786 l gs col0 s gr gr % arrowhead 15.000 slw n 4401 1861 m 4704 1786 l 4401 1710 l 4401 1861 l cp gs 0.00 setgray ef gr col0 s % Polyline 7.500 slw gs clippath 4562 5639 m 4562 5488 l 4212 5488 l 4515 5564 l 4212 5639 l cp eoclip n 2941 3486 m 3886 5564 l 4547 5564 l gs col0 s gr gr % arrowhead 15.000 slw n 4212 5639 m 4515 5564 l 4212 5488 l 4212 5639 l cp gs 0.00 setgray ef gr col0 s % Polyline 7.500 slw gs clippath 8245 1861 m 8245 1710 l 7895 1710 l 8198 1786 l 7895 1861 l cp eoclip n 7570 1786 m 8230 1786 l gs col0 s gr gr % arrowhead 15.000 slw n 7895 1861 m 8198 1786 l 7895 1710 l 7895 1861 l cp gs 0.00 setgray ef gr col0 s % Polyline 7.500 slw gs clippath 8056 5639 m 8056 5488 l 7706 5488 l 8009 5564 l 7706 5639 l cp eoclip n 7475 5564 m 8041 5564 l gs col0 s gr gr % arrowhead 15.000 slw n 7706 5639 m 8009 5564 l 7706 5488 l 7706 5639 l cp gs 0.00 setgray ef gr col0 s /Times-Roman ff 375.00 scf sf 6300 900 m gs 1 -1 sc (Short server) col0 sh gr /Times-Roman ff 375.00 scf sf 6375 4725 m gs 1 -1 sc (Long server) col0 sh gr /Times-Roman ff 375.00 scf sf 8700 1425 m gs 1 -1 sc (Short jobs first check) col0 sh gr /Times-Roman ff 375.00 scf sf 8700 1800 m gs 1 -1 sc (if long server is idle.) col0 sh gr /Times-Roman ff 375.00 scf sf 8700 2175 m gs 1 -1 sc (If so, go there.) col0 sh gr /Times-Roman ff 375.00 scf sf 8700 2550 m gs 1 -1 sc (Else, come here.) col0 sh gr /Times-Roman ff 375.00 scf sf 8700 5400 m gs 1 -1 sc (Long jobs always) col0 sh gr /Times-Roman ff 375.00 scf sf 8700 5850 m gs 1 -1 sc (dispatched here.) col0 sh gr % Polyline 7.500 slw n 1875 2775 m 2925 2775 l 2925 3825 l 1875 3825 l cp gs col0 s gr /Times-Roman ff 315.00 scf sf 1725 4125 m gs 1 -1 sc (Dispatcher) col0 sh gr F2psBegin10setmiterlimit0.060000.06000scF2psEnd rs %%EndDocument endTexFig 886 2810 a FC(Figure)g(1:)29 b(The)23 b Fx(CS-Immediate-Di)o(spa)o(tc) o(h)16 b FC(algorithm.)1110 3029 y 12787969 9472573 0 0 26970521 19931873 startTexFig 1110 3029 a %%BeginDocument: ../figures/algk1.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: algk1.eps %%Creator: fig2dev Version 3.2 Patchlevel 3d %%CreationDate: Tue Jul 30 22:17:39 2002 %%For: harchol@mor.sp.cs.cmu.edu (Mor Harchol-Balter) %%BoundingBox: 0 0 410 303 %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def F2psDictbeginF2psDict begin F2psDictbeginF2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 303 moveto 0 0 lineto 410 0 lineto 410 303 lineto closepath clip newpath -75.2 405.9 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def F2psBegin10setmiterlimit0.060000.06000scF2psBegin 10 setmiterlimit 0.06000 0.06000 sc % % Fig objects follow % 15.000 slw % Ellipse n 5437 2662 490 490 0 360 DrawEllipse gs col0 s gr % Ellipse n 5362 5736 490 490 0 360 DrawEllipse gs col0 s gr % Polyline n 1275 3600 m 3300 3600 l gs col0 s gr % Polyline n 3300 3600 m 3300 4875 l gs col0 s gr % Polyline n 1275 4875 m 3300 4875 l gs col0 s gr % Polyline n 2925 3600 m 2925 4875 l gs col0 s gr % Polyline n 2550 3600 m 2550 4875 l gs col0 s gr % Polyline n 2175 3600 m 2175 4875 l gs col0 s gr % Polyline n 1800 3600 m 1800 4875 l gs col0 s gr % Polyline 2 slj gs clippath 4999 2886 m 4923 2794 l 4648 3018 l 4919 2875 l 4724 3111 l cp eoclip n 3300 4200 m 4950 2850 l gs col0 s gr gr % arrowhead 0 slj n 4724 3111 m 4919 2875 l 4648 3018 l 4733 3026 l 4724 3111 l cp gs 0.00 setgray ef gr col0 s % Polyline 2 slj gs clippath 4847 5605 m 4925 5514 l 4656 5283 l 4845 5524 l 4578 5374 l cp eoclip n 3300 4200 m 4875 5550 l gs col0 s gr gr % arrowhead 0 slj n 4578 5374 m 4845 5524 l 4656 5283 l 4662 5367 l 4578 5374 l cp gs 0.00 setgray ef gr col0 s /Times-Roman ff 345.00 scf sf 3000 4350 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 345.00 scf sf 2625 4350 m gs 1 -1 sc (L) col0 sh gr /Times-Roman ff 345.00 scf sf 2250 4350 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 345.00 scf sf 1875 4350 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 330.00 scf sf 6075 5550 m gs 1 -1 sc (When free,) col0 sh gr /Times-Roman ff 330.00 scf sf 6075 2475 m gs 1 -1 sc (When free,) col0 sh gr /Times-Roman ff 330.00 scf sf 4650 5025 m gs 1 -1 sc (Long server) col0 sh gr /Times-Roman ff 330.00 scf sf 4650 1950 m gs 1 -1 sc (Short server) col0 sh gr /Times-Roman ff 330.00 scf sf 6150 2775 m gs 1 -1 sc (grab short job.) col0 sh gr /Times-Roman ff 330.00 scf sf 6075 5925 m gs 1 -1 sc (grab long job.) col0 sh gr /Times-Roman ff 330.00 scf sf 6075 6300 m gs 1 -1 sc (If no long,) col0 sh gr /Times-Roman ff 330.00 scf sf 6075 6675 m gs 1 -1 sc (grab short job.) col0 sh gr F2psBegin10setmiterlimit0.060000.06000scF2psEnd rs %%EndDocument endTexFig 1023 4425 a FC(Figure)24 b(2:)29 b(The)23 b Fx(CS-Central-Que)o(ue)16 b FC(algorithm.)120 4771 y FB(Remo)o(ving)24 b(the)f(distinction)h (between)e(short)i(and)e(long)120 4945 y FC(It)33 b(is)g(important)i (to)e(realize)i(that)f(the)g(terms)f(\223short\224)i(and)f (\223long\224)h(are)e(not)h(meant)g(to)f(necessarily)j(indicate)120 5058 y(the)e(length)h(of)f(the)g(job)l(.)60 b(There)34 b(is)g(nothing)i(in)d(our)h(analysis)i(that)f(requires)g(that)g (\223short\224)g(jobs)g(be)f(shorter)1897 5349 y(4)p eop %%Page: 5 7 5 6 bop 120 91 a FC(than)28 b(\223long\224)g(jobs.)39 b(These)27 b(names)h(are)f(simply)g(notational)j(con)l(v)o(eniences)h (to)c(indicate)h(which)g(jobs/host)h(are)120 204 y(the)f (\223donors\224)i(\(pro)o(viders)h(of)d(idle)g(c)o(ycles\))h(and)g (which)f(jobs/host)i(are)e(the)h(\223benef)o(actors\224)i (\(bene\002ciaries)g(of)120 317 y(the)d(idle)f(c)o(ycles\).)41 b(In)28 b(f)o(act,)g(throughout)i(we)d(will)g(consider)i(three)f (cases:)38 b(shorts)28 b(shorter)h(than)f(longs;)j(shorts)120 430 y(indistinguishable)i(from)28 b(longs;)j(and)d(\()f (pathologically\))33 b(shorts)c(longer)g(than)g(longs.)42 b(W)-7 b(e)27 b(will)g(\002nd)h(that)g(the)120 543 y(\223shorts\224)j (bene\002t)e(in)f(all)h(three)g(cases.)45 b(The)28 b(\223longs\224)j (suf)n(fer)e(little,)i(e)o(xcept)e(in)g(the)g(pathological)j(case)d (where)120 656 y(the)o(y)d(could)i(get)e(stuck)h(w)o(aiting)g(behind)h (a)d(\223short\224)j(job)e(that)h(is)f(not)g(short)h(at)f(all.)36 b(In)26 b(this)h(case)f(the)g(penalty)i(to)120 769 y(the)c (\223long\224)h(jobs)f(is)g(more)f(signi\002cant,)i(b)n(ut)f(still)h (is)e(dominated)j(by)d(the)h(bene\002ts)h(to)e(the)h(\223short\224)h (jobs.)120 1015 y FB(Dif\002culty)e(of)h(analysis)h(and)d(new)g (analytic)j(appr)n(oaches)120 1189 y FC(The)33 b(abo)o(v)o(e)i(c)o (ycle)f(stealing)i(idea)f(is)e(certainly)k(not)d(ne)n(w)-6 b(.)59 b(Policies)35 b(lik)o(e)g Fx(CS-Immediate-D)o(is)o(pa)o(tc)o(h) 120 1302 y FC(and)25 b Fx(CS-Central-Queue)o FC(,)18 b(as)25 b(well)g(as)g(others)h(of)f(a)g(similar)g(\003a)n(v)n(or)l(,)i (ha)n(v)o(e)e(been)h(suggested)i(in)d(countless)120 1415 y(papers.)36 b(Ho)n(we)n(v)o(er)24 b(until)j(no)n(w)d(the)i(analysis)i (of)d(such)h(policies)h(has)f(eluded)h(researchers.)37 b(Observ)o(e)26 b(that)g(e)n(v)o(en)120 1528 y(for)19 b(simplest)h(instance)h(of)d(our)h(problem)h(\226)e(where)h(job)h(arri) n(v)n(als)f(are)g(Poisson,)i(short)f(jobs)f(are)g(dra)o(wn)g(i.i.d.)26 b(from)120 1641 y(one)h(e)o(xponential)j(distrib)n(ution)g(and)d(long)h (jobs)f(are)g(dra)o(wn)g(i.i.d.)37 b(from)27 b(another)i(e)o (xponential)g(distrib)n(ution)i(\226)120 1753 y(the)25 b(continuous-time)k(Mark)o(o)o(v)d(chain,)g(while)f(relati)n(v)o(ely)i (easy)e(to)g(describe,)i(is)e(mathematically)j(intractable.)120 1866 y(This)c(is)g(due)h(to)f(the)g(f)o(act)h(that)g(the)f(stochastic)j (process)f(gro)n(ws)e(in\002nitely)i(in)e(tw)o(o)g(dimensions)i(and)f (it)f(contains)120 1979 y(no)35 b(structure)i(that)f(can)f(be)g(e)o (xploited)j(in)c(order)i(to)f(obtain)i(an)e(e)o(xact)g(solution.)66 b(While)35 b(truncation)j(of)d(the)120 2092 y(Mark)o(o)o(v)h(chain)h (is)e(possible,)41 b(the)36 b(errors)h(that)f(are)f(introduced)k(by)d (ignoring)i(portions)f(of)f(the)g(state)g(space)120 2205 y(\(in\002nite)c(in)f(tw)o(o)g(dimensions\))j(can)d(be)g(quite)i (signi\002cant,)h(especially)g(at)d(higher)i(traf)n(\002c)e (intensities.)54 b(Thus)120 2318 y(truncation)26 b(is)e(neither)h(suf)n (\002ciently)g(accurate)h(nor)e(rob)n(ust)h(for)f(our)g(purposes.)261 2431 y(This)g(paper)h(pro)o(vides)h(the)f(\002rst)f(analysis)i(\(to)e (our)h(kno)n(wledge\))h(of)e(the)h Fx(CS-Immediate-D)o(is)o(pa)o(tc)o (h)120 2544 y FC(and)k Fx(CS-Central-Que)o(ue)21 b FC(policies.)45 b(In)28 b(both)h(cases,)h(the)e(analysis)j(is)d(approximate,)k(b)n(ut)c (can)h(be)f(made)120 2657 y(as)c(close)g(to)g(e)o(xact)g(as)g(desired.) 31 b(Our)23 b(analysis)j(assumes)e(a)g(Poisson)g(arri)n(v)n(al)h (process)h(for)d(short)i(and)f(long)h(jobs.)120 2770 y(F)o(or)i(both)i(algorithms,)i(the)e(service)h(requirements)h(of)d (the)g(short)h(and)g(long)g(jobs)g(are)f(assumed)i(to)e(be)g(dra)o(wn) 120 2883 y(i.i.d.)44 b(from)28 b(an)o(y)h(general)h(phase-type)i (distrib)n(ution.)47 b(Our)28 b(approaches)k(for)d(analyzing)i Fx(CS-Immediate-)120 2995 y(Dispatch)16 b FC(and)22 b Fx(CS-Central-Que)o(ue)13 b FC(are)21 b(v)o(ery)g(dif)n(ferent,)i(b)n (ut)f(the)o(y)f(do)g(share)h(one)f(common)g(element:)120 3108 y(b)n(usy)k(period)g(approximation.)261 3221 y(F)o(or)d Fx(CS-Immediate-Dis)o(pa)o(tc)o(h)p FC(,)16 b(we)22 b(decompose)k(the)d (stochastic)j(process)f(representing)i(the)d(sys-)120 3334 y(tem)e(into)h(tw)o(o)g(processes,)i(one)e(corresponding)k(to)22 b(the)h(short)h(host)f(and)g(one)g(corresponding)k(to)22 b(the)h(long)h(host.)120 3447 y(W)-7 b(e)26 b(solv)o(e)h(the)g (stochastic)i(process)f(corresponding)j(to)c(the)g(long)g(host)g(e)o (xactly)-6 b(.)39 b(W)-7 b(e)26 b(then)h(deri)n(v)o(e)h(the)f(impact) 120 3560 y(of)i(the)h(long)g(host)g(on)f(the)h(short)g(host)g(and)g (use)g(this)g(to)f(determine)i(the)e(appropriate)k(stochastic)f (process)f(for)120 3673 y(the)e(short)g(host,)h(which)f(we)f(then)h (solv)o(e.)44 b(The)28 b(only)h(approximation)j(lies)d(in)f(the)h (impact)g(of)f(the)h(long)g(host')-5 b(s)120 3786 y(b)n(usy)26 b(period)f(on)g(the)g(short)g(host)g(process.)33 b(This)25 b(approximation)j(can)c(be)h(made)f(as)h(precise)h(as)e(desired,)i (since)120 3899 y(the)e(long)g(host')-5 b(s)25 b(b)n(usy)g(period)g (can)f(be)f(estimated)i(up)f(to)f(an)o(y)h(number)g(of)g(moments.)29 b(In)23 b(this)h(paper)h(we)e(match)120 4012 y(three)h(moments)h(and)f (v)o(erify)g(via)g(simulation)h(that)g(this)f(is)f(suf)n(\002cient,)i (in)e(Section)h(6.)261 4125 y(F)o(or)g Fx(CS-Central-Queue)o FC(,)19 b(the)25 b(abo)o(v)o(e)h(technique)i(of)d(decomposing)j (stochastic)g(processes)g(and)e(de-)120 4237 y(ri)n(ving)i(the)g (impact)f(of)g(one)h(on)f(the)h(other)g(does)g(not)f(w)o(ork.)40 b(Here)27 b(we)f(appear)j(to)e(need)h(a)f(Mark)o(o)o(v)g(chain)i(that) 120 4350 y(is)h(in\002nite)i(in)f(tw)o(o)f(dimensions,)k(since)e(we)e (must)g(k)o(eep)i(track)g(of)e(both)i(the)f(number)g(of)g(short)g(jobs) h(and)f(the)120 4463 y(number)36 b(of)e(long)i(jobs)f(in)g(the)g (system.)63 b(In)35 b(f)o(act,)j(e)n(v)o(en)d(in)f(the)i(case)f(where)g (short)h(and)f(long)h(jobs)f(are)g(in-)120 4576 y(distinguishable,)h (the)30 b Fx(CS-Central-Que)o(ue)22 b FC(polic)o(y)31 b(becomes)g(an)e(M/G/2/FCFS)f(polic)o(y)-6 b(,)32 b(which)e(is)g(not) 120 4689 y(analytically)g(tractable.)41 b(Our)26 b(solution)j(is)e(to)g (instead)h(use)f(the)g(transitions)j(between)e(states)g(to)f(k)o(eep)h (track)f(of)120 4802 y(the)33 b(rele)n(v)n(ant)g(information)i (concerning)h(the)c(delay)h(of)g(long)g(jobs,)i(making)e(our)g(Mark)o (o)o(v)g(chain)g(in\002nite)g(in)120 4915 y(only)23 b(one)g(dimension.) 30 b(This)22 b(is)g(done)h(by)g(modeling)h(these)f(transitions)i(as)d (certain)i(types)f(of)g(b)n(usy)g(periods,)h(for)120 5028 y(which)h(we)g(can)g(deri)n(v)o(e)h(an)o(y)f(number)h(of)f (moments.)34 b(W)-7 b(e)24 b(again)i(match)f(the)g(\002rst)g(three)h (moments)g(of)f(the)g(b)n(usy)1897 5349 y(5)p eop %%Page: 6 8 6 7 bop 120 91 a FC(periods,)25 b(and)f(v)o(erify)h(that)f(this)g(is)f (suf)n(\002cient)i(via)f(simulation)h(\(in)f(Section)h(6.\))261 204 y(F)o(or)e(both)h(the)g(abo)o(v)o(e)g(c)o(ycle)g(stealing)i (algorithms)f(we)e(also)h(deri)n(v)o(e)h(stability)g(conditions)i(in)c (Section)i(5.)120 446 y FB(Outline)120 620 y FC(Section)32 b(2)f(presents)i(preliminary)h(notation.)54 b(The)30 b(analysis)k(of)d Fx(CS-Immediate-D)o(isp)o(at)o(ch)24 b FC(is)31 b(gi)n(v)o(en)120 733 y(in)e(Section)h(3)f(and)g(the)h (analysis)h(of)e Fx(CS-Central-Que)o(ue)22 b FC(is)29 b(gi)n(v)o(en)g(in)g(Section)h(4.)45 b(Section)30 b(5)f(presents)120 846 y(stability)j(criteria)g(for)f(both)g(c)o(ycle)f(stealing)j (algorithms.)50 b(Section)31 b(6)f(v)n(alidates)i(the)f(analysis)h(of)e (both)h(algo-)120 959 y(rithms)g(against)i(simulation)g(and)e(limiting) h(cases.)52 b(Finally)31 b(Section)h(7)f(sho)n(ws)g(the)g(results)h(of) f(the)g(analysis,)120 1072 y(assessing)g(the)d(impro)o(v)o(ement)h(of)f (c)o(ycle)h(stealing)h(o)o(v)o(er)e Fx(Dedicated)23 b FC(assignment,)31 b(while)e(also)f(comparing)120 1185 y(the)c(tw)o(o)f(c)o(ycle)h(stealing)i(algorithms)f(in)f(terms)g(of)f (their)h(bene\002t)h(to)e(short)i(jobs)f(and)g(penalty)h(to)f(long)g (jobs.)120 1473 y FG(2)119 b(Notation)120 1680 y FC(Throughout)35 b(we)d(assume)i(that)g(short)f(\(respecti)n(v)o(ely)-6 b(,)39 b(long\))34 b(jobs)f(arri)n(v)o(e)h(according)h(to)e(a)f (Poisson)i(process)120 1793 y(with)d(rate)h Fu(\025)532 1807 y Ft(S)614 1793 y FC(\(respecti)n(v)o(ely)-6 b(,)36 b Fu(\025)1182 1807 y Ft(L)1234 1793 y FC(\).)52 b(The)31 b(size,)j(a.k.a.)52 b(service)33 b(requirement,)i(of)d(short)g(jobs)g (\(respecti)n(v)o(ely)-6 b(,)120 1906 y(long)30 b(jobs\))h(is)e (denoted)j(by)e(the)g(random)g(v)n(ariable)h Fu(X)1887 1920 y Ft(S)1967 1906 y FC(\(respecti)n(v)o(ely)-6 b(,)34 b Fu(X)2555 1920 y Ft(L)2608 1906 y FC(\).)46 b(The)29 b Fu(i)2908 1873 y Ft(th)3008 1906 y FC(moment)g(of)h(the)g(size)120 2019 y(of)j(a)g(short)h(\(respecti)n(v)o(ely)-6 b(,)38 b(long\))c(job)g(is)f(therefore)i Fu(E)5 b Fs([)p Fu(X)2037 1986 y Ft(i)2030 2045 y(S)2082 2019 y Fs(])32 b FC(\(respecti)n(v)o (ely)-6 b(,)38 b Fu(E)5 b Fs([)p Fu(X)2835 1986 y Ft(i)2828 2045 y(L)2882 2019 y Fs(])p FC(\).)57 b(F)o(or)32 b(readability)-6 b(,)38 b(we)120 2132 y(will)31 b(usually)i(start)f(out)f(by)g(sho)n (wing)i(the)e(case)h(where)f(job)h(sizes)g(are)f(e)o(xponentially)k (distrib)n(uted,)h(and)c(will)120 2245 y(use)d Fu(\026)324 2259 y Ft(S)402 2245 y FC(\(respecti)n(v)o(ely)i Fu(\026)950 2259 y Ft(L)1002 2245 y FC(\))c(to)i(denote)g(the)g(service)h(rate)e (of)h(short)g(\(respecti)n(v)o(ely)-6 b(,)32 b(long\))d(jobs,)h(where)f Fu(\026)3565 2259 y Ft(S)3649 2245 y Fs(=)120 2358 y(1)p Fu(=E)5 b Fs([)p Fu(X)382 2372 y Ft(S)435 2358 y Fs(])24 b FC(and)h Fu(\026)694 2372 y Ft(L)774 2358 y Fs(=)i(1)p Fu(=E)5 b Fs([)p Fu(X)1134 2372 y Ft(L)1188 2358 y Fs(])p FC(.)33 b(W)-7 b(e)24 b(de\002ne)h Fu(\032)1705 2372 y Ft(S)1780 2358 y FC(\(respecti)n(v)o(ely)-6 b(,)28 b Fu(\032)2334 2372 y Ft(L)2386 2358 y FC(\))c(to)h(be)g(the)g(load)h (created)h(by)e(short)g(jobs)120 2471 y(\(respecti)n(v)o(ely)-6 b(,)39 b(long)34 b(jobs\),)j(where)d Fu(\032)1374 2485 y Ft(S)1469 2471 y Fs(=)43 b Fu(\025)1636 2485 y Ft(S)1715 2471 y Fr(\001)27 b Fu(E)5 b Fs([)p Fu(X)1939 2485 y Ft(S)1991 2471 y Fs(])33 b FC(and)h Fu(\032)2260 2485 y Ft(L)2356 2471 y Fs(=)44 b Fu(\025)2524 2485 y Ft(L)2604 2471 y Fr(\001)27 b Fu(E)5 b Fs([)p Fu(X)2828 2485 y Ft(L)2881 2471 y Fs(])p FC(.)59 b(W)-7 b(e)32 b(assume)j(that)f(the)120 2584 y(\002rst)24 b(three)i(moments)f(of)f(the)h(b)n(usy)h(periods)h (are)d(\002nite,)h(and)g(the)g(queues)h(are)f(stable.)33 b(W)-7 b(e)24 b(discuss)i(stability)h(in)120 2697 y(greater)e(depth)g (in)e(Section)i(5.)261 2809 y(The)d(Laplace)i(T)m(ransform)f Fu(L)1198 2824 y Ft(f)1243 2809 y Fs(\()p Fu(s)p Fs(\))f FC(of)h(a)f(non-ne)o(gati)n(v)o(e)j(Lebesgue)f(inte)o(grable)h (function)g Fu(f)10 b Fs(\()p Fu(t)p Fs(\))22 b FC(\(on)h(the)f(pos-) 120 2922 y(iti)n(v)o(e)i(real)g(axis\))g(is)g(de\002ned)g(as)1254 3130 y Fu(L)1316 3145 y Ft(f)1361 3130 y Fs(\()p Fu(s)p Fs(\))i(=)1571 3145 y Ft(dist)1718 3015 y Fq(Z)1801 3042 y Fp(1)1764 3204 y FE(0)1891 3130 y Fu(e)1933 3093 y Fp(\000)p Ft(st)2051 3130 y Fu(f)10 b Fs(\()p Fu(t)p Fs(\))p Fu(dt;)38 b(s)25 b Fr(\025)f Fs(0)p Fu(:)120 3362 y FC(The)f(Laplace)i(T)m(ransform)f(of)g(a)f(continuous)k(R.V)-12 b(.)22 b Fu(X)7 b FC(,)23 b(often)h(denoted)i(by)2553 3339 y Fs(~)2527 3362 y Fu(X)7 b Fs(\()p Fu(s)p Fs(\))23 b FC(refers)i(to)f(the)f(Laplace)i(trans-)120 3475 y(form)e Fu(L)381 3490 y Ft(f)427 3475 y Fs(\()p Fu(s)p Fs(\))p FC(,)f(of)i(its)g(pdf)f Fu(f)10 b Fs(\()p Fu(x)p Fs(\))p FC(,)23 b(in)g(which)h(case)g Fu(L)1738 3490 y Ft(f)1784 3475 y Fs(\()p Fu(s)p Fs(\))h(=)g Fu(E)5 b Fs([)p Fu(e)2157 3442 y Fp(\000)p Ft(sX)2313 3475 y Fs(])p FC(.)120 3764 y FG(3)119 b(Cycle)31 b(Stealing)f(under)i(Immediate)d(Dispatch)120 3971 y FC(The)36 b Fx(CS-Immediate-Di)o(sp)o(at)o(ch)29 b FC(algorithm)38 b(is)e(sho)n(wn)h(in)f(Figure)h(1.)67 b(Under)37 b Fx(CS-Immediate-)120 4084 y(Dispatch)p FC(,)23 b(all)28 b(long)g(jobs)g(are)f(immediately)i(dispatched)i(to)c(the)h (long)g(host)g(upon)g(arri)n(v)n(al.)41 b(When)27 b(a)g(short)120 4197 y(job)k(arri)n(v)o(es,)h(it)e(is)g(dispatched)j(to)e(the)f(long)h (host)g(if)f(that)h(host)g(is)f(idle.)49 b(Otherwise,)33 b(it)c(is)i(dispatched)i(to)d(the)120 4310 y(short)25 b(host.)261 4423 y(Our)20 b(analytic)j(approach)f(in)l(v)n(olv)o(es)h (a)d(three)h(step)g(process.)30 b(The)20 b(\002rst)g(step)h(is)f(to)h (deri)n(v)o(e)g(the)f(mean)h(response)120 4535 y(times)g(for)g(the)g (long)h(jobs)g(only)-6 b(.)29 b(W)-7 b(e)20 b(do)h(this)g(in)g(tw)o(o)g (dif)n(ferent)i(w)o(ays,)e(\002rst)f(using)i(Matrix)g(Geometric)g (methods)120 4648 y(and)i(then)g(using)h(virtual)g(w)o(aiting)g(time)e (analysis.)31 b(W)-7 b(e)22 b(con\002rm)i(that)g(both)g(methods)h (yield)g(the)f(same)f(result.)261 4761 y(Figure)36 b(3\(a\))g(depicts)h (a)d(Mark)o(o)o(v)i(chain)h(describing)h(the)d(long)h(host,)j(under)d (the)g(assumption)h(that)f(job)120 4874 y(sizes)29 b(are)f(e)o (xponentially-distrib)o(ut)q(ed.)47 b(Each)28 b(state)g(represents)j (the)d(number)g(of)g(long)h(jobs)f(and)g(the)g(number)120 4987 y(of)e(short)h(jobs.)38 b(Figure)27 b(3\(b\))f(is)g(the)h(same)f (chain)h(generalized)j(to)c(the)g(case)h(of)f(phase-type)k(job)c(sizes) h(\(a)f(tw)o(o-)120 5100 y(phase)c(Coxian)f(is)f(sho)n(wn\).)28 b(Observ)o(e)21 b(that)g(the)g(number)g(of)g(short)g(jobs)g(at)g(the)f (long)h(host)h(is)e(either)h(0)f(or)h(1.)27 b(Long)1897 5349 y(6)p eop %%Page: 7 9 7 8 bop 570 0 a 21313290 5754582 0 0 50323046 14011514 startTexFig 570 0 a %%BeginDocument: ../figures/dispatch_large_exp.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: dispatch_large_exp.eps %%Creator: fig2dev Version 3.2 Patchlevel 3d %%CreationDate: Tue Apr 2 09:29:23 2002 %%For: harchol@mor.sp.cs.cmu.edu (Mor Harchol-Balter) %%BoundingBox: 0 0 765 213 %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def F2psDictbeginF2psDict begin F2psDictbeginF2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 213 moveto 0 0 lineto 765 0 lineto 765 213 lineto closepath clip newpath -18.0 257.6 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def F2psBegin10setmiterlimit0.060000.06000scF2psBegin 10 setmiterlimit 0.06000 0.06000 sc % % Fig objects follow % 15.000 slw % Ellipse n 12300 1575 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12600 1575 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12900 1575 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12375 3975 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12675 3975 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12975 3975 54 54 0 360 DrawEllipse gs col0 s gr /Symbol ff 300.00 scf sf 2775 1032 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 2963 1125 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 6000 1032 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 6188 1125 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 9375 957 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 9563 1050 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 2700 2214 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 300.00 scf sf 2888 2400 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 6000 2214 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 300.00 scf sf 6188 2400 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 9375 2289 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 300.00 scf sf 9563 2475 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 2700 3432 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 2888 3525 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 6000 3432 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 6188 3525 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 300 2664 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 300.00 scf sf 489 2850 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 300.00 scf sf 1950 2745 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 2130 2925 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 300.00 scf sf 3675 2739 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 300.00 scf sf 3864 2925 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 300.00 scf sf 7050 2739 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 300.00 scf sf 7239 2925 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 300.00 scf sf 10275 2739 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 300.00 scf sf 10464 2925 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 300.00 scf sf 9375 3432 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 9563 3525 m gs 1 -1 sc (L) col0 sh gr % Ellipse n 4725 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 8025 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 8025 3975 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 4725 3975 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 1350 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 1425 3975 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 11325 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 11306 3979 750 300 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 3958 1559 m 4017 1455 l 3767 1312 l 3946 1484 l 3707 1417 l cp eoclip n 2175 1425 m 2176 1424 l 2178 1423 l 2182 1421 l 2189 1418 l 2198 1413 l 2210 1407 l 2225 1399 l 2243 1391 l 2263 1381 l 2286 1370 l 2312 1358 l 2339 1345 l 2369 1333 l 2400 1320 l 2433 1307 l 2467 1294 l 2502 1281 l 2538 1269 l 2577 1258 l 2616 1247 l 2658 1237 l 2701 1228 l 2747 1219 l 2796 1212 l 2847 1206 l 2900 1202 l 2957 1199 l 3015 1199 l 3075 1200 l 3135 1204 l 3193 1209 l 3250 1217 l 3303 1225 l 3354 1236 l 3403 1247 l 3449 1259 l 3492 1272 l 3534 1285 l 3573 1299 l 3612 1314 l 3648 1329 l 3683 1344 l 3717 1360 l 3750 1376 l 3781 1391 l 3811 1407 l 3838 1421 l 3864 1435 l 3887 1448 l 3907 1460 l 3925 1470 l 3940 1479 l 3952 1486 l 3961 1492 l 3975 1500 l gs col0 s gr gr % arrowhead 0 slj n 3707 1417 m 3946 1484 l 3767 1312 l col0 s % Polyline 2 slj gs clippath 2200 1593 m 2126 1687 l 2352 1865 l 2201 1670 l 2426 1771 l cp eoclip n 3975 1650 m 3974 1651 l 3971 1652 l 3966 1655 l 3959 1659 l 3948 1665 l 3935 1672 l 3917 1682 l 3897 1692 l 3873 1705 l 3847 1719 l 3817 1733 l 3786 1749 l 3752 1765 l 3717 1781 l 3680 1798 l 3642 1814 l 3603 1830 l 3563 1845 l 3521 1860 l 3478 1875 l 3433 1888 l 3386 1901 l 3337 1912 l 3286 1923 l 3233 1932 l 3177 1939 l 3119 1945 l 3060 1949 l 3000 1950 l 2936 1949 l 2875 1944 l 2817 1938 l 2762 1929 l 2711 1919 l 2663 1907 l 2618 1895 l 2576 1881 l 2537 1866 l 2499 1850 l 2464 1833 l 2430 1816 l 2398 1799 l 2367 1781 l 2338 1764 l 2311 1747 l 2286 1730 l 2263 1715 l 2243 1700 l 2225 1688 l 2210 1677 l 2198 1668 l 2189 1661 l 2175 1650 l gs col0 s gr gr % arrowhead 0 slj n 2426 1771 m 2201 1670 l 2352 1865 l col0 s % Polyline 2 slj gs clippath 7183 1559 m 7242 1455 l 6992 1312 l 7171 1484 l 6932 1417 l cp eoclip n 5400 1425 m 5401 1424 l 5403 1423 l 5407 1421 l 5414 1418 l 5423 1413 l 5435 1407 l 5450 1399 l 5468 1391 l 5488 1381 l 5511 1370 l 5537 1358 l 5564 1345 l 5594 1333 l 5625 1320 l 5658 1307 l 5692 1294 l 5727 1281 l 5763 1269 l 5802 1258 l 5841 1247 l 5883 1237 l 5926 1228 l 5972 1219 l 6021 1212 l 6072 1206 l 6125 1202 l 6182 1199 l 6240 1199 l 6300 1200 l 6360 1204 l 6418 1209 l 6475 1217 l 6528 1225 l 6579 1236 l 6628 1247 l 6674 1259 l 6717 1272 l 6759 1285 l 6798 1299 l 6837 1314 l 6873 1329 l 6908 1344 l 6942 1360 l 6975 1376 l 7006 1391 l 7036 1407 l 7063 1421 l 7089 1435 l 7112 1448 l 7132 1460 l 7150 1470 l 7165 1479 l 7177 1486 l 7186 1492 l 7200 1500 l gs col0 s gr gr % arrowhead 0 slj n 6932 1417 m 7171 1484 l 6992 1312 l col0 s % Polyline 2 slj gs clippath 10558 1484 m 10617 1380 l 10367 1237 l 10546 1409 l 10307 1342 l cp eoclip n 8775 1350 m 8776 1349 l 8778 1348 l 8782 1346 l 8789 1343 l 8798 1338 l 8810 1332 l 8825 1324 l 8843 1316 l 8863 1306 l 8886 1295 l 8912 1283 l 8939 1270 l 8969 1258 l 9000 1245 l 9033 1232 l 9067 1219 l 9102 1206 l 9138 1194 l 9177 1183 l 9216 1172 l 9258 1162 l 9301 1153 l 9347 1144 l 9396 1137 l 9447 1131 l 9500 1127 l 9557 1124 l 9615 1124 l 9675 1125 l 9735 1129 l 9793 1134 l 9850 1142 l 9903 1150 l 9954 1161 l 10003 1172 l 10049 1184 l 10092 1197 l 10134 1210 l 10173 1224 l 10212 1239 l 10248 1254 l 10283 1269 l 10317 1285 l 10350 1301 l 10381 1316 l 10411 1332 l 10438 1346 l 10464 1360 l 10487 1373 l 10507 1385 l 10525 1395 l 10540 1404 l 10552 1411 l 10561 1417 l 10575 1425 l gs col0 s gr gr % arrowhead 0 slj n 10307 1342 m 10546 1409 l 10367 1237 l col0 s % Polyline 2 slj gs clippath 3958 3959 m 4017 3855 l 3767 3712 l 3946 3884 l 3707 3817 l cp eoclip n 2175 3825 m 2176 3824 l 2178 3823 l 2182 3821 l 2189 3818 l 2198 3813 l 2210 3807 l 2225 3799 l 2243 3791 l 2263 3781 l 2286 3770 l 2312 3758 l 2339 3745 l 2369 3733 l 2400 3720 l 2433 3707 l 2467 3694 l 2502 3681 l 2538 3669 l 2577 3658 l 2616 3647 l 2658 3637 l 2701 3628 l 2747 3619 l 2796 3612 l 2847 3606 l 2900 3602 l 2957 3599 l 3015 3599 l 3075 3600 l 3135 3604 l 3193 3609 l 3250 3617 l 3303 3625 l 3354 3636 l 3403 3647 l 3449 3659 l 3492 3672 l 3534 3685 l 3573 3699 l 3612 3714 l 3648 3729 l 3683 3744 l 3717 3760 l 3750 3776 l 3781 3791 l 3811 3807 l 3838 3821 l 3864 3835 l 3887 3848 l 3907 3860 l 3925 3870 l 3940 3879 l 3952 3886 l 3961 3892 l 3975 3900 l gs col0 s gr gr % arrowhead 0 slj n 3707 3817 m 3946 3884 l 3767 3712 l col0 s % Polyline 2 slj gs clippath 7183 3959 m 7242 3855 l 6992 3712 l 7171 3884 l 6932 3817 l cp eoclip n 5400 3825 m 5401 3824 l 5403 3823 l 5407 3821 l 5414 3818 l 5423 3813 l 5435 3807 l 5450 3799 l 5468 3791 l 5488 3781 l 5511 3770 l 5537 3758 l 5564 3745 l 5594 3733 l 5625 3720 l 5658 3707 l 5692 3694 l 5727 3681 l 5763 3669 l 5802 3658 l 5841 3647 l 5883 3637 l 5926 3628 l 5972 3619 l 6021 3612 l 6072 3606 l 6125 3602 l 6182 3599 l 6240 3599 l 6300 3600 l 6360 3604 l 6418 3609 l 6475 3617 l 6528 3625 l 6579 3636 l 6628 3647 l 6674 3659 l 6717 3672 l 6759 3685 l 6798 3699 l 6837 3714 l 6873 3729 l 6908 3744 l 6942 3760 l 6975 3776 l 7006 3791 l 7036 3807 l 7063 3821 l 7089 3835 l 7112 3848 l 7132 3860 l 7150 3870 l 7165 3879 l 7177 3886 l 7186 3892 l 7200 3900 l gs col0 s gr gr % arrowhead 0 slj n 6932 3817 m 7171 3884 l 6992 3712 l col0 s % Polyline 2 slj gs clippath 5500 1593 m 5426 1687 l 5652 1865 l 5501 1670 l 5726 1771 l cp eoclip n 7275 1650 m 7274 1651 l 7271 1652 l 7266 1655 l 7259 1659 l 7248 1665 l 7235 1672 l 7217 1682 l 7197 1692 l 7173 1705 l 7147 1719 l 7117 1733 l 7086 1749 l 7052 1765 l 7017 1781 l 6980 1798 l 6942 1814 l 6903 1830 l 6863 1845 l 6821 1860 l 6778 1875 l 6733 1888 l 6686 1901 l 6637 1912 l 6586 1923 l 6533 1932 l 6477 1939 l 6419 1945 l 6360 1949 l 6300 1950 l 6236 1949 l 6175 1944 l 6117 1938 l 6062 1929 l 6011 1919 l 5963 1907 l 5918 1895 l 5876 1881 l 5837 1866 l 5799 1850 l 5764 1833 l 5730 1816 l 5698 1799 l 5667 1781 l 5638 1764 l 5611 1747 l 5586 1730 l 5563 1715 l 5543 1700 l 5525 1688 l 5510 1677 l 5498 1668 l 5489 1661 l 5475 1650 l gs col0 s gr gr % arrowhead 0 slj n 5726 1771 m 5501 1670 l 5652 1865 l col0 s % Polyline 2 slj gs clippath 8800 1593 m 8726 1687 l 8952 1865 l 8801 1670 l 9026 1771 l cp eoclip n 10575 1650 m 10574 1651 l 10571 1652 l 10566 1655 l 10559 1659 l 10548 1665 l 10535 1672 l 10517 1682 l 10497 1692 l 10473 1705 l 10447 1719 l 10417 1733 l 10386 1749 l 10352 1765 l 10317 1781 l 10280 1798 l 10242 1814 l 10203 1830 l 10163 1845 l 10121 1860 l 10078 1875 l 10033 1888 l 9986 1901 l 9937 1912 l 9886 1923 l 9833 1932 l 9777 1939 l 9719 1945 l 9660 1949 l 9600 1950 l 9536 1949 l 9475 1944 l 9417 1938 l 9362 1929 l 9311 1919 l 9263 1907 l 9218 1895 l 9176 1881 l 9137 1866 l 9099 1850 l 9064 1833 l 9030 1816 l 8998 1799 l 8967 1781 l 8938 1764 l 8911 1747 l 8886 1730 l 8863 1715 l 8843 1700 l 8825 1688 l 8810 1677 l 8798 1668 l 8789 1661 l 8775 1650 l gs col0 s gr gr % arrowhead 0 slj n 9026 1771 m 8801 1670 l 8952 1865 l col0 s % Polyline 2 slj gs clippath 1516 3655 m 1617 3720 l 1773 3477 l 1593 3647 l 1672 3412 l cp eoclip n 1575 1875 m 1576 1876 l 1577 1878 l 1580 1882 l 1584 1889 l 1590 1898 l 1597 1910 l 1607 1925 l 1617 1943 l 1630 1963 l 1644 1986 l 1658 2012 l 1674 2039 l 1690 2069 l 1706 2100 l 1723 2133 l 1739 2167 l 1755 2202 l 1770 2238 l 1785 2277 l 1800 2316 l 1813 2358 l 1826 2401 l 1837 2447 l 1848 2496 l 1857 2547 l 1864 2600 l 1870 2657 l 1874 2715 l 1875 2775 l 1874 2835 l 1870 2893 l 1864 2950 l 1857 3003 l 1848 3054 l 1837 3103 l 1826 3149 l 1813 3192 l 1800 3234 l 1785 3273 l 1770 3312 l 1755 3348 l 1739 3383 l 1723 3417 l 1706 3450 l 1690 3481 l 1674 3511 l 1658 3538 l 1644 3564 l 1630 3587 l 1617 3607 l 1607 3625 l 1597 3640 l 1590 3652 l 1584 3661 l 1575 3675 l gs col0 s gr gr % arrowhead 0 slj n 1672 3412 m 1593 3647 l 1773 3477 l col0 s % Polyline 2 slj gs clippath 1106 1900 m 1012 1826 l 834 2052 l 1030 1901 l 928 2126 l cp eoclip n 1125 3675 m 1124 3674 l 1123 3672 l 1120 3668 l 1116 3662 l 1110 3653 l 1103 3641 l 1093 3626 l 1082 3609 l 1069 3588 l 1055 3565 l 1039 3540 l 1022 3512 l 1005 3482 l 986 3450 l 968 3417 l 949 3383 l 931 3347 l 913 3311 l 895 3273 l 877 3234 l 860 3194 l 844 3152 l 829 3110 l 814 3065 l 801 3018 l 788 2970 l 777 2919 l 767 2867 l 760 2812 l 754 2756 l 750 2700 l 749 2636 l 751 2575 l 756 2517 l 763 2462 l 772 2411 l 783 2363 l 796 2318 l 810 2276 l 825 2237 l 841 2199 l 858 2164 l 875 2130 l 893 2098 l 912 2067 l 930 2038 l 948 2011 l 965 1986 l 982 1963 l 997 1943 l 1010 1925 l 1022 1910 l 1031 1898 l 1039 1889 l 1050 1875 l gs col0 s gr gr % arrowhead 0 slj n 928 2126 m 1030 1901 l 834 2052 l col0 s % Polyline 2 slj gs clippath 4411 1898 m 4317 1824 l 4139 2050 l 4335 1899 l 4233 2124 l cp eoclip n 4430 3673 m 4429 3672 l 4428 3670 l 4425 3666 l 4421 3660 l 4415 3651 l 4408 3639 l 4398 3624 l 4387 3607 l 4374 3586 l 4360 3563 l 4344 3538 l 4327 3510 l 4310 3480 l 4291 3448 l 4273 3415 l 4254 3381 l 4236 3345 l 4218 3309 l 4200 3271 l 4182 3232 l 4165 3192 l 4149 3150 l 4134 3108 l 4119 3063 l 4106 3016 l 4093 2968 l 4082 2917 l 4072 2865 l 4065 2810 l 4059 2754 l 4055 2698 l 4054 2634 l 4056 2573 l 4061 2515 l 4068 2460 l 4077 2409 l 4088 2361 l 4101 2316 l 4115 2274 l 4130 2235 l 4146 2197 l 4163 2162 l 4180 2128 l 4198 2096 l 4217 2065 l 4235 2036 l 4253 2009 l 4270 1984 l 4287 1961 l 4302 1941 l 4315 1923 l 4327 1908 l 4336 1896 l 4344 1887 l 4355 1873 l gs col0 s gr gr % arrowhead 0 slj n 4233 2124 m 4335 1899 l 4139 2050 l col0 s % Polyline 2 slj gs clippath 7861 1898 m 7767 1824 l 7589 2050 l 7785 1899 l 7683 2124 l cp eoclip n 7880 3673 m 7879 3672 l 7878 3670 l 7875 3666 l 7871 3660 l 7865 3651 l 7858 3639 l 7848 3624 l 7837 3607 l 7824 3586 l 7810 3563 l 7794 3538 l 7777 3510 l 7760 3480 l 7741 3448 l 7723 3415 l 7704 3381 l 7686 3345 l 7668 3309 l 7650 3271 l 7632 3232 l 7615 3192 l 7599 3150 l 7584 3108 l 7569 3063 l 7556 3016 l 7543 2968 l 7532 2917 l 7522 2865 l 7515 2810 l 7509 2754 l 7505 2698 l 7504 2634 l 7506 2573 l 7511 2515 l 7518 2460 l 7527 2409 l 7538 2361 l 7551 2316 l 7565 2274 l 7580 2235 l 7596 2197 l 7613 2162 l 7630 2128 l 7648 2096 l 7667 2065 l 7685 2036 l 7703 2009 l 7720 1984 l 7737 1961 l 7752 1941 l 7765 1923 l 7777 1908 l 7786 1896 l 7794 1887 l 7805 1873 l gs col0 s gr gr % arrowhead 0 slj n 7683 2124 m 7785 1899 l 7589 2050 l col0 s % Polyline 2 slj gs clippath 11086 1898 m 10992 1824 l 10814 2050 l 11010 1899 l 10908 2124 l cp eoclip n 11105 3673 m 11104 3672 l 11103 3670 l 11100 3666 l 11096 3660 l 11090 3651 l 11083 3639 l 11073 3624 l 11062 3607 l 11049 3586 l 11035 3563 l 11019 3538 l 11002 3510 l 10985 3480 l 10966 3448 l 10948 3415 l 10929 3381 l 10911 3345 l 10893 3309 l 10875 3271 l 10857 3232 l 10840 3192 l 10824 3150 l 10809 3108 l 10794 3063 l 10781 3016 l 10768 2968 l 10757 2917 l 10747 2865 l 10740 2810 l 10734 2754 l 10730 2698 l 10729 2634 l 10731 2573 l 10736 2515 l 10743 2460 l 10752 2409 l 10763 2361 l 10776 2316 l 10790 2274 l 10805 2235 l 10821 2197 l 10838 2162 l 10855 2128 l 10873 2096 l 10892 2065 l 10910 2036 l 10928 2009 l 10945 1984 l 10962 1961 l 10977 1941 l 10990 1923 l 11002 1908 l 11011 1896 l 11019 1887 l 11030 1873 l gs col0 s gr gr % arrowhead 0 slj n 10908 2124 m 11010 1899 l 10814 2050 l col0 s % Polyline 2 slj gs clippath 10557 3978 m 10616 3874 l 10366 3731 l 10545 3903 l 10306 3836 l cp eoclip n 8774 3844 m 8775 3843 l 8777 3842 l 8781 3840 l 8788 3837 l 8797 3832 l 8809 3826 l 8824 3818 l 8842 3810 l 8862 3800 l 8885 3789 l 8911 3777 l 8938 3764 l 8968 3752 l 8999 3739 l 9032 3726 l 9066 3713 l 9101 3700 l 9137 3688 l 9176 3677 l 9215 3666 l 9257 3656 l 9300 3647 l 9346 3638 l 9395 3631 l 9446 3625 l 9499 3621 l 9556 3618 l 9614 3618 l 9674 3619 l 9734 3623 l 9792 3628 l 9849 3636 l 9902 3644 l 9953 3655 l 10002 3666 l 10048 3678 l 10091 3691 l 10133 3704 l 10172 3718 l 10211 3733 l 10247 3748 l 10282 3763 l 10316 3779 l 10349 3795 l 10380 3810 l 10410 3826 l 10437 3840 l 10463 3854 l 10486 3867 l 10506 3879 l 10524 3889 l 10539 3898 l 10551 3905 l 10560 3911 l 10574 3919 l gs col0 s gr gr % arrowhead 0 slj n 10306 3836 m 10545 3903 l 10366 3731 l col0 s /Times-Roman ff 315.00 scf sf 975 1725 m gs 1 -1 sc (0L,0S) col0 sh gr /Times-Roman ff 315.00 scf sf 4350 1725 m gs 1 -1 sc (1L,0S) col0 sh gr /Times-Roman ff 315.00 scf sf 7650 1725 m gs 1 -1 sc (2L,0S) col0 sh gr /Times-Roman ff 315.00 scf sf 1050 4125 m gs 1 -1 sc (0L,1S) col0 sh gr /Times-Roman ff 315.00 scf sf 4350 4125 m gs 1 -1 sc (1L,1S) col0 sh gr /Times-Roman ff 315.00 scf sf 7650 4125 m gs 1 -1 sc (2L,1S) col0 sh gr /Times-Roman ff 315.00 scf sf 10950 1725 m gs 1 -1 sc (3L,0S) col0 sh gr /Times-Roman ff 315.00 scf sf 10950 4125 m gs 1 -1 sc (3L,1S) col0 sh gr F2psBegin10setmiterlimit0.060000.06000scF2psEnd rs %%EndDocument endTexFig 1862 842 a Fo(\(a\))570 867 y 21313290 6820251 0 0 50059919 16182312 startTexFig 570 867 a %%BeginDocument: ../figures/dispatch_large_gen.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: dispatch_large_gen.eps %%Creator: fig2dev Version 3.2 Patchlevel 3d %%CreationDate: Tue Apr 2 10:07:52 2002 %%For: harchol@mor.sp.cs.cmu.edu (Mor Harchol-Balter) %%BoundingBox: 0 0 761 246 %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def F2psDictbeginF2psDict begin F2psDictbeginF2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 246 moveto 0 0 lineto 761 0 lineto 761 246 lineto closepath clip newpath -22.5 257.3 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def F2psBegin10setmiterlimit0.060000.06000scF2psBegin 10 setmiterlimit 0.06000 0.06000 sc % % Fig objects follow % 15.000 slw % Ellipse n 12300 1575 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12600 1575 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12900 1575 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12375 3975 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12675 3975 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12975 3975 54 54 0 360 DrawEllipse gs col0 s gr /Symbol ff 300.00 scf sf 2775 1032 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 2963 1125 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 6000 1032 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 6188 1125 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 9375 957 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 9563 1050 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 2700 3432 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 2888 3525 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 6000 3432 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 6188 3525 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 9375 3432 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 9563 3525 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 1875 2445 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 2055 2625 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 300.00 scf sf 4575 582 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 4763 675 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 7800 582 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 7988 675 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 6150 2607 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 6338 2700 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 9375 2607 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 9563 2700 m gs 1 -1 sc (L) col0 sh gr % Ellipse n 8025 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 8025 3975 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 4725 3975 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 1425 3975 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 11325 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 11325 3975 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 4761 1584 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 1275 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 900 2761 136 136 0 360 DrawEllipse gs col0 s gr % Ellipse n 6375 1837 136 136 0 360 DrawEllipse gs col0 s gr % Ellipse n 4275 2761 136 136 0 360 DrawEllipse gs col0 s gr % Ellipse n 7425 2761 136 136 0 360 DrawEllipse gs col0 s gr % Ellipse n 10650 2761 136 136 0 360 DrawEllipse gs col0 s gr % Ellipse n 9600 1762 136 136 0 360 DrawEllipse gs col0 s gr % Ellipse n 3000 1837 136 136 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 7183 1559 m 7242 1455 l 6992 1312 l 7171 1484 l 6932 1417 l cp eoclip n 5400 1425 m 5401 1424 l 5403 1423 l 5407 1421 l 5414 1418 l 5423 1413 l 5435 1407 l 5450 1399 l 5468 1391 l 5488 1381 l 5511 1370 l 5537 1358 l 5564 1345 l 5594 1333 l 5625 1320 l 5658 1307 l 5692 1294 l 5727 1281 l 5763 1269 l 5802 1258 l 5841 1247 l 5883 1237 l 5926 1228 l 5972 1219 l 6021 1212 l 6072 1206 l 6125 1202 l 6182 1199 l 6240 1199 l 6300 1200 l 6360 1204 l 6418 1209 l 6475 1217 l 6528 1225 l 6579 1236 l 6628 1247 l 6674 1259 l 6717 1272 l 6759 1285 l 6798 1299 l 6837 1314 l 6873 1329 l 6908 1344 l 6942 1360 l 6975 1376 l 7006 1391 l 7036 1407 l 7063 1421 l 7089 1435 l 7112 1448 l 7132 1460 l 7150 1470 l 7165 1479 l 7177 1486 l 7186 1492 l 7200 1500 l gs col0 s gr gr % arrowhead 0 slj n 6932 1417 m 7171 1484 l 6992 1312 l col0 s % Polyline 2 slj gs clippath 10558 1484 m 10617 1380 l 10367 1237 l 10546 1409 l 10307 1342 l cp eoclip n 8775 1350 m 8776 1349 l 8778 1348 l 8782 1346 l 8789 1343 l 8798 1338 l 8810 1332 l 8825 1324 l 8843 1316 l 8863 1306 l 8886 1295 l 8912 1283 l 8939 1270 l 8969 1258 l 9000 1245 l 9033 1232 l 9067 1219 l 9102 1206 l 9138 1194 l 9177 1183 l 9216 1172 l 9258 1162 l 9301 1153 l 9347 1144 l 9396 1137 l 9447 1131 l 9500 1127 l 9557 1124 l 9615 1124 l 9675 1125 l 9735 1129 l 9793 1134 l 9850 1142 l 9903 1150 l 9954 1161 l 10003 1172 l 10049 1184 l 10092 1197 l 10134 1210 l 10173 1224 l 10212 1239 l 10248 1254 l 10283 1269 l 10317 1285 l 10350 1301 l 10381 1316 l 10411 1332 l 10438 1346 l 10464 1360 l 10487 1373 l 10507 1385 l 10525 1395 l 10540 1404 l 10552 1411 l 10561 1417 l 10575 1425 l gs col0 s gr gr % arrowhead 0 slj n 10307 1342 m 10546 1409 l 10367 1237 l col0 s % Polyline 2 slj gs clippath 3958 3959 m 4017 3855 l 3767 3712 l 3946 3884 l 3707 3817 l cp eoclip n 2175 3825 m 2176 3824 l 2178 3823 l 2182 3821 l 2189 3818 l 2198 3813 l 2210 3807 l 2225 3799 l 2243 3791 l 2263 3781 l 2286 3770 l 2312 3758 l 2339 3745 l 2369 3733 l 2400 3720 l 2433 3707 l 2467 3694 l 2502 3681 l 2538 3669 l 2577 3658 l 2616 3647 l 2658 3637 l 2701 3628 l 2747 3619 l 2796 3612 l 2847 3606 l 2900 3602 l 2957 3599 l 3015 3599 l 3075 3600 l 3135 3604 l 3193 3609 l 3250 3617 l 3303 3625 l 3354 3636 l 3403 3647 l 3449 3659 l 3492 3672 l 3534 3685 l 3573 3699 l 3612 3714 l 3648 3729 l 3683 3744 l 3717 3760 l 3750 3776 l 3781 3791 l 3811 3807 l 3838 3821 l 3864 3835 l 3887 3848 l 3907 3860 l 3925 3870 l 3940 3879 l 3952 3886 l 3961 3892 l 3975 3900 l gs col0 s gr gr % arrowhead 0 slj n 3707 3817 m 3946 3884 l 3767 3712 l col0 s % Polyline 2 slj gs clippath 7183 3959 m 7242 3855 l 6992 3712 l 7171 3884 l 6932 3817 l cp eoclip n 5400 3825 m 5401 3824 l 5403 3823 l 5407 3821 l 5414 3818 l 5423 3813 l 5435 3807 l 5450 3799 l 5468 3791 l 5488 3781 l 5511 3770 l 5537 3758 l 5564 3745 l 5594 3733 l 5625 3720 l 5658 3707 l 5692 3694 l 5727 3681 l 5763 3669 l 5802 3658 l 5841 3647 l 5883 3637 l 5926 3628 l 5972 3619 l 6021 3612 l 6072 3606 l 6125 3602 l 6182 3599 l 6240 3599 l 6300 3600 l 6360 3604 l 6418 3609 l 6475 3617 l 6528 3625 l 6579 3636 l 6628 3647 l 6674 3659 l 6717 3672 l 6759 3685 l 6798 3699 l 6837 3714 l 6873 3729 l 6908 3744 l 6942 3760 l 6975 3776 l 7006 3791 l 7036 3807 l 7063 3821 l 7089 3835 l 7112 3848 l 7132 3860 l 7150 3870 l 7165 3879 l 7177 3886 l 7186 3892 l 7200 3900 l gs col0 s gr gr % arrowhead 0 slj n 6932 3817 m 7171 3884 l 6992 3712 l col0 s % Polyline 2 slj gs clippath 1516 3655 m 1617 3720 l 1773 3477 l 1593 3647 l 1672 3412 l cp eoclip n 1575 1875 m 1576 1876 l 1577 1878 l 1580 1882 l 1584 1889 l 1590 1898 l 1597 1910 l 1607 1925 l 1617 1943 l 1630 1963 l 1644 1986 l 1658 2012 l 1674 2039 l 1690 2069 l 1706 2100 l 1723 2133 l 1739 2167 l 1755 2202 l 1770 2238 l 1785 2277 l 1800 2316 l 1813 2358 l 1826 2401 l 1837 2447 l 1848 2496 l 1857 2547 l 1864 2600 l 1870 2657 l 1874 2715 l 1875 2775 l 1874 2835 l 1870 2893 l 1864 2950 l 1857 3003 l 1848 3054 l 1837 3103 l 1826 3149 l 1813 3192 l 1800 3234 l 1785 3273 l 1770 3312 l 1755 3348 l 1739 3383 l 1723 3417 l 1706 3450 l 1690 3481 l 1674 3511 l 1658 3538 l 1644 3564 l 1630 3587 l 1617 3607 l 1607 3625 l 1597 3640 l 1590 3652 l 1584 3661 l 1575 3675 l gs col0 s gr gr % arrowhead 0 slj n 1672 3412 m 1593 3647 l 1773 3477 l col0 s % Polyline 2 slj gs clippath 10557 3978 m 10616 3874 l 10366 3731 l 10545 3903 l 10306 3836 l cp eoclip n 8774 3844 m 8775 3843 l 8777 3842 l 8781 3840 l 8788 3837 l 8797 3832 l 8809 3826 l 8824 3818 l 8842 3810 l 8862 3800 l 8885 3789 l 8911 3777 l 8938 3764 l 8968 3752 l 8999 3739 l 9032 3726 l 9066 3713 l 9101 3700 l 9137 3688 l 9176 3677 l 9215 3666 l 9257 3656 l 9300 3647 l 9346 3638 l 9395 3631 l 9446 3625 l 9499 3621 l 9556 3618 l 9614 3618 l 9674 3619 l 9734 3623 l 9792 3628 l 9849 3636 l 9902 3644 l 9953 3655 l 10002 3666 l 10048 3678 l 10091 3691 l 10133 3704 l 10172 3718 l 10211 3733 l 10247 3748 l 10282 3763 l 10316 3779 l 10349 3795 l 10380 3810 l 10410 3826 l 10437 3840 l 10463 3854 l 10486 3867 l 10506 3879 l 10524 3889 l 10539 3898 l 10551 3905 l 10560 3911 l 10574 3919 l gs col0 s gr gr % arrowhead 0 slj n 10306 3836 m 10545 3903 l 10366 3731 l col0 s % Polyline 2 slj gs clippath 3958 1559 m 4017 1455 l 3767 1312 l 3946 1484 l 3707 1417 l cp eoclip n 2175 1425 m 2176 1424 l 2178 1423 l 2182 1421 l 2189 1418 l 2198 1413 l 2210 1407 l 2225 1399 l 2243 1391 l 2263 1381 l 2286 1370 l 2312 1358 l 2339 1345 l 2369 1333 l 2400 1320 l 2433 1307 l 2467 1294 l 2502 1281 l 2538 1269 l 2577 1258 l 2616 1247 l 2658 1237 l 2701 1228 l 2747 1219 l 2796 1212 l 2847 1206 l 2900 1202 l 2957 1199 l 3015 1199 l 3075 1200 l 3135 1204 l 3193 1209 l 3250 1217 l 3303 1225 l 3354 1236 l 3403 1247 l 3449 1259 l 3492 1272 l 3534 1285 l 3573 1299 l 3612 1314 l 3648 1329 l 3683 1344 l 3717 1360 l 3750 1376 l 3781 1391 l 3811 1407 l 3838 1421 l 3864 1435 l 3887 1448 l 3907 1460 l 3925 1470 l 3940 1479 l 3952 1486 l 3961 1492 l 3975 1500 l gs col0 s gr gr % arrowhead 0 slj n 3707 1417 m 3946 1484 l 3767 1312 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 6254 1766 m 6359 1709 l 6223 1456 l 6284 1696 l 6117 1513 l cp eoclip n 3000 1725 m 3001 1724 l 3002 1722 l 3004 1718 l 3008 1712 l 3014 1702 l 3021 1690 l 3031 1675 l 3043 1655 l 3057 1633 l 3074 1606 l 3093 1576 l 3115 1542 l 3139 1505 l 3166 1465 l 3195 1421 l 3225 1376 l 3258 1328 l 3292 1278 l 3329 1227 l 3366 1175 l 3405 1122 l 3445 1069 l 3487 1015 l 3529 962 l 3573 909 l 3617 857 l 3662 805 l 3709 755 l 3757 705 l 3805 657 l 3855 611 l 3906 566 l 3959 523 l 4013 482 l 4069 443 l 4126 406 l 4186 372 l 4247 341 l 4310 313 l 4376 287 l 4443 266 l 4512 249 l 4582 236 l 4653 228 l 4725 225 l 4796 228 l 4867 236 l 4936 249 l 5003 266 l 5068 287 l 5131 313 l 5191 341 l 5250 372 l 5306 406 l 5359 443 l 5411 482 l 5461 523 l 5510 566 l 5556 611 l 5602 657 l 5645 705 l 5688 755 l 5730 805 l 5770 857 l 5809 909 l 5847 962 l 5884 1015 l 5920 1069 l 5955 1122 l 5989 1175 l 6021 1227 l 6052 1278 l 6082 1328 l 6110 1376 l 6136 1421 l 6160 1465 l 6183 1505 l 6203 1542 l 6221 1576 l 6238 1606 l 6252 1633 l 6264 1655 l 6274 1675 l 6282 1690 l 6289 1702 l 6293 1712 l 6300 1725 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 6117 1513 m 6284 1696 l 6223 1456 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 9554 1766 m 9659 1709 l 9523 1456 l 9584 1696 l 9417 1513 l cp eoclip n 6300 1725 m 6301 1724 l 6302 1722 l 6304 1718 l 6308 1712 l 6314 1702 l 6321 1690 l 6331 1675 l 6343 1655 l 6357 1633 l 6374 1606 l 6393 1576 l 6415 1542 l 6439 1505 l 6466 1465 l 6495 1421 l 6525 1376 l 6558 1328 l 6592 1278 l 6629 1227 l 6666 1175 l 6705 1122 l 6745 1069 l 6787 1015 l 6829 962 l 6873 909 l 6917 857 l 6962 805 l 7009 755 l 7057 705 l 7105 657 l 7155 611 l 7206 566 l 7259 523 l 7313 482 l 7369 443 l 7426 406 l 7486 372 l 7547 341 l 7610 313 l 7676 287 l 7743 266 l 7812 249 l 7882 236 l 7953 228 l 8025 225 l 8096 228 l 8167 236 l 8236 249 l 8303 266 l 8368 287 l 8431 313 l 8491 341 l 8550 372 l 8606 406 l 8659 443 l 8711 482 l 8761 523 l 8810 566 l 8856 611 l 8902 657 l 8945 705 l 8988 755 l 9030 805 l 9070 857 l 9109 909 l 9147 962 l 9184 1015 l 9220 1069 l 9255 1122 l 9289 1175 l 9321 1227 l 9352 1278 l 9382 1328 l 9410 1376 l 9436 1421 l 9460 1465 l 9483 1505 l 9503 1542 l 9521 1576 l 9538 1606 l 9552 1633 l 9564 1655 l 9574 1675 l 9582 1690 l 9589 1702 l 9593 1712 l 9600 1725 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 9417 1513 m 9584 1696 l 9523 1456 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 4134 2836 m 4144 2716 l 3857 2692 l 4092 2772 l 3847 2811 l cp eoclip n 1050 2775 m 1051 2775 l 1053 2775 l 1056 2774 l 1062 2774 l 1070 2773 l 1081 2772 l 1095 2771 l 1112 2770 l 1132 2768 l 1155 2766 l 1181 2764 l 1211 2762 l 1243 2760 l 1278 2757 l 1315 2754 l 1354 2751 l 1396 2748 l 1439 2745 l 1484 2742 l 1530 2739 l 1577 2736 l 1626 2733 l 1676 2730 l 1727 2727 l 1779 2724 l 1833 2722 l 1888 2719 l 1945 2716 l 2003 2714 l 2064 2712 l 2126 2709 l 2190 2707 l 2257 2706 l 2326 2704 l 2398 2703 l 2471 2702 l 2547 2701 l 2623 2700 l 2700 2700 l 2785 2700 l 2868 2701 l 2948 2702 l 3024 2703 l 3098 2705 l 3167 2707 l 3233 2709 l 3296 2711 l 3355 2714 l 3412 2717 l 3466 2719 l 3518 2722 l 3568 2726 l 3615 2729 l 3662 2732 l 3706 2735 l 3749 2739 l 3790 2742 l 3829 2746 l 3867 2749 l 3902 2752 l 3936 2755 l 3967 2758 l 3995 2761 l 4021 2764 l 4044 2766 l 4063 2768 l 4080 2770 l 4094 2772 l 4105 2773 l 4113 2774 l 4125 2775 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 3847 2811 m 4092 2772 l 3857 2692 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 7285 2835 m 7294 2716 l 7007 2693 l 7242 2772 l 6998 2813 l cp eoclip n 4425 2775 m 4426 2775 l 4428 2775 l 4431 2774 l 4437 2773 l 4445 2772 l 4456 2771 l 4470 2769 l 4487 2767 l 4506 2765 l 4529 2762 l 4554 2759 l 4582 2756 l 4612 2753 l 4645 2749 l 4679 2746 l 4716 2742 l 4754 2739 l 4794 2735 l 4835 2731 l 4879 2728 l 4924 2725 l 4972 2721 l 5022 2718 l 5074 2715 l 5129 2713 l 5188 2710 l 5250 2708 l 5316 2705 l 5385 2704 l 5459 2702 l 5536 2701 l 5617 2700 l 5700 2700 l 5775 2700 l 5850 2701 l 5924 2702 l 5996 2703 l 6066 2704 l 6134 2706 l 6200 2708 l 6263 2710 l 6324 2713 l 6384 2715 l 6441 2718 l 6497 2721 l 6552 2723 l 6605 2726 l 6657 2729 l 6708 2733 l 6758 2736 l 6806 2739 l 6853 2742 l 6899 2745 l 6943 2749 l 6985 2752 l 7025 2755 l 7062 2758 l 7097 2760 l 7129 2763 l 7158 2765 l 7184 2767 l 7206 2769 l 7225 2771 l 7240 2772 l 7252 2773 l 7262 2774 l 7275 2775 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 6998 2813 m 7242 2772 l 7007 2693 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 10509 2836 m 10519 2716 l 10232 2692 l 10467 2772 l 10222 2811 l cp eoclip n 7575 2775 m 7576 2775 l 7578 2775 l 7582 2774 l 7588 2774 l 7596 2773 l 7608 2772 l 7622 2770 l 7640 2768 l 7661 2766 l 7684 2764 l 7711 2761 l 7741 2758 l 7773 2755 l 7808 2752 l 7845 2749 l 7884 2746 l 7924 2742 l 7966 2739 l 8010 2735 l 8056 2732 l 8103 2729 l 8151 2726 l 8201 2722 l 8253 2719 l 8308 2717 l 8364 2714 l 8423 2711 l 8485 2709 l 8549 2707 l 8617 2705 l 8688 2703 l 8763 2702 l 8840 2701 l 8919 2700 l 9000 2700 l 9077 2700 l 9153 2701 l 9227 2702 l 9299 2703 l 9369 2704 l 9436 2706 l 9500 2708 l 9562 2710 l 9621 2713 l 9678 2715 l 9733 2718 l 9787 2721 l 9838 2723 l 9888 2726 l 9937 2729 l 9984 2733 l 10030 2736 l 10075 2739 l 10118 2742 l 10160 2745 l 10200 2749 l 10238 2752 l 10274 2755 l 10308 2758 l 10340 2760 l 10369 2763 l 10395 2765 l 10418 2767 l 10438 2769 l 10455 2771 l 10469 2772 l 10480 2773 l 10488 2774 l 10500 2775 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 10222 2811 m 10467 2772 l 10232 2692 l col0 s % Polyline 2 slj gs clippath 1209 1863 m 1097 1818 l 991 2086 l 1136 1886 l 1102 2131 l cp eoclip n 848 2605 m 1148 1855 l gs col0 s gr gr % arrowhead 0 slj n 1102 2131 m 1136 1886 l 991 2086 l col0 s % Polyline 2 slj gs clippath 901 2878 m 789 2923 l 896 3191 l 863 2946 l 1007 3146 l cp eoclip n 1151 3665 m 851 2915 l gs col0 s gr gr % arrowhead 0 slj n 1007 3146 m 863 2946 l 896 3191 l col0 s % Polyline 2 slj gs clippath 1104 1904 m 1015 1823 l 821 2035 l 1028 1899 l 910 2116 l cp eoclip n 1050 3675 m 1049 3674 l 1048 3672 l 1045 3668 l 1041 3662 l 1035 3653 l 1027 3641 l 1017 3626 l 1005 3609 l 991 3588 l 976 3565 l 960 3540 l 942 3512 l 924 3482 l 905 3450 l 886 3417 l 867 3383 l 848 3347 l 829 3311 l 811 3273 l 793 3234 l 776 3194 l 760 3152 l 744 3110 l 730 3065 l 717 3018 l 705 2970 l 695 2919 l 687 2867 l 680 2812 l 676 2756 l 675 2700 l 677 2641 l 681 2583 l 688 2528 l 698 2476 l 709 2427 l 722 2382 l 737 2339 l 752 2298 l 769 2260 l 787 2224 l 806 2190 l 825 2157 l 845 2126 l 865 2096 l 886 2067 l 906 2040 l 926 2015 l 946 1991 l 964 1969 l 981 1949 l 997 1932 l 1011 1917 l 1022 1904 l 1032 1894 l 1039 1887 l 1050 1875 l gs col0 s gr gr % arrowhead 0 slj n 910 2116 m 1028 1899 l 821 2035 l col0 s % Polyline 2 slj gs clippath 5472 1588 m 5448 1705 l 5730 1761 l 5507 1656 l 5754 1644 l cp eoclip n 6225 1800 m 5475 1650 l gs col0 s gr gr % arrowhead 0 slj n 5754 1644 m 5507 1656 l 5730 1761 l col0 s % Polyline 2 slj gs clippath 6499 1743 m 6520 1861 l 6804 1810 l 6558 1794 l 6783 1692 l cp eoclip n 7350 1650 m 6525 1800 l gs col0 s gr gr % arrowhead 0 slj n 6783 1692 m 6558 1794 l 6804 1810 l col0 s % Polyline 2 slj gs clippath 5419 1666 m 5354 1767 l 5597 1923 l 5428 1743 l 5662 1822 l cp eoclip n 7425 1725 m 7424 1726 l 7422 1727 l 7418 1729 l 7411 1732 l 7402 1737 l 7390 1744 l 7375 1752 l 7356 1761 l 7335 1772 l 7311 1784 l 7284 1797 l 7255 1811 l 7223 1826 l 7190 1841 l 7155 1856 l 7119 1872 l 7082 1887 l 7043 1902 l 7003 1917 l 6961 1931 l 6918 1944 l 6873 1957 l 6827 1970 l 6779 1981 l 6728 1991 l 6675 2001 l 6619 2009 l 6561 2016 l 6500 2021 l 6438 2024 l 6375 2025 l 6308 2024 l 6243 2020 l 6180 2014 l 6120 2007 l 6064 1998 l 6011 1987 l 5961 1976 l 5913 1963 l 5868 1950 l 5825 1935 l 5784 1920 l 5745 1905 l 5708 1889 l 5671 1873 l 5637 1856 l 5604 1840 l 5573 1824 l 5543 1808 l 5517 1794 l 5492 1780 l 5471 1767 l 5452 1757 l 5436 1747 l 5424 1740 l 5414 1734 l 5400 1725 l gs col0 s gr gr % arrowhead 0 slj n 5662 1822 m 5428 1743 l 5597 1923 l col0 s % Polyline 2 slj gs clippath 4584 1863 m 4472 1818 l 4366 2086 l 4511 1886 l 4477 2131 l cp eoclip n 4223 2605 m 4523 1855 l gs col0 s gr gr % arrowhead 0 slj n 4477 2131 m 4511 1886 l 4366 2086 l col0 s % Polyline 2 slj gs clippath 4479 1904 m 4390 1823 l 4196 2035 l 4403 1899 l 4285 2116 l cp eoclip n 4425 3675 m 4424 3674 l 4423 3672 l 4420 3668 l 4416 3662 l 4410 3653 l 4402 3641 l 4392 3626 l 4380 3609 l 4366 3588 l 4351 3565 l 4335 3540 l 4317 3512 l 4299 3482 l 4280 3450 l 4261 3417 l 4242 3383 l 4223 3347 l 4204 3311 l 4186 3273 l 4168 3234 l 4151 3194 l 4135 3152 l 4119 3110 l 4105 3065 l 4092 3018 l 4080 2970 l 4070 2919 l 4062 2867 l 4055 2812 l 4051 2756 l 4050 2700 l 4052 2641 l 4056 2583 l 4063 2528 l 4073 2476 l 4084 2427 l 4097 2382 l 4112 2339 l 4127 2298 l 4144 2260 l 4162 2224 l 4181 2190 l 4200 2157 l 4220 2126 l 4240 2096 l 4261 2067 l 4281 2040 l 4301 2015 l 4321 1991 l 4339 1969 l 4356 1949 l 4372 1932 l 4386 1917 l 4397 1904 l 4407 1894 l 4414 1887 l 4425 1875 l gs col0 s gr gr % arrowhead 0 slj n 4285 2116 m 4403 1899 l 4196 2035 l col0 s % Polyline 2 slj gs clippath 7734 1863 m 7622 1818 l 7516 2086 l 7661 1886 l 7627 2131 l cp eoclip n 7373 2605 m 7673 1855 l gs col0 s gr gr % arrowhead 0 slj n 7627 2131 m 7661 1886 l 7516 2086 l col0 s % Polyline 2 slj gs clippath 7426 2878 m 7314 2923 l 7421 3191 l 7388 2946 l 7532 3146 l cp eoclip n 7676 3665 m 7376 2915 l gs col0 s gr gr % arrowhead 0 slj n 7532 3146 m 7388 2946 l 7421 3191 l col0 s % Polyline 2 slj gs clippath 7629 1904 m 7540 1823 l 7346 2035 l 7553 1899 l 7435 2116 l cp eoclip n 7575 3675 m 7574 3674 l 7573 3672 l 7570 3668 l 7566 3662 l 7560 3653 l 7552 3641 l 7542 3626 l 7530 3609 l 7516 3588 l 7501 3565 l 7485 3540 l 7467 3512 l 7449 3482 l 7430 3450 l 7411 3417 l 7392 3383 l 7373 3347 l 7354 3311 l 7336 3273 l 7318 3234 l 7301 3194 l 7285 3152 l 7269 3110 l 7255 3065 l 7242 3018 l 7230 2970 l 7220 2919 l 7212 2867 l 7205 2812 l 7201 2756 l 7200 2700 l 7202 2641 l 7206 2583 l 7213 2528 l 7223 2476 l 7234 2427 l 7247 2382 l 7262 2339 l 7277 2298 l 7294 2260 l 7312 2224 l 7331 2190 l 7350 2157 l 7370 2126 l 7390 2096 l 7411 2067 l 7431 2040 l 7451 2015 l 7471 1991 l 7489 1969 l 7506 1949 l 7522 1932 l 7536 1917 l 7547 1904 l 7557 1894 l 7564 1887 l 7575 1875 l gs col0 s gr gr % arrowhead 0 slj n 7435 2116 m 7553 1899 l 7346 2035 l col0 s % Polyline 2 slj gs clippath 10959 1863 m 10847 1818 l 10741 2086 l 10886 1886 l 10852 2131 l cp eoclip n 10598 2605 m 10898 1855 l gs col0 s gr gr % arrowhead 0 slj n 10852 2131 m 10886 1886 l 10741 2086 l col0 s % Polyline 2 slj gs clippath 10651 2878 m 10539 2923 l 10646 3191 l 10613 2946 l 10757 3146 l cp eoclip n 10901 3665 m 10601 2915 l gs col0 s gr gr % arrowhead 0 slj n 10757 3146 m 10613 2946 l 10646 3191 l col0 s % Polyline 2 slj gs clippath 10854 1904 m 10765 1823 l 10571 2035 l 10778 1899 l 10660 2116 l cp eoclip n 10800 3675 m 10799 3674 l 10798 3672 l 10795 3668 l 10791 3662 l 10785 3653 l 10777 3641 l 10767 3626 l 10755 3609 l 10741 3588 l 10726 3565 l 10710 3540 l 10692 3512 l 10674 3482 l 10655 3450 l 10636 3417 l 10617 3383 l 10598 3347 l 10579 3311 l 10561 3273 l 10543 3234 l 10526 3194 l 10510 3152 l 10494 3110 l 10480 3065 l 10467 3018 l 10455 2970 l 10445 2919 l 10437 2867 l 10430 2812 l 10426 2756 l 10425 2700 l 10427 2641 l 10431 2583 l 10438 2528 l 10448 2476 l 10459 2427 l 10472 2382 l 10487 2339 l 10502 2298 l 10519 2260 l 10537 2224 l 10556 2190 l 10575 2157 l 10595 2126 l 10615 2096 l 10636 2067 l 10656 2040 l 10676 2015 l 10696 1991 l 10714 1969 l 10731 1949 l 10747 1932 l 10761 1917 l 10772 1904 l 10782 1894 l 10789 1887 l 10800 1875 l gs col0 s gr gr % arrowhead 0 slj n 10660 2116 m 10778 1899 l 10571 2035 l col0 s % Polyline 2 slj gs clippath 8697 1513 m 8673 1630 l 8955 1686 l 8732 1581 l 8979 1569 l cp eoclip n 9450 1725 m 8700 1575 l gs col0 s gr gr % arrowhead 0 slj n 8979 1569 m 8732 1581 l 8955 1686 l col0 s % Polyline 2 slj gs clippath 9724 1668 m 9745 1786 l 10029 1735 l 9783 1719 l 10008 1617 l cp eoclip n 10575 1575 m 9750 1725 l gs col0 s gr gr % arrowhead 0 slj n 10008 1617 m 9783 1719 l 10029 1735 l col0 s % Polyline 2 slj gs clippath 8644 1591 m 8579 1692 l 8822 1848 l 8653 1668 l 8887 1747 l cp eoclip n 10650 1650 m 10649 1651 l 10647 1652 l 10643 1654 l 10636 1657 l 10627 1662 l 10615 1669 l 10600 1677 l 10581 1686 l 10560 1697 l 10536 1709 l 10509 1722 l 10480 1736 l 10448 1751 l 10415 1766 l 10380 1781 l 10344 1797 l 10307 1812 l 10268 1827 l 10228 1842 l 10186 1856 l 10143 1869 l 10098 1882 l 10052 1895 l 10004 1906 l 9953 1916 l 9900 1926 l 9844 1934 l 9786 1941 l 9725 1946 l 9663 1949 l 9600 1950 l 9533 1949 l 9468 1945 l 9405 1939 l 9345 1932 l 9289 1923 l 9236 1912 l 9186 1901 l 9138 1888 l 9093 1875 l 9050 1860 l 9009 1845 l 8970 1830 l 8933 1814 l 8896 1798 l 8862 1781 l 8829 1765 l 8798 1749 l 8768 1733 l 8742 1719 l 8717 1705 l 8696 1692 l 8677 1682 l 8661 1672 l 8649 1665 l 8639 1659 l 8625 1650 l gs col0 s gr gr % arrowhead 0 slj n 8887 1747 m 8653 1668 l 8822 1848 l col0 s % Polyline 2 slj gs clippath 2097 1588 m 2073 1705 l 2355 1761 l 2132 1656 l 2379 1644 l cp eoclip n 2850 1800 m 2100 1650 l gs col0 s gr gr % arrowhead 0 slj n 2379 1644 m 2132 1656 l 2355 1761 l col0 s % Polyline 2 slj gs clippath 3124 1743 m 3145 1861 l 3429 1810 l 3183 1794 l 3408 1692 l cp eoclip n 3975 1650 m 3150 1800 l gs col0 s gr gr % arrowhead 0 slj n 3408 1692 m 3183 1794 l 3429 1810 l col0 s % Polyline 2 slj gs clippath 2044 1666 m 1979 1767 l 2222 1923 l 2053 1743 l 2287 1822 l cp eoclip n 4050 1725 m 4049 1726 l 4047 1727 l 4043 1729 l 4036 1732 l 4027 1737 l 4015 1744 l 4000 1752 l 3981 1761 l 3960 1772 l 3936 1784 l 3909 1797 l 3880 1811 l 3848 1826 l 3815 1841 l 3780 1856 l 3744 1872 l 3707 1887 l 3668 1902 l 3628 1917 l 3586 1931 l 3543 1944 l 3498 1957 l 3452 1970 l 3404 1981 l 3353 1991 l 3300 2001 l 3244 2009 l 3186 2016 l 3125 2021 l 3063 2024 l 3000 2025 l 2933 2024 l 2868 2020 l 2805 2014 l 2745 2007 l 2689 1998 l 2636 1987 l 2586 1976 l 2538 1963 l 2493 1950 l 2450 1935 l 2409 1920 l 2370 1905 l 2333 1889 l 2296 1873 l 2262 1856 l 2229 1840 l 2198 1824 l 2168 1808 l 2142 1794 l 2117 1780 l 2096 1767 l 2077 1757 l 2061 1747 l 2049 1740 l 2039 1734 l 2025 1725 l gs col0 s gr gr % arrowhead 0 slj n 2287 1822 m 2053 1743 l 2222 1923 l col0 s % Polyline 2 slj gs clippath 4276 2878 m 4164 2923 l 4271 3191 l 4238 2946 l 4382 3146 l cp eoclip n 4526 3665 m 4226 2915 l gs col0 s gr gr % arrowhead 0 slj n 4382 3146 m 4238 2946 l 4271 3191 l col0 s /Times-Roman ff 315.00 scf sf 975 1725 m gs 1 -1 sc (0L,0S) col0 sh gr /Times-Roman ff 315.00 scf sf 4350 1725 m gs 1 -1 sc (1L,0S) col0 sh gr /Times-Roman ff 315.00 scf sf 7650 1725 m gs 1 -1 sc (2L,0S) col0 sh gr /Times-Roman ff 315.00 scf sf 1050 4125 m gs 1 -1 sc (0L,1S) col0 sh gr /Times-Roman ff 315.00 scf sf 4350 4125 m gs 1 -1 sc (1L,1S) col0 sh gr /Times-Roman ff 315.00 scf sf 7650 4125 m gs 1 -1 sc (2L,1S) col0 sh gr /Times-Roman ff 315.00 scf sf 10950 4125 m gs 1 -1 sc (3L,1S) col0 sh gr /Times-Roman ff 315.00 scf sf 10950 1725 m gs 1 -1 sc (3L,0S) col0 sh gr /Times-Roman ff 210.00 scf sf 525 2925 m gs 1 -1 sc (2) col0 sh gr /Times-Roman ff 210.00 scf sf 3900 2925 m gs 1 -1 sc (2) col0 sh gr /Times-Roman ff 210.00 scf sf 3000 2325 m gs 1 -1 sc (2) col0 sh gr /Times-Roman ff 210.00 scf sf 2625 1725 m gs 1 -1 sc (3) col0 sh gr /Times-Roman ff 210.00 scf sf 3600 1725 m gs 1 -1 sc (1) col0 sh gr /Times-Roman ff 270.00 scf sf 5850 1650 m gs 1 -1 sc (L) col0 sh gr /Times-Roman ff 210.00 scf sf 6000 1725 m gs 1 -1 sc (3) col0 sh gr /Times-Roman ff 270.00 scf sf 6225 2250 m gs 1 -1 sc (L) col0 sh gr /Times-Roman ff 210.00 scf sf 6375 2325 m gs 1 -1 sc (2) col0 sh gr /Times-Roman ff 270.00 scf sf 6825 1650 m gs 1 -1 sc (L) col0 sh gr /Times-Roman ff 210.00 scf sf 6975 1725 m gs 1 -1 sc (1) col0 sh gr /Times-Roman ff 210.00 scf sf 7650 2550 m gs 1 -1 sc (3) col0 sh gr /Times-Roman ff 210.00 scf sf 7725 3450 m gs 1 -1 sc (1) col0 sh gr /Times-Roman ff 210.00 scf sf 7050 2925 m gs 1 -1 sc (2) col0 sh gr /Times-Roman ff 210.00 scf sf 4575 3450 m gs 1 -1 sc (1) col0 sh gr /Times-Roman ff 210.00 scf sf 4500 2550 m gs 1 -1 sc (3) col0 sh gr /Times-Roman ff 210.00 scf sf 10875 2550 m gs 1 -1 sc (3) col0 sh gr /Times-Roman ff 210.00 scf sf 10950 3450 m gs 1 -1 sc (1) col0 sh gr /Times-Roman ff 210.00 scf sf 1125 2550 m gs 1 -1 sc (3) col0 sh gr /Times-Roman ff 210.00 scf sf 1200 3450 m gs 1 -1 sc (1) col0 sh gr /Times-Roman ff 270.00 scf sf 9075 1575 m gs 1 -1 sc (L) col0 sh gr /Times-Roman ff 210.00 scf sf 9225 1650 m gs 1 -1 sc (3) col0 sh gr /Times-Roman ff 270.00 scf sf 10050 1575 m gs 1 -1 sc (L) col0 sh gr /Times-Roman ff 210.00 scf sf 10200 1650 m gs 1 -1 sc (1) col0 sh gr /Times-Roman ff 270.00 scf sf 9450 2175 m gs 1 -1 sc (L) col0 sh gr /Times-Roman ff 210.00 scf sf 9600 2250 m gs 1 -1 sc (2) col0 sh gr /Times-Roman ff 210.00 scf sf 10275 2925 m gs 1 -1 sc (2) col0 sh gr /Times-Roman ff 240.00 scf sf 375 2850 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 240.00 scf sf 975 2475 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 240.00 scf sf 1050 3375 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 240.00 scf sf 2475 1650 m gs 1 -1 sc (L) col0 sh gr /Times-Roman ff 240.00 scf sf 3450 1650 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 2850 2607 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 3038 2700 m gs 1 -1 sc (L) col0 sh gr /Times-Roman ff 240.00 scf sf 2850 2250 m gs 1 -1 sc (L) col0 sh gr /Times-Roman ff 240.00 scf sf 3750 2850 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 240.00 scf sf 4350 2475 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 240.00 scf sf 4425 3375 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 240.00 scf sf 6900 2850 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 240.00 scf sf 7500 2475 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 240.00 scf sf 7575 3375 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 240.00 scf sf 10725 2475 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 240.00 scf sf 10125 2850 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 240.00 scf sf 10800 3375 m gs 1 -1 sc (S) col0 sh gr F2psBegin10setmiterlimit0.060000.06000scF2psEnd rs %%EndDocument endTexFig 1859 1844 a Fo(\(b\))120 2040 y FC(Figure)25 b(3:)31 b(Mark)o(o)o(v)25 b(chain)g(for)g(long)g(host.)32 b(\(a\))24 b(Sho)n(wn)g(where)h(job)g(sizes)g(are)g(e)o(xponentially-distrib)o(ut) q(ed)q(.)36 b(\(b\))120 2153 y(Sho)n(wn)23 b(where)h(job)g(sizes)g(ha)n (v)o(e)g(a)f(phase-type)k(distrib)n(ution)g(\(tw)o(o-phase)f(Coxian\).) 120 2430 y(jobs)h(arri)n(v)o(e)h(with)e(rate)h Fu(\025)934 2444 y Ft(L)1012 2430 y FC(at)g(e)n(v)o(ery)g(state.)39 b(Short)27 b(jobs)g(arri)n(v)o(e)g(only)h(when)f(the)g(long)g(host)h (is)e(idle.)39 b(W)-7 b(e)25 b(solv)o(e)120 2543 y(the)j(chain)g(in)f (Figure)h(3\(b\))g(to)g(obtain)g(the)g(steady-state)j(mean)c(number)i (of)e(long)h(jobs)g(e)o(xactly)h(using)g(Matrix)120 2656 y(Geometric)23 b(methods.)29 b(W)-7 b(e)21 b(then)h(apply)h(Little')-5 b(s)23 b(La)o(w)d([19)q(])h(to)h(obtain)h(the)f(mean)g(response)i(time) e(of)f(long)i(jobs.)261 2768 y(The)j(Matrix)i(Geometric)f(method)h(is)e (due)i(to)e(Neuts)h([20)q(])g(and)g(described)i(also)e(in)g([16)q(].)38 b(It)26 b(is)h(a)f(compact)120 2881 y(and)g(f)o(ast)g(method)h(for)e (solving)j(QBD)23 b(\(quasi-birth-death)q(\))31 b(Mark)o(o)o(v)26 b(chains)h(which)f(are)g(in\002nite)g(in)f(only)i(one)120 2994 y(dimension,)37 b(where)32 b(the)h(chain)h(repeats)g(itself)g (after)f(some)g(point.)57 b(The)32 b(repeating)j(portion)g(is)d (represented)120 3107 y(as)f(po)n(wers)h(of)f(a)g(generator)j(matrix)e (which)f(can)h(be)f(added,)k(as)c(one)h(adds)g(a)f(geometric)i(series,) h(to)d(produce)120 3220 y(a)c(single)i(matrix.)41 b(Ev)o(ery)27 b(plot)i(in)e(this)h(paper)h(which)f(used)g(Matrix)g(Geometric)g (analysis)i(\(to)e(solv)o(e)g(multiple)120 3333 y(instances)21 b(with)d(dif)n(ferent)j(parameter)f(v)n(alues\))g(w)o(as)e(produced)j (within)e(a)f(couple)i(of)e(seconds)j(using)f(the)e(Matlab)120 3446 y(6)23 b(en)l(vironment.)261 3559 y(An)h(alternati)n(v)o(e)j(w)o (ay)e(to)g(deduce)h(the)g(mean)f(response)i(time)d(for)h(the)h(long)f (jobs)h(is)f(to)f(use)i(virtual)g(w)o(aiting)120 3672 y(time)31 b(analysis.)52 b(W)-7 b(e)30 b(include)j(this)e(analysis)i (in)e(the)g(Appendix.)52 b(Belo)n(w)30 b(we)g(simply)i(state)g(its)e (result.)52 b Fu(T)3613 3639 y FE(\()p Ft(L)p FE(\))120 3785 y FC(represents)26 b(the)e(response)i(time)d(of)h(long)g(jobs.)834 4025 y Fq(e)817 4052 y Fu(T)883 4014 y FE(\()p Ft(L)p FE(\))990 4052 y Fs(\()p Fu(s)p Fs(\))83 b(=)1352 3990 y Fu(s)20 b Fs(+)f Fu(\025)1558 4004 y Ft(S)1629 3990 y Fr(\000)1746 3964 y Fq(e)1720 3990 y Fu(X)1795 4004 y Ft(S)1847 3990 y Fs(\()p Fu(s)p Fs(\))p Fu(\025)2013 4004 y Ft(S)p 1350 4031 716 4 v 1350 4127 a Fu(s)h Fr(\000)f Fu(\025)1556 4141 y Ft(L)1629 4127 y Fs(+)1745 4101 y Fq(e)1720 4127 y Fu(X)1795 4141 y Ft(L)1847 4127 y Fs(\()p Fu(s)p Fs(\))p Fu(\025)2013 4141 y Ft(L)2096 4052 y Fr(\001)h Fu(\031)2193 4066 y FE(0)2253 4052 y Fr(\001)2302 4025 y Fq(g)2298 4052 y Fu(X)2373 4066 y Ft(L)2426 4052 y Fs(\()p Fu(s)p Fs(\))p Fu(;)807 4320 y(E)5 b Fs([)p Fu(T)970 4283 y FE(\()p Ft(L)p FE(\))1078 4320 y Fs(])83 b(=)1428 4259 y Fu(\032)1475 4273 y Ft(L)p 1350 4299 256 4 v 1350 4383 a Fs(1)20 b Fr(\000)g Fu(\032)1553 4397 y Ft(L)1648 4259 y Fu(E)5 b Fs([)p Fu(X)1827 4226 y FE(2)1820 4284 y Ft(L)1873 4259 y Fs(])p 1625 4299 296 4 v 1625 4383 a(2)p Fu(E)g Fs([)p Fu(X)1842 4397 y Ft(L)1896 4383 y Fs(])1951 4320 y(+)2130 4259 y Fu(\032)2177 4273 y Ft(S)p 2052 4299 255 4 v 2052 4383 a Fs(1)21 b(+)f Fu(\032)2256 4397 y Ft(S)2349 4259 y Fu(E)5 b Fs([)p Fu(X)2528 4226 y FE(2)2521 4284 y Ft(S)2573 4259 y Fs(])p 2326 4299 295 4 v 2326 4383 a(2)p Fu(E)g Fs([)p Fu(X)2543 4397 y Ft(S)2596 4383 y Fs(])2651 4320 y(+)20 b Fu(E)5 b Fs([)p Fu(X)2914 4334 y Ft(L)2967 4320 y Fs(])p Fu(;)120 4662 y FC(where)1663 4792 y Fu(\031)1715 4806 y FE(0)1780 4792 y Fs(=)1886 4730 y(1)20 b Fr(\000)g Fu(\032)2089 4744 y Ft(L)p 1886 4771 256 4 v 1887 4854 a Fs(1)g(+)g Fu(\032)2090 4868 y Ft(S)2151 4792 y Fu(;)120 4996 y FC(represents)26 b(the)e(fraction)i(of)d(time)g(that)h(the)g(long)h (host)f(is)f(idle.)1897 5349 y(7)p eop %%Page: 8 10 8 9 bop 261 91 a FC(The)20 b(second)j(step)e(is)f(to)h(deri)n(v)o(e)g (all)g(moments)g(for)g(the)g(b)n(usy)g(and)g(idle)h(periods)g(of)f(the) f(long)i(host,)f(for)g(use)g(in)120 204 y(our)g(analysis)h(of)f(the)f (short)i(host.)28 b(The)20 b(long)h(host)g(idle)g(time)g(is)f(e)o (xponentially-distri)q(b)n(u)q(ted)26 b(with)21 b(rate)f Fu(\025)3453 218 y Ft(L)3514 204 y Fs(+)9 b Fu(\025)3647 218 y Ft(S)3697 204 y FC(.)120 317 y(T)-7 b(o)23 b(deri)n(v)o(e)i(the)g (length)h(of)e(the)h(b)n(usy)g(period)h(for)f(the)g(long)g(host,)g(we)e (need)j(to)e(distinguish)k(between)d(tw)o(o)f(types)120 430 y(of)c(b)n(usy)i(periods:)29 b(\(1\))21 b(A)e(b)n(usy)i(period)h (made)f(up)f(entirely)i(of)f(long)g(jobs,)g(the)g(duration)h(of)f (which)f(we)g(represent)120 543 y(by)26 b(the)h(r)-5 b(.v)f(.)25 b Fu(B)577 557 y Ft(L)629 543 y FC(;)i(and)g(\(2\))f(A)f(b) n(usy)i(period)h(started)f(by)f(one)h(short)g(job)g(follo)n(wed)g(by)f (zero)h(or)f(more)g(long)h(jobs,)120 656 y(the)d(duration)i(of)d(which) h(we)f(represent)j(by)d(the)h(r)-5 b(.v)f(.)23 b Fu(B)1857 670 y Ft(S)t(L)1956 656 y FC(.)28 b(W)-7 b(e)22 b(then)j(ha)n(v)o(e)f (the)g(follo)n(wing:)1234 834 y Fq(g)1234 860 y Fu(B)1303 874 y Ft(L)1355 860 y Fs(\()p Fu(s)p Fs(\))83 b(=)1709 834 y Fq(g)1705 860 y Fu(X)1780 874 y Ft(L)1832 860 y Fs(\()p Fu(s)20 b Fs(+)g Fu(\025)2074 874 y Ft(L)2147 860 y Fr(\000)g Fu(\025)2291 874 y Ft(L)2343 834 y Fq(g)2343 860 y Fu(B)2412 874 y Ft(L)2464 860 y Fs(\()p Fu(s)p Fs(\)\);)1211 972 y Fq(g)1187 998 y Fu(B)1256 1012 y Ft(S)t(L)1355 998 y Fs(\()p Fu(s)p Fs(\))83 b(=)1708 972 y Fq(g)1705 998 y Fu(X)1780 1012 y Ft(S)1831 998 y Fs(\()p Fu(s)20 b Fs(+)g Fu(\025)2073 1012 y Ft(L)2145 998 y Fr(\000)g Fu(\025)2289 1012 y Ft(L)2342 972 y Fq(g)2341 998 y Fu(B)2410 1012 y Ft(L)2463 998 y Fs(\()p Fu(s)p Fs(\)\))p Fu(:)261 1189 y FC(From)26 b(these)i(transforms)h(we)d (compute)i(the)f(\002rst)f(three)i(moments)f(of)g(each)h(type)f(of)g(b) n(usy)h(period)g(as)f(fol-)120 1289 y(lo)n(ws:)853 1500 y Fn(E)14 b Fm(f)o Fl(B)1026 1512 y Fk(L)1076 1500 y Fm(g)83 b Fj(=)1358 1443 y Fn(E)14 b Fm(f)p Fl(X)1538 1455 y Fk(L)1587 1443 y Fm(g)p 1358 1480 271 4 v 1376 1556 a Fj(1)k Fm(\000)g Fl(\032)1562 1568 y Fk(L)1639 1500 y Fj(;)180 b Fn(E)14 b Fm(f)o Fl(B)2015 1512 y Fk(S)s(L)2109 1500 y Fm(g)23 b Fj(=)2271 1443 y Fn(E)14 b Fm(f)p Fl(X)2451 1455 y Fk(S)2499 1443 y Fm(g)p 2271 1480 270 4 v 2288 1556 a Fj(1)k Fm(\000)g Fl(\032)2474 1568 y Fk(L)2550 1500 y Fj(;)839 1738 y Fn(E)908 1671 y Fq(\010)956 1738 y Fl(B)1023 1704 y Fi(2)1019 1758 y Fk(L)1069 1671 y Fq(\011)1201 1738 y Fj(=)1385 1676 y Fn(E)1454 1609 y Fq(\010)1502 1676 y Fl(X)1578 1646 y Fi(2)1571 1699 y Fk(L)1621 1609 y Fq(\011)p 1358 1719 338 4 v 1358 1795 a Fj(\(1)g Fm(\000)g Fl(\032)1576 1807 y Fk(L)1626 1795 y Fj(\))1658 1771 y Fi(3)1706 1738 y Fj(;)795 1981 y Fn(E)864 1914 y Fq(\010)913 1981 y Fl(B)980 1946 y Fi(2)976 2001 y Fk(S)s(L)1069 1914 y Fq(\011)1201 1981 y Fj(=)82 b Fn(E)14 b Fm(f)p Fl(X)1528 1993 y Fk(S)1576 1981 y Fm(g)k(\001)g Fl(\025)1725 1993 y Fk(L)1794 1981 y Fm(\001)1872 1919 y Fn(E)1941 1852 y Fq(\010)1989 1919 y Fl(X)2065 1889 y Fi(2)2058 1942 y Fk(L)2108 1852 y Fq(\011)p 1845 1962 V 1845 2038 a Fj(\(1)h Fm(\000)f Fl(\032)2064 2050 y Fk(L)2113 2038 y Fj(\))2145 2014 y Fi(3)2211 1981 y Fj(+)2452 1925 y(1)p 2304 1962 V 2304 2038 a(\(1)g Fm(\000)g Fl(\032)2522 2050 y Fk(L)2572 2038 y Fj(\))2604 2014 y Fi(2)2670 1981 y Fm(\001)g Fn(E)2781 1914 y Fq(\010)2829 1981 y Fl(X)2905 1946 y Fi(2)2898 2001 y Fk(S)2946 1914 y Fq(\011)3008 1981 y Fj(;)839 2224 y Fn(E)908 2156 y Fq(\010)956 2224 y Fl(B)1023 2189 y Fi(3)1019 2244 y Fk(L)1069 2156 y Fq(\011)1201 2224 y Fj(=)1358 2162 y(3)p Fl(\025)1448 2174 y Fk(L)1498 2162 y Fj(\()p Fn(E)1599 2095 y Fq(\010)1648 2162 y Fl(X)1724 2132 y Fi(2)1717 2185 y Fk(L)1766 2095 y Fq(\011)1815 2162 y Fj(\))1847 2132 y Fi(2)p 1358 2205 527 4 v 1452 2281 a Fj(\(1)h Fm(\000)f Fl(\032)1671 2293 y Fk(L)1720 2281 y Fj(\))1752 2257 y Fi(5)1913 2224 y Fj(+)2032 2162 y Fn(E)2101 2095 y Fq(\010)2150 2162 y Fl(X)2226 2132 y Fi(3)2219 2185 y Fk(L)2268 2095 y Fq(\011)p 2006 2205 338 4 v 2006 2281 a Fj(\(1)g Fm(\000)g Fl(\032)2224 2293 y Fk(L)2273 2281 y Fj(\))2305 2257 y Fi(4)2353 2224 y Fj(;)795 2467 y Fn(E)864 2399 y Fq(\010)913 2467 y Fl(B)980 2432 y Fi(3)976 2487 y Fk(S)s(L)1069 2399 y Fq(\011)1201 2467 y Fj(=)1358 2405 y Fl(\025)1406 2375 y Fi(2)1406 2428 y Fk(L)1456 2405 y Fn(E)c Fm(f)p Fl(X)1636 2417 y Fk(S)1684 2405 y Fm(g)k(\001)g Fj(3)g Fm(\001)h Fj(\()p Fn(E)1988 2338 y Fq(\010)2037 2405 y Fl(X)2113 2375 y Fi(2)2106 2428 y Fk(L)2155 2338 y Fq(\011)2204 2405 y Fj(\))2236 2375 y Fi(2)p 1358 2447 916 4 v 1647 2524 a Fj(\(1)f Fm(\000)g Fl(\032)1865 2536 y Fk(L)1915 2524 y Fj(\))1947 2500 y Fi(5)2302 2467 y Fj(+)2422 2405 y Fn(E)2491 2338 y Fq(\010)2539 2405 y Fl(X)2615 2375 y Fi(3)2608 2428 y Fk(S)2656 2338 y Fq(\011)p 2395 2447 338 4 v 2395 2524 a Fj(\(1)g Fm(\000)g Fl(\032)2613 2536 y Fk(L)2662 2524 y Fj(\))2694 2500 y Fi(3)2742 2467 y Fj(;)1348 2710 y(+)1423 2648 y(3)p Fl(\025)1513 2660 y Fk(L)1562 2648 y Fn(E)1632 2581 y Fq(\010)1680 2648 y Fl(X)1756 2618 y Fi(2)1749 2671 y Fk(L)1798 2581 y Fq(\011)1865 2648 y Fj(+)g Fn(E)2018 2581 y Fq(\010)2066 2648 y Fl(X)2142 2618 y Fi(2)2135 2671 y Fk(S)2183 2581 y Fq(\011)2250 2648 y Fj(+)g Fl(\025)2381 2660 y Fk(L)2431 2648 y Fn(E)c Fm(f)p Fl(X)2611 2660 y Fk(S)2659 2648 y Fm(g)f Fn(E)2783 2581 y Fq(\010)2831 2648 y Fl(X)2907 2618 y Fi(3)2900 2671 y Fk(L)2950 2581 y Fq(\011)p 1423 2690 1576 4 v 2042 2766 a Fj(\(1)18 b Fm(\000)g Fl(\032)2260 2778 y Fk(L)2310 2766 y Fj(\))2342 2742 y Fi(4)3008 2710 y Fl(:)145 2941 y FC(T)-7 b(o)25 b(obtain)i(the)f(moments)g(of)g(a)f(general)j(b)n(usy)e(period)i(for)d (the)h(long)h(host,)g(observ)o(e)g(that)f(a)g(b)n(usy)h(period)g(is)e (of)120 3053 y(type)h Fu(B)370 3067 y Ft(S)t(L)494 3053 y FC(with)f(probability)j Fu(\025)1156 3067 y Ft(S)1207 3053 y Fu(=)p Fs(\()p Fu(\025)1340 3067 y Ft(S)1414 3053 y Fs(+)21 b Fu(\025)1559 3067 y Ft(L)1611 3053 y Fs(\))k FC(and)h(of)f(type)i Fu(B)2178 3067 y Ft(L)2254 3053 y FC(with)f(probability)i Fu(\025)2917 3067 y Ft(L)2969 3053 y Fu(=)p Fs(\()p Fu(\025)3102 3067 y Ft(S)3176 3053 y Fs(+)21 b Fu(\025)3321 3067 y Ft(L)3373 3053 y Fs(\))p FC(.)34 b(Hence,)120 3166 y(denoting)26 b(by)e Fu(B)j FC(the)d(duration)h(of)f(a)f(general)i(b)n(usy)g(period,)f(we)f(ha)n(v) o(e)966 3410 y FB(E)1042 3316 y Fq(n)1097 3410 y Fu(B)1171 3373 y Ft(`)1204 3316 y Fq(o)1284 3410 y Fs(=)1499 3349 y Fu(\025)1552 3363 y Ft(S)p 1390 3389 321 4 v 1390 3473 a Fu(\025)1443 3487 y Ft(S)1514 3473 y Fs(+)d Fu(\025)1658 3487 y Ft(L)1720 3410 y FB(E)1796 3316 y Fq(n)1852 3410 y Fu(B)1926 3373 y Ft(`)1921 3433 y(S)t(L)2019 3316 y Fq(o)2095 3410 y Fs(+)2303 3349 y Fu(\025)2356 3363 y Ft(L)p 2196 3389 V 2196 3473 a Fu(\025)2249 3487 y Ft(S)2320 3473 y Fs(+)g Fu(\025)2464 3487 y Ft(L)2526 3410 y FB(E)2602 3316 y Fq(n)2657 3410 y Fu(B)2731 3373 y Ft(`)2726 3433 y(L)2778 3316 y Fq(o)2849 3410 y Fu(:)261 3727 y FC(W)-7 b(e)25 b(no)n(w)f(construct)k(a)d(phase-type)j(distrib)n(ution)h(to)c (match)h(as)f(man)o(y)h(moments)f(of)h(the)f(long)h(host')-5 b(s)27 b(b)n(usy)120 3840 y(period)32 b(as)e(are)h(of)f(interest.)52 b(Man)o(y)30 b(methods)i(e)o(xist)f(for)g(matching)h(moments)f(to)f (phase-type)k(distrib)n(utions:)120 3953 y([14)q(,)22 b(4,)g(15].)28 b(W)-7 b(e)22 b(\002nd)g(that)h(simply)g(\002tting)g(a)f (tw)o(o-phase)j(Coxian)e(distrib)n(ution)j(to)d(the)g(\002rst)f(three)h (moments)g(of)120 4066 y(the)h(long)g(host')-5 b(s)25 b(b)n(usy)g(period)g(w)o(orks)f(suf)n(\002ciently)h(well)f(for)f(our)h (purposes.)261 4179 y(Our)30 b(last)h(step)g(is)g(to)f(analyze)j(the)e (short)g(host.)51 b(The)30 b(arri)n(v)n(al)h(rate)g(at)g(the)f(short)i (host)f(is)g Fu(\025)3211 4193 y Ft(S)3291 4179 y FC(only)h(during)120 4292 y(times)22 b(when)f(the)h(long)h(host)f(is)f(b)n(usy)-6 b(.)30 b(When)22 b(the)f(long)i(host)f(is)g(idle,)g(the)g(arri)n(v)n (al)g(rate)g(at)g(the)g(short)g(host)g(is)g(zero.)120 4405 y(T)-7 b(o)26 b(represent)k(the)e(short)g(host,)h(we)d(therefore)k (need)e(a)f(w)o(ay)g(of)g(representing)k(the)d(duration)h(of)e(a)g(b)n (usy)i(period)120 4518 y(at)g(the)g(long)h(host.)46 b(Figure)30 b(4\(a\))f(is)g(a)g(simpli\002ed)h(vie)n(w)e(of)h(the)h(Mark)o(o)o(v)f (chain)i(model)e(of)g(the)g(short)h(host.)46 b(It)120 4631 y(assumes)27 b(that)f(the)f(job)h(sizes)h(are)e(e)o (xponentially-distr)q(ib)o(ute)q(d)31 b(and)26 b(sho)n(ws)f(the)h(b)n (usy)h(period)g(duration)g(for)f(the)120 4744 y(long)f(host)g(is)f(sho) n(wn)h(as)f(a)g(bold)h(transition)i(mark)o(ed)e Fu(B)5 b FC(.)29 b(Figure)c(4\(b\))g(is)f(the)h(Mark)o(o)o(v)g(chain)g(that)g (we)e(actually)120 4857 y(solv)o(e)k(for)g(the)f(short)i(host.)38 b(Here)26 b(the)h(job)g(sizes)g(are)g(dra)o(wn)f(from)h(a)e(tw)o (o-phase)k(Coxian,)f(used)f(to)f(match)h(the)120 4969 y(\002rst)22 b(three)i(moments)f(of)g(the)g(respecti)n(v)o(e)h(job)g (size)f(distrib)n(ution.)32 b(Also)22 b(the)h(length)i(of)d(the)h(b)n (usy)h(period)g(for)f(the)120 5082 y(long)h(host)h(is)e(matched)i(for)e (the)h(\002rst)f(three)i(moments)f(by)g(a)f(tw)o(o-phase)i(Coxian)g (distrib)n(ution.)1897 5349 y(8)p eop %%Page: 9 11 9 10 bop 450 0 a 23207776 7194408 0 0 51243991 16379658 startTexFig 450 0 a %%BeginDocument: ../figures/dispatch_small_exp.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: dispatch_small_exp.eps %%Creator: fig2dev Version 3.2 Patchlevel 3d %%CreationDate: Tue Apr 2 10:33:10 2002 %%For: harchol@mor.sp.cs.cmu.edu (Mor Harchol-Balter) %%BoundingBox: 0 0 779 249 %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def F2psDictbeginF2psDict begin F2psDictbeginF2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 249 moveto 0 0 lineto 779 0 lineto 779 249 lineto closepath clip newpath -4.5 288.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def F2psBegin10setmiterlimit0.060000.06000scF2psBegin 10 setmiterlimit 0.06000 0.06000 sc % % Fig objects follow % 15.000 slw % Ellipse n 12300 1575 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12600 1575 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12900 1575 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12375 3975 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12675 3975 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12975 3975 54 54 0 360 DrawEllipse gs col0 s gr /Symbol ff 300.00 scf sf 2775 945 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 2955 1125 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 300.00 scf sf 6075 945 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 6255 1125 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 300.00 scf sf 9375 870 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 9555 1050 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 300.00 scf sf 6075 2214 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 300.00 scf sf 6264 2400 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 300.00 scf sf 9375 2214 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 300.00 scf sf 9564 2400 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 300.00 scf sf 9450 4614 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 300.00 scf sf 9639 4800 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 300.00 scf sf 6075 4614 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 300.00 scf sf 6264 4800 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 300.00 scf sf 2775 4614 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 300.00 scf sf 2964 4800 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 300.00 scf sf 10350 2832 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 10538 2925 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 9750 2832 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 9938 2925 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 345.00 scf sf 10125 2850 m gs 1 -1 sc (+) col0 sh gr /Symbol ff 300.00 scf sf 675 2907 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 863 3000 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 75 2907 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 263 3000 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 345.00 scf sf 450 2925 m gs 1 -1 sc (+) col0 sh gr /Symbol ff 300.00 scf sf 3675 2907 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 3863 3000 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 3075 2907 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 3263 3000 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 345.00 scf sf 3450 2925 m gs 1 -1 sc (+) col0 sh gr /Symbol ff 300.00 scf sf 7125 2907 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 7313 3000 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 6525 2907 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 6713 3000 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 345.00 scf sf 6900 2925 m gs 1 -1 sc (+) col0 sh gr /Symbol ff 300.00 scf sf 2775 2214 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 300.00 scf sf 2964 2400 m gs 1 -1 sc (S) col0 sh gr % Ellipse n 4725 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 8025 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 8025 3975 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 4725 3975 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 1350 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 1425 3975 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 11325 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 11306 3979 750 300 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 3958 1559 m 4017 1455 l 3767 1312 l 3946 1484 l 3707 1417 l cp eoclip n 2175 1425 m 2176 1424 l 2178 1423 l 2182 1421 l 2189 1418 l 2198 1413 l 2210 1407 l 2225 1399 l 2243 1391 l 2263 1381 l 2286 1370 l 2312 1358 l 2339 1345 l 2369 1333 l 2400 1320 l 2433 1307 l 2467 1294 l 2502 1281 l 2538 1269 l 2577 1258 l 2616 1247 l 2658 1237 l 2701 1228 l 2747 1219 l 2796 1212 l 2847 1206 l 2900 1202 l 2957 1199 l 3015 1199 l 3075 1200 l 3135 1204 l 3193 1209 l 3250 1217 l 3303 1225 l 3354 1236 l 3403 1247 l 3449 1259 l 3492 1272 l 3534 1285 l 3573 1299 l 3612 1314 l 3648 1329 l 3683 1344 l 3717 1360 l 3750 1376 l 3781 1391 l 3811 1407 l 3838 1421 l 3864 1435 l 3887 1448 l 3907 1460 l 3925 1470 l 3940 1479 l 3952 1486 l 3961 1492 l 3975 1500 l gs col0 s gr gr % arrowhead 0 slj n 3707 1417 m 3946 1484 l 3767 1312 l col0 s % Polyline 2 slj gs clippath 2200 1593 m 2126 1687 l 2352 1865 l 2201 1670 l 2426 1771 l cp eoclip n 3975 1650 m 3974 1651 l 3971 1652 l 3966 1655 l 3959 1659 l 3948 1665 l 3935 1672 l 3917 1682 l 3897 1692 l 3873 1705 l 3847 1719 l 3817 1733 l 3786 1749 l 3752 1765 l 3717 1781 l 3680 1798 l 3642 1814 l 3603 1830 l 3563 1845 l 3521 1860 l 3478 1875 l 3433 1888 l 3386 1901 l 3337 1912 l 3286 1923 l 3233 1932 l 3177 1939 l 3119 1945 l 3060 1949 l 3000 1950 l 2936 1949 l 2875 1944 l 2817 1938 l 2762 1929 l 2711 1919 l 2663 1907 l 2618 1895 l 2576 1881 l 2537 1866 l 2499 1850 l 2464 1833 l 2430 1816 l 2398 1799 l 2367 1781 l 2338 1764 l 2311 1747 l 2286 1730 l 2263 1715 l 2243 1700 l 2225 1688 l 2210 1677 l 2198 1668 l 2189 1661 l 2175 1650 l gs col0 s gr gr % arrowhead 0 slj n 2426 1771 m 2201 1670 l 2352 1865 l col0 s % Polyline 2 slj gs clippath 7183 1559 m 7242 1455 l 6992 1312 l 7171 1484 l 6932 1417 l cp eoclip n 5400 1425 m 5401 1424 l 5403 1423 l 5407 1421 l 5414 1418 l 5423 1413 l 5435 1407 l 5450 1399 l 5468 1391 l 5488 1381 l 5511 1370 l 5537 1358 l 5564 1345 l 5594 1333 l 5625 1320 l 5658 1307 l 5692 1294 l 5727 1281 l 5763 1269 l 5802 1258 l 5841 1247 l 5883 1237 l 5926 1228 l 5972 1219 l 6021 1212 l 6072 1206 l 6125 1202 l 6182 1199 l 6240 1199 l 6300 1200 l 6360 1204 l 6418 1209 l 6475 1217 l 6528 1225 l 6579 1236 l 6628 1247 l 6674 1259 l 6717 1272 l 6759 1285 l 6798 1299 l 6837 1314 l 6873 1329 l 6908 1344 l 6942 1360 l 6975 1376 l 7006 1391 l 7036 1407 l 7063 1421 l 7089 1435 l 7112 1448 l 7132 1460 l 7150 1470 l 7165 1479 l 7177 1486 l 7186 1492 l 7200 1500 l gs col0 s gr gr % arrowhead 0 slj n 6932 1417 m 7171 1484 l 6992 1312 l col0 s % Polyline 2 slj gs clippath 10558 1484 m 10617 1380 l 10367 1237 l 10546 1409 l 10307 1342 l cp eoclip n 8775 1350 m 8776 1349 l 8778 1348 l 8782 1346 l 8789 1343 l 8798 1338 l 8810 1332 l 8825 1324 l 8843 1316 l 8863 1306 l 8886 1295 l 8912 1283 l 8939 1270 l 8969 1258 l 9000 1245 l 9033 1232 l 9067 1219 l 9102 1206 l 9138 1194 l 9177 1183 l 9216 1172 l 9258 1162 l 9301 1153 l 9347 1144 l 9396 1137 l 9447 1131 l 9500 1127 l 9557 1124 l 9615 1124 l 9675 1125 l 9735 1129 l 9793 1134 l 9850 1142 l 9903 1150 l 9954 1161 l 10003 1172 l 10049 1184 l 10092 1197 l 10134 1210 l 10173 1224 l 10212 1239 l 10248 1254 l 10283 1269 l 10317 1285 l 10350 1301 l 10381 1316 l 10411 1332 l 10438 1346 l 10464 1360 l 10487 1373 l 10507 1385 l 10525 1395 l 10540 1404 l 10552 1411 l 10561 1417 l 10575 1425 l gs col0 s gr gr % arrowhead 0 slj n 10307 1342 m 10546 1409 l 10367 1237 l col0 s % Polyline 2 slj gs clippath 5500 1593 m 5426 1687 l 5652 1865 l 5501 1670 l 5726 1771 l cp eoclip n 7275 1650 m 7274 1651 l 7271 1652 l 7266 1655 l 7259 1659 l 7248 1665 l 7235 1672 l 7217 1682 l 7197 1692 l 7173 1705 l 7147 1719 l 7117 1733 l 7086 1749 l 7052 1765 l 7017 1781 l 6980 1798 l 6942 1814 l 6903 1830 l 6863 1845 l 6821 1860 l 6778 1875 l 6733 1888 l 6686 1901 l 6637 1912 l 6586 1923 l 6533 1932 l 6477 1939 l 6419 1945 l 6360 1949 l 6300 1950 l 6236 1949 l 6175 1944 l 6117 1938 l 6062 1929 l 6011 1919 l 5963 1907 l 5918 1895 l 5876 1881 l 5837 1866 l 5799 1850 l 5764 1833 l 5730 1816 l 5698 1799 l 5667 1781 l 5638 1764 l 5611 1747 l 5586 1730 l 5563 1715 l 5543 1700 l 5525 1688 l 5510 1677 l 5498 1668 l 5489 1661 l 5475 1650 l gs col0 s gr gr % arrowhead 0 slj n 5726 1771 m 5501 1670 l 5652 1865 l col0 s % Polyline 2 slj gs clippath 8800 1593 m 8726 1687 l 8952 1865 l 8801 1670 l 9026 1771 l cp eoclip n 10575 1650 m 10574 1651 l 10571 1652 l 10566 1655 l 10559 1659 l 10548 1665 l 10535 1672 l 10517 1682 l 10497 1692 l 10473 1705 l 10447 1719 l 10417 1733 l 10386 1749 l 10352 1765 l 10317 1781 l 10280 1798 l 10242 1814 l 10203 1830 l 10163 1845 l 10121 1860 l 10078 1875 l 10033 1888 l 9986 1901 l 9937 1912 l 9886 1923 l 9833 1932 l 9777 1939 l 9719 1945 l 9660 1949 l 9600 1950 l 9536 1949 l 9475 1944 l 9417 1938 l 9362 1929 l 9311 1919 l 9263 1907 l 9218 1895 l 9176 1881 l 9137 1866 l 9099 1850 l 9064 1833 l 9030 1816 l 8998 1799 l 8967 1781 l 8938 1764 l 8911 1747 l 8886 1730 l 8863 1715 l 8843 1700 l 8825 1688 l 8810 1677 l 8798 1668 l 8789 1661 l 8775 1650 l gs col0 s gr gr % arrowhead 0 slj n 9026 1771 m 8801 1670 l 8952 1865 l col0 s % Polyline 2 slj gs clippath 1106 1900 m 1012 1826 l 834 2052 l 1030 1901 l 928 2126 l cp eoclip n 1125 3675 m 1124 3674 l 1123 3672 l 1120 3668 l 1116 3662 l 1110 3653 l 1103 3641 l 1093 3626 l 1082 3609 l 1069 3588 l 1055 3565 l 1039 3540 l 1022 3512 l 1005 3482 l 986 3450 l 968 3417 l 949 3383 l 931 3347 l 913 3311 l 895 3273 l 877 3234 l 860 3194 l 844 3152 l 829 3110 l 814 3065 l 801 3018 l 788 2970 l 777 2919 l 767 2867 l 760 2812 l 754 2756 l 750 2700 l 749 2636 l 751 2575 l 756 2517 l 763 2462 l 772 2411 l 783 2363 l 796 2318 l 810 2276 l 825 2237 l 841 2199 l 858 2164 l 875 2130 l 893 2098 l 912 2067 l 930 2038 l 948 2011 l 965 1986 l 982 1963 l 997 1943 l 1010 1925 l 1022 1910 l 1031 1898 l 1039 1889 l 1050 1875 l gs col0 s gr gr % arrowhead 0 slj n 928 2126 m 1030 1901 l 834 2052 l col0 s % Polyline 2 slj gs clippath 4411 1898 m 4317 1824 l 4139 2050 l 4335 1899 l 4233 2124 l cp eoclip n 4430 3673 m 4429 3672 l 4428 3670 l 4425 3666 l 4421 3660 l 4415 3651 l 4408 3639 l 4398 3624 l 4387 3607 l 4374 3586 l 4360 3563 l 4344 3538 l 4327 3510 l 4310 3480 l 4291 3448 l 4273 3415 l 4254 3381 l 4236 3345 l 4218 3309 l 4200 3271 l 4182 3232 l 4165 3192 l 4149 3150 l 4134 3108 l 4119 3063 l 4106 3016 l 4093 2968 l 4082 2917 l 4072 2865 l 4065 2810 l 4059 2754 l 4055 2698 l 4054 2634 l 4056 2573 l 4061 2515 l 4068 2460 l 4077 2409 l 4088 2361 l 4101 2316 l 4115 2274 l 4130 2235 l 4146 2197 l 4163 2162 l 4180 2128 l 4198 2096 l 4217 2065 l 4235 2036 l 4253 2009 l 4270 1984 l 4287 1961 l 4302 1941 l 4315 1923 l 4327 1908 l 4336 1896 l 4344 1887 l 4355 1873 l gs col0 s gr gr % arrowhead 0 slj n 4233 2124 m 4335 1899 l 4139 2050 l col0 s % Polyline 2 slj gs clippath 7861 1898 m 7767 1824 l 7589 2050 l 7785 1899 l 7683 2124 l cp eoclip n 7880 3673 m 7879 3672 l 7878 3670 l 7875 3666 l 7871 3660 l 7865 3651 l 7858 3639 l 7848 3624 l 7837 3607 l 7824 3586 l 7810 3563 l 7794 3538 l 7777 3510 l 7760 3480 l 7741 3448 l 7723 3415 l 7704 3381 l 7686 3345 l 7668 3309 l 7650 3271 l 7632 3232 l 7615 3192 l 7599 3150 l 7584 3108 l 7569 3063 l 7556 3016 l 7543 2968 l 7532 2917 l 7522 2865 l 7515 2810 l 7509 2754 l 7505 2698 l 7504 2634 l 7506 2573 l 7511 2515 l 7518 2460 l 7527 2409 l 7538 2361 l 7551 2316 l 7565 2274 l 7580 2235 l 7596 2197 l 7613 2162 l 7630 2128 l 7648 2096 l 7667 2065 l 7685 2036 l 7703 2009 l 7720 1984 l 7737 1961 l 7752 1941 l 7765 1923 l 7777 1908 l 7786 1896 l 7794 1887 l 7805 1873 l gs col0 s gr gr % arrowhead 0 slj n 7683 2124 m 7785 1899 l 7589 2050 l col0 s % Polyline 2 slj gs clippath 11086 1898 m 10992 1824 l 10814 2050 l 11010 1899 l 10908 2124 l cp eoclip n 11105 3673 m 11104 3672 l 11103 3670 l 11100 3666 l 11096 3660 l 11090 3651 l 11083 3639 l 11073 3624 l 11062 3607 l 11049 3586 l 11035 3563 l 11019 3538 l 11002 3510 l 10985 3480 l 10966 3448 l 10948 3415 l 10929 3381 l 10911 3345 l 10893 3309 l 10875 3271 l 10857 3232 l 10840 3192 l 10824 3150 l 10809 3108 l 10794 3063 l 10781 3016 l 10768 2968 l 10757 2917 l 10747 2865 l 10740 2810 l 10734 2754 l 10730 2698 l 10729 2634 l 10731 2573 l 10736 2515 l 10743 2460 l 10752 2409 l 10763 2361 l 10776 2316 l 10790 2274 l 10805 2235 l 10821 2197 l 10838 2162 l 10855 2128 l 10873 2096 l 10892 2065 l 10910 2036 l 10928 2009 l 10945 1984 l 10962 1961 l 10977 1941 l 10990 1923 l 11002 1908 l 11011 1896 l 11019 1887 l 11030 1873 l gs col0 s gr gr % arrowhead 0 slj n 10908 2124 m 11010 1899 l 10814 2050 l col0 s % Polyline 2 slj gs clippath 2200 3993 m 2126 4087 l 2352 4265 l 2201 4070 l 2426 4171 l cp eoclip n 3975 4050 m 3974 4051 l 3971 4052 l 3966 4055 l 3959 4059 l 3948 4065 l 3935 4072 l 3917 4082 l 3897 4092 l 3873 4105 l 3847 4119 l 3817 4133 l 3786 4149 l 3752 4165 l 3717 4181 l 3680 4198 l 3642 4214 l 3603 4230 l 3563 4245 l 3521 4260 l 3478 4275 l 3433 4288 l 3386 4301 l 3337 4312 l 3286 4323 l 3233 4332 l 3177 4339 l 3119 4345 l 3060 4349 l 3000 4350 l 2936 4349 l 2875 4344 l 2817 4338 l 2762 4329 l 2711 4319 l 2663 4307 l 2618 4295 l 2576 4281 l 2537 4266 l 2499 4250 l 2464 4233 l 2430 4216 l 2398 4199 l 2367 4181 l 2338 4164 l 2311 4147 l 2286 4130 l 2263 4115 l 2243 4100 l 2225 4088 l 2210 4077 l 2198 4068 l 2189 4061 l 2175 4050 l gs col0 s gr gr % arrowhead 0 slj n 2426 4171 m 2201 4070 l 2352 4265 l col0 s % Polyline 2 slj gs clippath 5500 3993 m 5426 4087 l 5652 4265 l 5501 4070 l 5726 4171 l cp eoclip n 7275 4050 m 7274 4051 l 7271 4052 l 7266 4055 l 7259 4059 l 7248 4065 l 7235 4072 l 7217 4082 l 7197 4092 l 7173 4105 l 7147 4119 l 7117 4133 l 7086 4149 l 7052 4165 l 7017 4181 l 6980 4198 l 6942 4214 l 6903 4230 l 6863 4245 l 6821 4260 l 6778 4275 l 6733 4288 l 6686 4301 l 6637 4312 l 6586 4323 l 6533 4332 l 6477 4339 l 6419 4345 l 6360 4349 l 6300 4350 l 6236 4349 l 6175 4344 l 6117 4338 l 6062 4329 l 6011 4319 l 5963 4307 l 5918 4295 l 5876 4281 l 5837 4266 l 5799 4250 l 5764 4233 l 5730 4216 l 5698 4199 l 5667 4181 l 5638 4164 l 5611 4147 l 5586 4130 l 5563 4115 l 5543 4100 l 5525 4088 l 5510 4077 l 5498 4068 l 5489 4061 l 5475 4050 l gs col0 s gr gr % arrowhead 0 slj n 5726 4171 m 5501 4070 l 5652 4265 l col0 s % Polyline 2 slj gs clippath 8800 3993 m 8726 4087 l 8952 4265 l 8801 4070 l 9026 4171 l cp eoclip n 10575 4050 m 10574 4051 l 10571 4052 l 10566 4055 l 10559 4059 l 10548 4065 l 10535 4072 l 10517 4082 l 10497 4092 l 10473 4105 l 10447 4119 l 10417 4133 l 10386 4149 l 10352 4165 l 10317 4181 l 10280 4198 l 10242 4214 l 10203 4230 l 10163 4245 l 10121 4260 l 10078 4275 l 10033 4288 l 9986 4301 l 9937 4312 l 9886 4323 l 9833 4332 l 9777 4339 l 9719 4345 l 9660 4349 l 9600 4350 l 9536 4349 l 9475 4344 l 9417 4338 l 9362 4329 l 9311 4319 l 9263 4307 l 9218 4295 l 9176 4281 l 9137 4266 l 9099 4250 l 9064 4233 l 9030 4216 l 8998 4199 l 8967 4181 l 8938 4164 l 8911 4147 l 8886 4130 l 8863 4115 l 8843 4100 l 8825 4088 l 8810 4077 l 8798 4068 l 8789 4061 l 8775 4050 l gs col0 s gr gr % arrowhead 0 slj n 9026 4171 m 8801 4070 l 8952 4265 l col0 s % Polyline 2 slj 60.000 slw gs clippath 1578 3647 m 1704 3728 l 1945 3354 l 1720 3566 l 1819 3273 l cp eoclip n 1575 1875 m 1576 1876 l 1577 1879 l 1579 1884 l 1583 1891 l 1589 1902 l 1596 1915 l 1605 1933 l 1615 1953 l 1627 1977 l 1640 2003 l 1654 2033 l 1668 2064 l 1684 2098 l 1699 2133 l 1715 2170 l 1731 2208 l 1746 2247 l 1761 2287 l 1776 2329 l 1790 2372 l 1803 2417 l 1816 2464 l 1828 2513 l 1839 2564 l 1850 2617 l 1858 2673 l 1866 2731 l 1871 2790 l 1875 2850 l 1876 2914 l 1875 2975 l 1872 3033 l 1867 3088 l 1860 3139 l 1852 3187 l 1843 3232 l 1833 3274 l 1821 3313 l 1809 3351 l 1796 3386 l 1783 3420 l 1769 3452 l 1755 3483 l 1742 3512 l 1728 3539 l 1715 3564 l 1702 3587 l 1691 3607 l 1680 3625 l 1672 3640 l 1664 3652 l 1659 3661 l 1650 3675 l gs col0 s gr gr % arrowhead 0 slj n 1819 3273 m 1720 3566 l 1945 3354 l 1819 3273 l cp gs 0.00 setgray ef gr col0 s % Polyline 2 slj gs clippath 4974 3641 m 5100 3722 l 5341 3348 l 5116 3560 l 5215 3267 l cp eoclip n 4971 1869 m 4972 1870 l 4973 1873 l 4975 1878 l 4979 1885 l 4985 1896 l 4992 1909 l 5001 1927 l 5011 1947 l 5023 1971 l 5036 1997 l 5050 2027 l 5064 2058 l 5080 2092 l 5095 2127 l 5111 2164 l 5127 2202 l 5142 2241 l 5157 2281 l 5172 2323 l 5186 2366 l 5199 2411 l 5212 2458 l 5224 2507 l 5235 2558 l 5246 2611 l 5254 2667 l 5262 2725 l 5267 2784 l 5271 2844 l 5272 2908 l 5271 2969 l 5268 3027 l 5263 3082 l 5256 3133 l 5248 3181 l 5239 3226 l 5229 3268 l 5217 3307 l 5205 3345 l 5192 3380 l 5179 3414 l 5165 3446 l 5151 3477 l 5138 3506 l 5124 3533 l 5111 3558 l 5098 3581 l 5087 3601 l 5076 3619 l 5068 3634 l 5060 3646 l 5055 3655 l 5046 3669 l gs col0 s gr gr % arrowhead 0 slj n 5215 3267 m 5116 3560 l 5341 3348 l 5215 3267 l cp gs 0.00 setgray ef gr col0 s % Polyline 2 slj gs clippath 11649 3641 m 11775 3722 l 12016 3348 l 11791 3560 l 11890 3267 l cp eoclip n 11646 1869 m 11647 1870 l 11648 1873 l 11650 1878 l 11654 1885 l 11660 1896 l 11667 1909 l 11676 1927 l 11686 1947 l 11698 1971 l 11711 1997 l 11725 2027 l 11739 2058 l 11755 2092 l 11770 2127 l 11786 2164 l 11802 2202 l 11817 2241 l 11832 2281 l 11847 2323 l 11861 2366 l 11874 2411 l 11887 2458 l 11899 2507 l 11910 2558 l 11921 2611 l 11929 2667 l 11937 2725 l 11942 2784 l 11946 2844 l 11947 2908 l 11946 2969 l 11943 3027 l 11938 3082 l 11931 3133 l 11923 3181 l 11914 3226 l 11904 3268 l 11892 3307 l 11880 3345 l 11867 3380 l 11854 3414 l 11840 3446 l 11826 3477 l 11813 3506 l 11799 3533 l 11786 3558 l 11773 3581 l 11762 3601 l 11751 3619 l 11743 3634 l 11735 3646 l 11730 3655 l 11721 3669 l gs col0 s gr gr % arrowhead 0 slj n 11890 3267 m 11791 3560 l 12016 3348 l 11890 3267 l cp gs 0.00 setgray ef gr col0 s % Polyline 2 slj gs clippath 8403 3647 m 8529 3728 l 8770 3354 l 8545 3566 l 8644 3273 l cp eoclip n 8400 1875 m 8401 1876 l 8402 1879 l 8404 1884 l 8408 1891 l 8414 1902 l 8421 1915 l 8430 1933 l 8440 1953 l 8452 1977 l 8465 2003 l 8479 2033 l 8493 2064 l 8509 2098 l 8524 2133 l 8540 2170 l 8556 2208 l 8571 2247 l 8586 2287 l 8601 2329 l 8615 2372 l 8628 2417 l 8641 2464 l 8653 2513 l 8664 2564 l 8675 2617 l 8683 2673 l 8691 2731 l 8696 2790 l 8700 2850 l 8701 2914 l 8700 2975 l 8697 3033 l 8692 3088 l 8685 3139 l 8677 3187 l 8668 3232 l 8658 3274 l 8646 3313 l 8634 3351 l 8621 3386 l 8608 3420 l 8594 3452 l 8580 3483 l 8567 3512 l 8553 3539 l 8540 3564 l 8527 3587 l 8516 3607 l 8505 3625 l 8497 3640 l 8489 3652 l 8484 3661 l 8475 3675 l gs col0 s gr gr % arrowhead 0 slj n 8644 3273 m 8545 3566 l 8770 3354 l 8644 3273 l cp gs 0.00 setgray ef gr col0 s /Times-Roman ff 315.00 scf sf 750 1725 m gs 1 -1 sc (Lbusy,0S) col0 sh gr /Times-Roman ff 315.00 scf sf 4125 1725 m gs 1 -1 sc (Lbusy,1S) col0 sh gr /Times-Roman ff 315.00 scf sf 7425 1725 m gs 1 -1 sc (Lbusy,2S) col0 sh gr /Times-Roman ff 315.00 scf sf 10725 1725 m gs 1 -1 sc (Lbusy,3S) col0 sh gr /Times-Roman ff 315.00 scf sf 900 4125 m gs 1 -1 sc (Lidle,0S) col0 sh gr /Times-Roman ff 315.00 scf sf 4200 4125 m gs 1 -1 sc (Lidle,1S) col0 sh gr /Times-Roman ff 315.00 scf sf 7575 4125 m gs 1 -1 sc (Lidle,2S) col0 sh gr /Times-Roman ff 315.00 scf sf 10875 4125 m gs 1 -1 sc (Lidle,3S) col0 sh gr /Times-Roman ff 360.00 scf sf 1950 2925 m gs 1 -1 sc (B) col0 sh gr /Times-Roman ff 360.00 scf sf 5325 2925 m gs 1 -1 sc (B) col0 sh gr /Times-Roman ff 360.00 scf sf 8775 2925 m gs 1 -1 sc (B) col0 sh gr /Times-Roman ff 360.00 scf sf 12000 2850 m gs 1 -1 sc (B) col0 sh gr F2psBegin10setmiterlimit0.060000.06000scF2psEnd rs %%EndDocument endTexFig 1862 1024 a Fo(\(a\))360 1049 y 24628676 8373745 0 0 50915082 17695293 startTexFig 360 1049 a %%BeginDocument: ../figures/dispatch_small_gen.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: dispatch_small_gen.eps %%Creator: fig2dev Version 3.2 Patchlevel 3d %%CreationDate: Tue Apr 16 09:06:16 2002 %%For: harchol@mor.sp.cs.cmu.edu (Mor Harchol-Balter) %%BoundingBox: 0 0 774 269 %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def F2psDictbeginF2psDict begin F2psDictbeginF2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 269 moveto 0 0 lineto 774 0 lineto 774 269 lineto closepath clip newpath -9.0 274.5 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def F2psBegin10setmiterlimit0.060000.06000scF2psBegin 10 setmiterlimit 0.06000 0.06000 sc % % Fig objects follow % 15.000 slw % Ellipse n 12300 1575 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12600 1575 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12900 1575 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12375 3975 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12675 3975 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12975 3975 54 54 0 360 DrawEllipse gs col0 s gr /Symbol ff 300.00 scf sf 9375 870 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 9555 1050 m gs 1 -1 sc (S) col0 sh gr % Ellipse n 1575 2850 106 106 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 1516 2794 m 1636 2784 l 1611 2497 l 1572 2742 l 1492 2507 l cp eoclip n 1500 1875 m 1575 2775 l gs col0 s gr gr % arrowhead 0 slj n 1492 2507 m 1572 2742 l 1611 2497 l col0 s % Polyline 2 slj gs clippath 1438 3683 m 1557 3696 l 1590 3410 l 1504 3642 l 1470 3396 l cp eoclip n 1575 3000 m 1500 3675 l gs col0 s gr gr % arrowhead 0 slj n 1470 3396 m 1504 3642 l 1590 3410 l col0 s % Polyline 2 slj gs clippath 1513 3668 m 1626 3709 l 1723 3438 l 1586 3644 l 1610 3397 l cp eoclip n 1575 1875 m 1575 1876 l 1576 1879 l 1577 1884 l 1579 1891 l 1582 1902 l 1586 1915 l 1591 1933 l 1596 1953 l 1602 1977 l 1609 2003 l 1617 2033 l 1624 2064 l 1632 2098 l 1641 2133 l 1649 2170 l 1657 2208 l 1665 2247 l 1673 2287 l 1680 2329 l 1687 2372 l 1694 2417 l 1700 2464 l 1706 2513 l 1711 2564 l 1716 2617 l 1720 2673 l 1723 2731 l 1724 2790 l 1725 2850 l 1724 2914 l 1722 2975 l 1719 3033 l 1715 3088 l 1710 3139 l 1704 3187 l 1697 3232 l 1690 3274 l 1683 3313 l 1675 3351 l 1667 3386 l 1658 3420 l 1649 3452 l 1641 3483 l 1632 3512 l 1623 3539 l 1615 3564 l 1607 3587 l 1600 3607 l 1594 3625 l 1588 3640 l 1584 3652 l 1580 3661 l 1575 3675 l gs col0 s gr gr % arrowhead 0 slj n 1610 3397 m 1586 3644 l 1723 3438 l col0 s /Times-Roman ff 315.00 scf sf 750 1725 m gs 1 -1 sc (Lbusy,0S) col0 sh gr % Ellipse n 11625 2850 106 106 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 11566 2794 m 11686 2784 l 11661 2497 l 11622 2742 l 11542 2507 l cp eoclip n 11550 1875 m 11625 2775 l gs col0 s gr gr % arrowhead 0 slj n 11542 2507 m 11622 2742 l 11661 2497 l col0 s % Polyline 2 slj gs clippath 11488 3683 m 11607 3696 l 11640 3410 l 11554 3642 l 11520 3396 l cp eoclip n 11625 3000 m 11550 3675 l gs col0 s gr gr % arrowhead 0 slj n 11520 3396 m 11554 3642 l 11640 3410 l col0 s % Polyline 2 slj gs clippath 11563 3668 m 11676 3709 l 11773 3438 l 11636 3644 l 11660 3397 l cp eoclip n 11625 1875 m 11625 1876 l 11626 1879 l 11627 1884 l 11629 1891 l 11632 1902 l 11636 1915 l 11641 1933 l 11646 1953 l 11652 1977 l 11659 2003 l 11667 2033 l 11674 2064 l 11682 2098 l 11691 2133 l 11699 2170 l 11707 2208 l 11715 2247 l 11723 2287 l 11730 2329 l 11737 2372 l 11744 2417 l 11750 2464 l 11756 2513 l 11761 2564 l 11766 2617 l 11770 2673 l 11773 2731 l 11774 2790 l 11775 2850 l 11774 2914 l 11772 2975 l 11769 3033 l 11765 3088 l 11760 3139 l 11754 3187 l 11747 3232 l 11740 3274 l 11733 3313 l 11725 3351 l 11717 3386 l 11708 3420 l 11699 3452 l 11691 3483 l 11682 3512 l 11673 3539 l 11665 3564 l 11657 3587 l 11650 3607 l 11644 3625 l 11638 3640 l 11634 3652 l 11630 3661 l 11625 3675 l gs col0 s gr gr % arrowhead 0 slj n 11660 3397 m 11636 3644 l 11773 3438 l col0 s % Ellipse n 9675 1725 106 106 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 9725 1668 m 9745 1786 l 10029 1739 l 9783 1720 l 10009 1621 l cp eoclip n 10650 1575 m 9750 1725 l gs col0 s gr gr % arrowhead 0 slj n 10009 1621 m 9783 1720 l 10029 1739 l col0 s % Polyline 2 slj gs clippath 8770 1513 m 8749 1631 l 9033 1682 l 8808 1581 l 9054 1564 l cp eoclip n 9600 1725 m 8775 1575 l gs col0 s gr gr % arrowhead 0 slj n 9054 1564 m 8808 1581 l 9033 1682 l col0 s % Polyline 2 slj gs clippath 8796 1592 m 8728 1690 l 8965 1854 l 8802 1669 l 9033 1756 l cp eoclip n 10650 1650 m 10649 1651 l 10646 1652 l 10642 1655 l 10635 1659 l 10624 1665 l 10611 1672 l 10594 1682 l 10574 1692 l 10551 1705 l 10526 1719 l 10497 1733 l 10466 1749 l 10434 1765 l 10399 1781 l 10363 1798 l 10326 1814 l 10287 1830 l 10247 1845 l 10205 1860 l 10162 1875 l 10117 1888 l 10070 1901 l 10021 1912 l 9969 1923 l 9915 1932 l 9858 1939 l 9799 1945 l 9737 1949 l 9675 1950 l 9613 1949 l 9552 1945 l 9494 1939 l 9439 1932 l 9387 1923 l 9338 1912 l 9292 1901 l 9248 1888 l 9207 1875 l 9167 1860 l 9129 1845 l 9093 1830 l 9058 1814 l 9025 1798 l 8993 1781 l 8963 1765 l 8934 1749 l 8907 1733 l 8882 1719 l 8860 1705 l 8840 1692 l 8823 1682 l 8808 1672 l 8797 1665 l 8788 1659 l 8775 1650 l gs col0 s gr gr % arrowhead 0 slj n 9033 1756 m 8802 1669 l 8965 1854 l col0 s /Symbol ff 300.00 scf sf 750 2607 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 938 2700 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 150 2607 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 338 2700 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 345.00 scf sf 525 2625 m gs 1 -1 sc (+) col0 sh gr % Ellipse n 4950 2850 106 106 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 4891 2794 m 5011 2784 l 4986 2497 l 4947 2742 l 4867 2507 l cp eoclip n 4875 1875 m 4950 2775 l gs col0 s gr gr % arrowhead 0 slj n 4867 2507 m 4947 2742 l 4986 2497 l col0 s % Polyline 2 slj gs clippath 4813 3683 m 4932 3696 l 4965 3410 l 4879 3642 l 4845 3396 l cp eoclip n 4950 3000 m 4875 3675 l gs col0 s gr gr % arrowhead 0 slj n 4845 3396 m 4879 3642 l 4965 3410 l col0 s % Polyline 2 slj gs clippath 4888 3668 m 5001 3709 l 5098 3438 l 4961 3644 l 4985 3397 l cp eoclip n 4950 1875 m 4950 1876 l 4951 1879 l 4952 1884 l 4954 1891 l 4957 1902 l 4961 1915 l 4966 1933 l 4971 1953 l 4977 1977 l 4984 2003 l 4992 2033 l 4999 2064 l 5007 2098 l 5016 2133 l 5024 2170 l 5032 2208 l 5040 2247 l 5048 2287 l 5055 2329 l 5062 2372 l 5069 2417 l 5075 2464 l 5081 2513 l 5086 2564 l 5091 2617 l 5095 2673 l 5098 2731 l 5099 2790 l 5100 2850 l 5099 2914 l 5097 2975 l 5094 3033 l 5090 3088 l 5085 3139 l 5079 3187 l 5072 3232 l 5065 3274 l 5058 3313 l 5050 3351 l 5042 3386 l 5033 3420 l 5024 3452 l 5016 3483 l 5007 3512 l 4998 3539 l 4990 3564 l 4982 3587 l 4975 3607 l 4969 3625 l 4963 3640 l 4959 3652 l 4955 3661 l 4950 3675 l gs col0 s gr gr % arrowhead 0 slj n 4985 3397 m 4961 3644 l 5098 3438 l col0 s /Symbol ff 240.00 scf sf 5100 2325 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 240.00 scf sf 5250 2400 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 300.00 scf sf 6075 945 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 6255 1125 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 11250 2325 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 240.00 scf sf 11400 2400 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 240.00 scf sf 11250 3375 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 240.00 scf sf 11400 3450 m gs 1 -1 sc (3) col0 sh gr /Times-Roman ff 240.00 scf sf 9975 3375 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 10125 3450 m gs 1 -1 sc (2) col0 sh gr /Times-Roman ff 240.00 scf sf 9975 2175 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 10125 2250 m gs 1 -1 sc (2) col0 sh gr /Times-Roman ff 240.00 scf sf 9975 4500 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 10125 4575 m gs 1 -1 sc (2) col0 sh gr /Times-Roman ff 240.00 scf sf 9975 3900 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 10125 3975 m gs 1 -1 sc (1) col0 sh gr /Times-Roman ff 240.00 scf sf 9975 1575 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 10125 1650 m gs 1 -1 sc (1) col0 sh gr /Times-Roman ff 240.00 scf sf 9000 2850 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 9150 2925 m gs 1 -1 sc (3) col0 sh gr /Times-Roman ff 240.00 scf sf 9000 3900 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 9150 3975 m gs 1 -1 sc (3) col0 sh gr /Times-Roman ff 240.00 scf sf 9150 1575 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 9300 1650 m gs 1 -1 sc (3) col0 sh gr /Times-Roman ff 240.00 scf sf 9975 2775 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 10125 2850 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 300.00 scf sf 7500 2532 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 7688 2625 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 6900 2532 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 7088 2625 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 300.00 scf sf 2775 945 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 2955 1125 m gs 1 -1 sc (S) col0 sh gr % Ellipse n 3000 4050 106 106 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 3050 3993 m 3070 4111 l 3354 4064 l 3108 4045 l 3334 3946 l cp eoclip n 3975 3900 m 3075 4050 l gs col0 s gr gr % arrowhead 0 slj n 3334 3946 m 3108 4045 l 3354 4064 l col0 s % Polyline 2 slj gs clippath 2095 3838 m 2074 3956 l 2358 4007 l 2133 3906 l 2379 3889 l cp eoclip n 2925 4050 m 2100 3900 l gs col0 s gr gr % arrowhead 0 slj n 2379 3889 m 2133 3906 l 2358 4007 l col0 s % Polyline 2 slj gs clippath 2121 3917 m 2053 4015 l 2290 4179 l 2127 3994 l 2358 4081 l cp eoclip n 3975 3975 m 3974 3976 l 3971 3977 l 3967 3980 l 3960 3984 l 3949 3990 l 3936 3997 l 3919 4007 l 3899 4017 l 3876 4030 l 3851 4044 l 3822 4058 l 3791 4074 l 3759 4090 l 3724 4106 l 3688 4123 l 3651 4139 l 3612 4155 l 3572 4170 l 3530 4185 l 3487 4200 l 3442 4213 l 3395 4226 l 3346 4237 l 3294 4248 l 3240 4257 l 3183 4264 l 3124 4270 l 3062 4274 l 3000 4275 l 2938 4274 l 2877 4270 l 2819 4264 l 2764 4257 l 2712 4248 l 2663 4237 l 2617 4226 l 2573 4213 l 2532 4200 l 2492 4185 l 2454 4170 l 2418 4155 l 2383 4139 l 2350 4123 l 2318 4106 l 2288 4090 l 2259 4074 l 2232 4058 l 2207 4044 l 2185 4030 l 2165 4017 l 2148 4007 l 2133 3997 l 2122 3990 l 2113 3984 l 2100 3975 l gs col0 s gr gr % arrowhead 0 slj n 2358 4081 m 2127 3994 l 2290 4179 l col0 s % Ellipse n 3000 1725 106 106 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 3050 1668 m 3070 1786 l 3354 1739 l 3108 1720 l 3334 1621 l cp eoclip n 3975 1575 m 3075 1725 l gs col0 s gr gr % arrowhead 0 slj n 3334 1621 m 3108 1720 l 3354 1739 l col0 s % Polyline 2 slj gs clippath 2095 1513 m 2074 1631 l 2358 1682 l 2133 1581 l 2379 1564 l cp eoclip n 2925 1725 m 2100 1575 l gs col0 s gr gr % arrowhead 0 slj n 2379 1564 m 2133 1581 l 2358 1682 l col0 s % Polyline 2 slj gs clippath 2121 1592 m 2053 1690 l 2290 1854 l 2127 1669 l 2358 1756 l cp eoclip n 3975 1650 m 3974 1651 l 3971 1652 l 3967 1655 l 3960 1659 l 3949 1665 l 3936 1672 l 3919 1682 l 3899 1692 l 3876 1705 l 3851 1719 l 3822 1733 l 3791 1749 l 3759 1765 l 3724 1781 l 3688 1798 l 3651 1814 l 3612 1830 l 3572 1845 l 3530 1860 l 3487 1875 l 3442 1888 l 3395 1901 l 3346 1912 l 3294 1923 l 3240 1932 l 3183 1939 l 3124 1945 l 3062 1949 l 3000 1950 l 2938 1949 l 2877 1945 l 2819 1939 l 2764 1932 l 2712 1923 l 2663 1912 l 2617 1901 l 2573 1888 l 2532 1875 l 2492 1860 l 2454 1845 l 2418 1830 l 2383 1814 l 2350 1798 l 2318 1781 l 2288 1765 l 2259 1749 l 2232 1733 l 2207 1719 l 2185 1705 l 2165 1692 l 2148 1682 l 2133 1672 l 2122 1665 l 2113 1659 l 2100 1650 l gs col0 s gr gr % arrowhead 0 slj n 2358 1756 m 2127 1669 l 2290 1854 l col0 s % Polyline 2 slj gs clippath 4411 1898 m 4317 1824 l 4139 2050 l 4335 1899 l 4233 2124 l cp eoclip n 4430 3673 m 4429 3672 l 4428 3670 l 4425 3666 l 4421 3660 l 4415 3651 l 4408 3639 l 4398 3624 l 4387 3607 l 4374 3586 l 4360 3563 l 4344 3538 l 4327 3510 l 4310 3480 l 4291 3448 l 4273 3415 l 4254 3381 l 4236 3345 l 4218 3309 l 4200 3271 l 4182 3232 l 4165 3192 l 4149 3150 l 4134 3108 l 4119 3063 l 4106 3016 l 4093 2968 l 4082 2917 l 4072 2865 l 4065 2810 l 4059 2754 l 4055 2698 l 4054 2634 l 4056 2573 l 4061 2515 l 4068 2460 l 4077 2409 l 4088 2361 l 4101 2316 l 4115 2274 l 4130 2235 l 4146 2197 l 4163 2162 l 4180 2128 l 4198 2096 l 4217 2065 l 4235 2036 l 4253 2009 l 4270 1984 l 4287 1961 l 4302 1941 l 4315 1923 l 4327 1908 l 4336 1896 l 4344 1887 l 4355 1873 l gs col0 s gr gr % arrowhead 0 slj n 4233 2124 m 4335 1899 l 4139 2050 l col0 s % Polyline 2 slj gs clippath 1654 2863 m 1616 2977 l 1889 3067 l 1681 2935 l 1927 2953 l cp eoclip n 4875 2850 m 4874 2850 l 4872 2851 l 4869 2852 l 4864 2854 l 4856 2856 l 4845 2860 l 4832 2864 l 4816 2869 l 4797 2875 l 4774 2882 l 4749 2890 l 4720 2899 l 4689 2908 l 4656 2918 l 4620 2929 l 4581 2940 l 4541 2951 l 4499 2963 l 4455 2974 l 4410 2986 l 4364 2998 l 4316 3009 l 4267 3021 l 4216 3032 l 4165 3044 l 4111 3054 l 4056 3065 l 4000 3075 l 3941 3085 l 3880 3094 l 3817 3103 l 3751 3112 l 3683 3120 l 3613 3127 l 3539 3133 l 3463 3139 l 3385 3144 l 3306 3147 l 3225 3150 l 3140 3151 l 3057 3151 l 2976 3150 l 2898 3147 l 2823 3144 l 2751 3139 l 2682 3134 l 2617 3128 l 2554 3122 l 2493 3114 l 2435 3106 l 2379 3098 l 2325 3089 l 2273 3080 l 2223 3071 l 2174 3061 l 2127 3051 l 2081 3041 l 2037 3030 l 1994 3020 l 1953 3010 l 1914 3000 l 1877 2990 l 1843 2981 l 1811 2972 l 1782 2964 l 1755 2956 l 1732 2950 l 1712 2944 l 1695 2939 l 1681 2935 l 1670 2931 l 1662 2929 l 1650 2925 l gs col0 s gr gr % arrowhead 0 slj n 1927 2953 m 1681 2935 l 1889 3067 l col0 s % Polyline 2 slj gs clippath 2869 3927 m 2986 3902 l 2926 3620 l 2918 3868 l 2809 3645 l cp eoclip n 2925 1800 m 2925 1801 l 2924 1803 l 2923 1806 l 2921 1812 l 2918 1819 l 2914 1829 l 2909 1842 l 2904 1858 l 2898 1875 l 2891 1896 l 2883 1918 l 2876 1942 l 2868 1969 l 2859 1997 l 2851 2027 l 2843 2058 l 2835 2091 l 2827 2126 l 2820 2163 l 2813 2203 l 2806 2244 l 2800 2289 l 2794 2336 l 2789 2388 l 2784 2443 l 2780 2502 l 2777 2565 l 2776 2631 l 2775 2700 l 2776 2762 l 2777 2824 l 2779 2885 l 2782 2945 l 2786 3002 l 2790 3058 l 2795 3112 l 2800 3164 l 2806 3214 l 2811 3263 l 2818 3311 l 2824 3357 l 2831 3402 l 2838 3446 l 2845 3489 l 2852 3531 l 2859 3572 l 2867 3611 l 2874 3649 l 2881 3685 l 2887 3719 l 2894 3750 l 2899 3779 l 2905 3805 l 2910 3828 l 2914 3847 l 2917 3863 l 2920 3876 l 2922 3886 l 2925 3900 l gs col0 s gr gr % arrowhead 0 slj n 2809 3645 m 2918 3868 l 2926 3620 l col0 s % Polyline 2 slj gs clippath 2941 3919 m 3061 3909 l 3036 3622 l 2997 3867 l 2917 3632 l cp eoclip n 2925 3000 m 3000 3900 l gs col0 s gr gr % arrowhead 0 slj n 2917 3632 m 2997 3867 l 3036 3622 l col0 s % Polyline 2 slj gs clippath 2980 2866 m 2989 2986 l 3277 2962 l 3033 2922 l 3267 2843 l cp eoclip n 4875 2775 m 3000 2925 l gs col0 s gr gr % arrowhead 0 slj n 3267 2843 m 3033 2922 l 3277 2962 l col0 s /Times-Roman ff 240.00 scf sf 2475 1575 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 2625 1650 m gs 1 -1 sc (3) col0 sh gr /Symbol ff 240.00 scf sf 4575 2325 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 240.00 scf sf 4725 2400 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 240.00 scf sf 4575 3375 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 240.00 scf sf 4725 3450 m gs 1 -1 sc (3) col0 sh gr /Symbol ff 240.00 scf sf 1200 2325 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 240.00 scf sf 1350 2400 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 240.00 scf sf 1200 3375 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 240.00 scf sf 1350 3450 m gs 1 -1 sc (3) col0 sh gr /Symbol ff 240.00 scf sf 1725 2325 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 240.00 scf sf 1875 2400 m gs 1 -1 sc (2) col0 sh gr /Times-Roman ff 240.00 scf sf 3300 2775 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 3450 2850 m gs 1 -1 sc (1) col0 sh gr /Times-Roman ff 240.00 scf sf 3300 3375 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 3450 3450 m gs 1 -1 sc (2) col0 sh gr /Times-Roman ff 240.00 scf sf 3300 2175 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 3450 2250 m gs 1 -1 sc (2) col0 sh gr /Times-Roman ff 240.00 scf sf 3300 4500 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 3450 4575 m gs 1 -1 sc (2) col0 sh gr /Times-Roman ff 240.00 scf sf 3300 3900 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 3450 3975 m gs 1 -1 sc (1) col0 sh gr /Times-Roman ff 240.00 scf sf 3300 1575 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 3450 1650 m gs 1 -1 sc (1) col0 sh gr /Times-Roman ff 240.00 scf sf 2325 3900 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 2475 3975 m gs 1 -1 sc (3) col0 sh gr /Symbol ff 240.00 scf sf 7875 2325 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 240.00 scf sf 8025 2400 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 240.00 scf sf 7875 3375 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 240.00 scf sf 8025 3450 m gs 1 -1 sc (3) col0 sh gr /Times-Roman ff 240.00 scf sf 6600 3375 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 6750 3450 m gs 1 -1 sc (2) col0 sh gr /Times-Roman ff 240.00 scf sf 6600 2175 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 6750 2250 m gs 1 -1 sc (2) col0 sh gr /Times-Roman ff 240.00 scf sf 6600 4500 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 6750 4575 m gs 1 -1 sc (2) col0 sh gr /Times-Roman ff 240.00 scf sf 6600 3900 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 6750 3975 m gs 1 -1 sc (1) col0 sh gr /Times-Roman ff 240.00 scf sf 6600 1575 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 6750 1650 m gs 1 -1 sc (1) col0 sh gr /Times-Roman ff 240.00 scf sf 5625 2850 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 5775 2925 m gs 1 -1 sc (3) col0 sh gr /Times-Roman ff 240.00 scf sf 5625 3900 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 5775 3975 m gs 1 -1 sc (3) col0 sh gr /Times-Roman ff 240.00 scf sf 5775 1575 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 5925 1650 m gs 1 -1 sc (3) col0 sh gr /Times-Roman ff 240.00 scf sf 6600 2775 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 6750 2850 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 240.00 scf sf 8400 2325 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 240.00 scf sf 8550 2400 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 240.00 scf sf 11775 2325 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 240.00 scf sf 11925 2400 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 240.00 scf sf 3000 2325 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 240.00 scf sf 3150 2400 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 240.00 scf sf 3000 3525 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 240.00 scf sf 3150 3600 m gs 1 -1 sc (3) col0 sh gr /Symbol ff 240.00 scf sf 2475 2325 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 240.00 scf sf 2625 2400 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 240.00 scf sf 5775 2325 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 240.00 scf sf 5925 2400 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 240.00 scf sf 9150 2325 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 240.00 scf sf 9300 2400 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 300.00 scf sf 10875 2382 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 11063 2475 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 10275 2382 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 10463 2475 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 345.00 scf sf 10650 2400 m gs 1 -1 sc (+) col0 sh gr /Symbol ff 300.00 scf sf 4125 2457 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 4313 2550 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 3525 2457 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 3713 2550 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 345.00 scf sf 3900 2475 m gs 1 -1 sc (+) col0 sh gr /Symbol ff 240.00 scf sf 6300 2325 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 240.00 scf sf 6450 2400 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 240.00 scf sf 9675 2325 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 240.00 scf sf 9825 2400 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 240.00 scf sf 6300 3525 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 240.00 scf sf 6450 3600 m gs 1 -1 sc (3) col0 sh gr /Symbol ff 240.00 scf sf 9675 3525 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 240.00 scf sf 9825 3600 m gs 1 -1 sc (3) col0 sh gr /Symbol ff 255.00 scf sf 4350 825 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 255.00 scf sf 4500 975 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 255.00 scf sf 7650 825 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 255.00 scf sf 7800 975 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 255.00 scf sf 2550 375 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 255.00 scf sf 2700 525 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 255.00 scf sf 3813 300 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 255.00 scf sf 3963 450 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 255.00 scf sf 5613 375 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 255.00 scf sf 5763 525 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 255.00 scf sf 7113 300 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 255.00 scf sf 7263 450 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 255.00 scf sf 9063 300 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 255.00 scf sf 9213 450 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 240.00 scf sf 2325 2850 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 2475 2925 m gs 1 -1 sc (3) col0 sh gr /Symbol ff 180.00 scf sf 2469 2573 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 180.00 scf sf 2585 2630 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 180.00 scf sf 2100 2573 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 180.00 scf sf 2216 2630 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 2331 2584 m gs 1 -1 sc (+) col0 sh gr /Symbol ff 180.00 scf sf 5769 2648 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 180.00 scf sf 5885 2705 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 180.00 scf sf 5400 2648 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 180.00 scf sf 5516 2705 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 5631 2659 m gs 1 -1 sc (+) col0 sh gr /Symbol ff 180.00 scf sf 9144 2648 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 180.00 scf sf 9260 2705 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 180.00 scf sf 8775 2648 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 180.00 scf sf 8891 2705 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 9006 2659 m gs 1 -1 sc (+) col0 sh gr % Ellipse n 4725 3975 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 1425 3975 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 11325 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 11306 3979 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 1350 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 4685 1543 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 8025 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 8025 3975 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 9600 2881 106 106 0 360 DrawEllipse gs col0 s gr % Ellipse n 6375 4050 106 106 0 360 DrawEllipse gs col0 s gr % Ellipse n 8250 2850 106 106 0 360 DrawEllipse gs col0 s gr % Ellipse n 6300 1725 106 106 0 360 DrawEllipse gs col0 s gr % Ellipse n 2925 2881 106 106 0 360 DrawEllipse gs col0 s gr % Ellipse n 9675 3975 106 106 0 360 DrawEllipse gs col0 s gr % Ellipse n 6225 2881 106 106 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 7183 1559 m 7242 1455 l 6992 1312 l 7171 1484 l 6932 1417 l cp eoclip n 5400 1425 m 5401 1424 l 5403 1423 l 5407 1421 l 5414 1418 l 5423 1413 l 5435 1407 l 5450 1399 l 5468 1391 l 5488 1381 l 5511 1370 l 5537 1358 l 5564 1345 l 5594 1333 l 5625 1320 l 5658 1307 l 5692 1294 l 5727 1281 l 5763 1269 l 5802 1258 l 5841 1247 l 5883 1237 l 5926 1228 l 5972 1219 l 6021 1212 l 6072 1206 l 6125 1202 l 6182 1199 l 6240 1199 l 6300 1200 l 6360 1204 l 6418 1209 l 6475 1217 l 6528 1225 l 6579 1236 l 6628 1247 l 6674 1259 l 6717 1272 l 6759 1285 l 6798 1299 l 6837 1314 l 6873 1329 l 6908 1344 l 6942 1360 l 6975 1376 l 7006 1391 l 7036 1407 l 7063 1421 l 7089 1435 l 7112 1448 l 7132 1460 l 7150 1470 l 7165 1479 l 7177 1486 l 7186 1492 l 7200 1500 l gs col0 s gr gr % arrowhead 0 slj n 6932 1417 m 7171 1484 l 6992 1312 l col0 s % Polyline 2 slj gs clippath 10558 1484 m 10617 1380 l 10367 1237 l 10546 1409 l 10307 1342 l cp eoclip n 8775 1350 m 8776 1349 l 8778 1348 l 8782 1346 l 8789 1343 l 8798 1338 l 8810 1332 l 8825 1324 l 8843 1316 l 8863 1306 l 8886 1295 l 8912 1283 l 8939 1270 l 8969 1258 l 9000 1245 l 9033 1232 l 9067 1219 l 9102 1206 l 9138 1194 l 9177 1183 l 9216 1172 l 9258 1162 l 9301 1153 l 9347 1144 l 9396 1137 l 9447 1131 l 9500 1127 l 9557 1124 l 9615 1124 l 9675 1125 l 9735 1129 l 9793 1134 l 9850 1142 l 9903 1150 l 9954 1161 l 10003 1172 l 10049 1184 l 10092 1197 l 10134 1210 l 10173 1224 l 10212 1239 l 10248 1254 l 10283 1269 l 10317 1285 l 10350 1301 l 10381 1316 l 10411 1332 l 10438 1346 l 10464 1360 l 10487 1373 l 10507 1385 l 10525 1395 l 10540 1404 l 10552 1411 l 10561 1417 l 10575 1425 l gs col0 s gr gr % arrowhead 0 slj n 10307 1342 m 10546 1409 l 10367 1237 l col0 s % Polyline 2 slj gs clippath 1106 1900 m 1012 1826 l 834 2052 l 1030 1901 l 928 2126 l cp eoclip n 1125 3675 m 1124 3674 l 1123 3672 l 1120 3668 l 1116 3662 l 1110 3653 l 1103 3641 l 1093 3626 l 1082 3609 l 1069 3588 l 1055 3565 l 1039 3540 l 1022 3512 l 1005 3482 l 986 3450 l 968 3417 l 949 3383 l 931 3347 l 913 3311 l 895 3273 l 877 3234 l 860 3194 l 844 3152 l 829 3110 l 814 3065 l 801 3018 l 788 2970 l 777 2919 l 767 2867 l 760 2812 l 754 2756 l 750 2700 l 749 2636 l 751 2575 l 756 2517 l 763 2462 l 772 2411 l 783 2363 l 796 2318 l 810 2276 l 825 2237 l 841 2199 l 858 2164 l 875 2130 l 893 2098 l 912 2067 l 930 2038 l 948 2011 l 965 1986 l 982 1963 l 997 1943 l 1010 1925 l 1022 1910 l 1031 1898 l 1039 1889 l 1050 1875 l gs col0 s gr gr % arrowhead 0 slj n 928 2126 m 1030 1901 l 834 2052 l col0 s % Polyline 2 slj gs clippath 11070 1892 m 10976 1818 l 10798 2044 l 10994 1893 l 10892 2118 l cp eoclip n 11089 3667 m 11088 3666 l 11087 3664 l 11084 3660 l 11080 3654 l 11074 3645 l 11067 3633 l 11057 3618 l 11046 3601 l 11033 3580 l 11019 3557 l 11003 3532 l 10986 3504 l 10969 3474 l 10950 3442 l 10932 3409 l 10913 3375 l 10895 3339 l 10877 3303 l 10859 3265 l 10841 3226 l 10824 3186 l 10808 3144 l 10793 3102 l 10778 3057 l 10765 3010 l 10752 2962 l 10741 2911 l 10731 2859 l 10724 2804 l 10718 2748 l 10714 2692 l 10713 2628 l 10715 2567 l 10720 2509 l 10727 2454 l 10736 2403 l 10747 2355 l 10760 2310 l 10774 2268 l 10789 2229 l 10805 2191 l 10822 2156 l 10839 2122 l 10857 2090 l 10876 2059 l 10894 2030 l 10912 2003 l 10929 1978 l 10946 1955 l 10961 1935 l 10974 1917 l 10986 1902 l 10995 1890 l 11003 1881 l 11014 1867 l gs col0 s gr gr % arrowhead 0 slj n 10892 2118 m 10994 1893 l 10798 2044 l col0 s % Polyline 2 slj gs clippath 7911 1916 m 7817 1842 l 7639 2068 l 7835 1917 l 7733 2142 l cp eoclip n 7930 3691 m 7929 3690 l 7928 3688 l 7925 3684 l 7921 3678 l 7915 3669 l 7908 3657 l 7898 3642 l 7887 3625 l 7874 3604 l 7860 3581 l 7844 3556 l 7827 3528 l 7810 3498 l 7791 3466 l 7773 3433 l 7754 3399 l 7736 3363 l 7718 3327 l 7700 3289 l 7682 3250 l 7665 3210 l 7649 3168 l 7634 3126 l 7619 3081 l 7606 3034 l 7593 2986 l 7582 2935 l 7572 2883 l 7565 2828 l 7559 2772 l 7555 2716 l 7554 2652 l 7556 2591 l 7561 2533 l 7568 2478 l 7577 2427 l 7588 2379 l 7601 2334 l 7615 2292 l 7630 2253 l 7646 2215 l 7663 2180 l 7680 2146 l 7698 2114 l 7717 2083 l 7735 2054 l 7753 2027 l 7770 2002 l 7787 1979 l 7802 1959 l 7815 1941 l 7827 1926 l 7836 1914 l 7844 1905 l 7855 1891 l gs col0 s gr gr % arrowhead 0 slj n 7733 2142 m 7835 1917 l 7639 2068 l col0 s % Polyline 2 slj gs clippath 9539 2785 m 9658 2794 l 9681 2507 l 9603 2742 l 9561 2498 l cp eoclip n 9675 1800 m 9600 2775 l gs col0 s gr gr % arrowhead 0 slj n 9561 2498 m 9603 2742 l 9681 2507 l col0 s % Polyline 2 slj gs clippath 8313 2789 m 8306 2908 l 8593 2926 l 8358 2852 l 8601 2807 l cp eoclip n 9525 2925 m 8325 2850 l gs col0 s gr gr % arrowhead 0 slj n 8601 2807 m 8358 2852 l 8593 2926 l col0 s % Polyline 2 slj gs clippath 8329 2863 m 8291 2977 l 8564 3067 l 8356 2935 l 8602 2953 l cp eoclip n 11550 2850 m 11549 2850 l 11547 2851 l 11544 2852 l 11539 2854 l 11531 2856 l 11520 2860 l 11507 2864 l 11491 2869 l 11472 2875 l 11449 2882 l 11424 2890 l 11395 2899 l 11364 2908 l 11331 2918 l 11295 2929 l 11256 2940 l 11216 2951 l 11174 2963 l 11130 2974 l 11085 2986 l 11039 2998 l 10991 3009 l 10942 3021 l 10891 3032 l 10840 3044 l 10786 3054 l 10731 3065 l 10675 3075 l 10616 3085 l 10555 3094 l 10492 3103 l 10426 3112 l 10358 3120 l 10288 3127 l 10214 3133 l 10138 3139 l 10060 3144 l 9981 3147 l 9900 3150 l 9815 3151 l 9732 3151 l 9651 3150 l 9573 3147 l 9498 3144 l 9426 3139 l 9357 3134 l 9292 3128 l 9229 3122 l 9168 3114 l 9110 3106 l 9054 3098 l 9000 3089 l 8948 3080 l 8898 3071 l 8849 3061 l 8802 3051 l 8756 3041 l 8712 3030 l 8669 3020 l 8628 3010 l 8589 3000 l 8552 2990 l 8518 2981 l 8486 2972 l 8457 2964 l 8430 2956 l 8407 2950 l 8387 2944 l 8370 2939 l 8356 2935 l 8345 2931 l 8337 2929 l 8325 2925 l gs col0 s gr gr % arrowhead 0 slj n 8602 2953 m 8356 2935 l 8564 3067 l col0 s % Polyline 2 slj gs clippath 9544 3927 m 9661 3902 l 9601 3620 l 9593 3868 l 9484 3645 l cp eoclip n 9600 1800 m 9600 1801 l 9599 1803 l 9598 1806 l 9596 1812 l 9593 1819 l 9589 1829 l 9584 1842 l 9579 1858 l 9573 1875 l 9566 1896 l 9558 1918 l 9551 1942 l 9543 1969 l 9534 1997 l 9526 2027 l 9518 2058 l 9510 2091 l 9502 2126 l 9495 2163 l 9488 2203 l 9481 2244 l 9475 2289 l 9469 2336 l 9464 2388 l 9459 2443 l 9455 2502 l 9452 2565 l 9451 2631 l 9450 2700 l 9451 2762 l 9452 2824 l 9454 2885 l 9457 2945 l 9461 3002 l 9465 3058 l 9470 3112 l 9475 3164 l 9481 3214 l 9486 3263 l 9493 3311 l 9499 3357 l 9506 3402 l 9513 3446 l 9520 3489 l 9527 3531 l 9534 3572 l 9542 3611 l 9549 3649 l 9556 3685 l 9562 3719 l 9569 3750 l 9574 3779 l 9580 3805 l 9585 3828 l 9589 3847 l 9592 3863 l 9595 3876 l 9597 3886 l 9600 3900 l gs col0 s gr gr % arrowhead 0 slj n 9484 3645 m 9593 3868 l 9601 3620 l col0 s % Polyline 2 slj gs clippath 9616 3919 m 9736 3909 l 9711 3622 l 9672 3867 l 9592 3632 l cp eoclip n 9600 3000 m 9675 3900 l gs col0 s gr gr % arrowhead 0 slj n 9592 3632 m 9672 3867 l 9711 3622 l col0 s % Polyline 2 slj gs clippath 9655 2866 m 9664 2986 l 9952 2962 l 9708 2922 l 9942 2843 l cp eoclip n 11550 2775 m 9675 2925 l gs col0 s gr gr % arrowhead 0 slj n 9942 2843 m 9708 2922 l 9952 2962 l col0 s % Polyline 2 slj gs clippath 6425 3993 m 6445 4111 l 6729 4064 l 6483 4045 l 6709 3946 l cp eoclip n 7350 3900 m 6450 4050 l gs col0 s gr gr % arrowhead 0 slj n 6709 3946 m 6483 4045 l 6729 4064 l col0 s % Polyline 2 slj gs clippath 5470 3838 m 5449 3956 l 5733 4007 l 5508 3906 l 5754 3889 l cp eoclip n 6300 4050 m 5475 3900 l gs col0 s gr gr % arrowhead 0 slj n 5754 3889 m 5508 3906 l 5733 4007 l col0 s % Polyline 2 slj gs clippath 5496 3917 m 5428 4015 l 5665 4179 l 5502 3994 l 5733 4081 l cp eoclip n 7350 3975 m 7349 3976 l 7346 3977 l 7342 3980 l 7335 3984 l 7324 3990 l 7311 3997 l 7294 4007 l 7274 4017 l 7251 4030 l 7226 4044 l 7197 4058 l 7166 4074 l 7134 4090 l 7099 4106 l 7063 4123 l 7026 4139 l 6987 4155 l 6947 4170 l 6905 4185 l 6862 4200 l 6817 4213 l 6770 4226 l 6721 4237 l 6669 4248 l 6615 4257 l 6558 4264 l 6499 4270 l 6437 4274 l 6375 4275 l 6313 4274 l 6252 4270 l 6194 4264 l 6139 4257 l 6087 4248 l 6038 4237 l 5992 4226 l 5948 4213 l 5907 4200 l 5867 4185 l 5829 4170 l 5793 4155 l 5758 4139 l 5725 4123 l 5693 4106 l 5663 4090 l 5634 4074 l 5607 4058 l 5582 4044 l 5560 4030 l 5540 4017 l 5523 4007 l 5508 3997 l 5497 3990 l 5488 3984 l 5475 3975 l gs col0 s gr gr % arrowhead 0 slj n 5733 4081 m 5502 3994 l 5665 4179 l col0 s % Polyline 2 slj gs clippath 8191 2794 m 8311 2784 l 8286 2497 l 8247 2742 l 8167 2507 l cp eoclip n 8175 1875 m 8250 2775 l gs col0 s gr gr % arrowhead 0 slj n 8167 2507 m 8247 2742 l 8286 2497 l col0 s % Polyline 2 slj gs clippath 8113 3683 m 8232 3696 l 8265 3410 l 8179 3642 l 8145 3396 l cp eoclip n 8250 3000 m 8175 3675 l gs col0 s gr gr % arrowhead 0 slj n 8145 3396 m 8179 3642 l 8265 3410 l col0 s % Polyline 2 slj gs clippath 8188 3668 m 8301 3709 l 8398 3438 l 8261 3644 l 8285 3397 l cp eoclip n 8250 1875 m 8250 1876 l 8251 1879 l 8252 1884 l 8254 1891 l 8257 1902 l 8261 1915 l 8266 1933 l 8271 1953 l 8277 1977 l 8284 2003 l 8292 2033 l 8299 2064 l 8307 2098 l 8316 2133 l 8324 2170 l 8332 2208 l 8340 2247 l 8348 2287 l 8355 2329 l 8362 2372 l 8369 2417 l 8375 2464 l 8381 2513 l 8386 2564 l 8391 2617 l 8395 2673 l 8398 2731 l 8399 2790 l 8400 2850 l 8399 2914 l 8397 2975 l 8394 3033 l 8390 3088 l 8385 3139 l 8379 3187 l 8372 3232 l 8365 3274 l 8358 3313 l 8350 3351 l 8342 3386 l 8333 3420 l 8324 3452 l 8316 3483 l 8307 3512 l 8298 3539 l 8290 3564 l 8282 3587 l 8275 3607 l 8269 3625 l 8263 3640 l 8259 3652 l 8255 3661 l 8250 3675 l gs col0 s gr gr % arrowhead 0 slj n 8285 3397 m 8261 3644 l 8398 3438 l col0 s % Polyline 2 slj gs clippath 6350 1668 m 6370 1786 l 6654 1739 l 6408 1720 l 6634 1621 l cp eoclip n 7275 1575 m 6375 1725 l gs col0 s gr gr % arrowhead 0 slj n 6634 1621 m 6408 1720 l 6654 1739 l col0 s % Polyline 2 slj gs clippath 5395 1513 m 5374 1631 l 5658 1682 l 5433 1581 l 5679 1564 l cp eoclip n 6225 1725 m 5400 1575 l gs col0 s gr gr % arrowhead 0 slj n 5679 1564 m 5433 1581 l 5658 1682 l col0 s % Polyline 2 slj gs clippath 5421 1592 m 5353 1690 l 5590 1854 l 5427 1669 l 5658 1756 l cp eoclip n 7275 1650 m 7274 1651 l 7271 1652 l 7267 1655 l 7260 1659 l 7249 1665 l 7236 1672 l 7219 1682 l 7199 1692 l 7176 1705 l 7151 1719 l 7122 1733 l 7091 1749 l 7059 1765 l 7024 1781 l 6988 1798 l 6951 1814 l 6912 1830 l 6872 1845 l 6830 1860 l 6787 1875 l 6742 1888 l 6695 1901 l 6646 1912 l 6594 1923 l 6540 1932 l 6483 1939 l 6424 1945 l 6362 1949 l 6300 1950 l 6238 1949 l 6177 1945 l 6119 1939 l 6064 1932 l 6012 1923 l 5963 1912 l 5917 1901 l 5873 1888 l 5832 1875 l 5792 1860 l 5754 1845 l 5718 1830 l 5683 1814 l 5650 1798 l 5618 1781 l 5588 1765 l 5559 1749 l 5532 1733 l 5507 1719 l 5485 1705 l 5465 1692 l 5448 1682 l 5433 1672 l 5422 1665 l 5413 1659 l 5400 1650 l gs col0 s gr gr % arrowhead 0 slj n 5658 1756 m 5427 1669 l 5590 1854 l col0 s % Polyline 2 slj gs clippath 2864 2785 m 2983 2794 l 3006 2507 l 2928 2742 l 2886 2498 l cp eoclip n 3000 1800 m 2925 2775 l gs col0 s gr gr % arrowhead 0 slj n 2886 2498 m 2928 2742 l 3006 2507 l col0 s % Polyline 2 slj gs clippath 1638 2789 m 1631 2908 l 1918 2926 l 1683 2852 l 1926 2807 l cp eoclip n 2850 2925 m 1650 2850 l gs col0 s gr gr % arrowhead 0 slj n 1926 2807 m 1683 2852 l 1918 2926 l col0 s % Polyline 2 slj gs clippath 3928 1574 m 3987 1470 l 3737 1327 l 3916 1499 l 3677 1432 l cp eoclip n 2145 1440 m 2146 1439 l 2148 1438 l 2152 1436 l 2159 1433 l 2168 1428 l 2180 1422 l 2195 1414 l 2213 1406 l 2233 1396 l 2256 1385 l 2282 1373 l 2309 1360 l 2339 1348 l 2370 1335 l 2403 1322 l 2437 1309 l 2472 1296 l 2508 1284 l 2547 1273 l 2586 1262 l 2628 1252 l 2671 1243 l 2717 1234 l 2766 1227 l 2817 1221 l 2870 1217 l 2927 1214 l 2985 1214 l 3045 1215 l 3105 1219 l 3163 1224 l 3220 1232 l 3273 1240 l 3324 1251 l 3373 1262 l 3419 1274 l 3462 1287 l 3504 1300 l 3543 1314 l 3582 1329 l 3618 1344 l 3653 1359 l 3687 1375 l 3720 1391 l 3751 1406 l 3781 1422 l 3808 1436 l 3834 1450 l 3857 1463 l 3877 1475 l 3895 1485 l 3910 1494 l 3922 1501 l 3931 1507 l 3945 1515 l gs col0 s gr gr % arrowhead 0 slj n 3677 1432 m 3916 1499 l 3737 1327 l col0 s % Polyline 2 slj gs clippath 9725 3918 m 9745 4036 l 10029 3989 l 9783 3970 l 10009 3871 l cp eoclip n 10650 3825 m 9750 3975 l gs col0 s gr gr % arrowhead 0 slj n 10009 3871 m 9783 3970 l 10029 3989 l col0 s % Polyline 2 slj gs clippath 8770 3763 m 8749 3881 l 9033 3932 l 8808 3831 l 9054 3814 l cp eoclip n 9600 3975 m 8775 3825 l gs col0 s gr gr % arrowhead 0 slj n 9054 3814 m 8808 3831 l 9033 3932 l col0 s % Polyline 2 slj gs clippath 8796 3842 m 8728 3940 l 8965 4104 l 8802 3919 l 9033 4006 l cp eoclip n 10650 3900 m 10649 3901 l 10646 3902 l 10642 3905 l 10635 3909 l 10624 3915 l 10611 3922 l 10594 3932 l 10574 3942 l 10551 3955 l 10526 3969 l 10497 3983 l 10466 3999 l 10434 4015 l 10399 4031 l 10363 4048 l 10326 4064 l 10287 4080 l 10247 4095 l 10205 4110 l 10162 4125 l 10117 4138 l 10070 4151 l 10021 4162 l 9969 4173 l 9915 4182 l 9858 4189 l 9799 4195 l 9737 4199 l 9675 4200 l 9613 4199 l 9552 4195 l 9494 4189 l 9439 4182 l 9387 4173 l 9338 4162 l 9292 4151 l 9248 4138 l 9207 4125 l 9167 4110 l 9129 4095 l 9093 4080 l 9058 4064 l 9025 4048 l 8993 4031 l 8963 4015 l 8934 3999 l 8907 3983 l 8882 3969 l 8860 3955 l 8840 3942 l 8823 3932 l 8808 3922 l 8797 3915 l 8788 3909 l 8775 3900 l gs col0 s gr gr % arrowhead 0 slj n 9033 4006 m 8802 3919 l 8965 4104 l col0 s % Polyline 2 slj gs clippath 6164 2785 m 6283 2794 l 6306 2507 l 6228 2742 l 6186 2498 l cp eoclip n 6300 1800 m 6225 2775 l gs col0 s gr gr % arrowhead 0 slj n 6186 2498 m 6228 2742 l 6306 2507 l col0 s % Polyline 2 slj gs clippath 4938 2789 m 4931 2908 l 5218 2926 l 4983 2852 l 5226 2807 l cp eoclip n 6150 2925 m 4950 2850 l gs col0 s gr gr % arrowhead 0 slj n 5226 2807 m 4983 2852 l 5218 2926 l col0 s % Polyline 2 slj gs clippath 4954 2863 m 4916 2977 l 5189 3067 l 4981 2935 l 5227 2953 l cp eoclip n 8175 2850 m 8174 2850 l 8172 2851 l 8169 2852 l 8164 2854 l 8156 2856 l 8145 2860 l 8132 2864 l 8116 2869 l 8097 2875 l 8074 2882 l 8049 2890 l 8020 2899 l 7989 2908 l 7956 2918 l 7920 2929 l 7881 2940 l 7841 2951 l 7799 2963 l 7755 2974 l 7710 2986 l 7664 2998 l 7616 3009 l 7567 3021 l 7516 3032 l 7465 3044 l 7411 3054 l 7356 3065 l 7300 3075 l 7241 3085 l 7180 3094 l 7117 3103 l 7051 3112 l 6983 3120 l 6913 3127 l 6839 3133 l 6763 3139 l 6685 3144 l 6606 3147 l 6525 3150 l 6440 3151 l 6357 3151 l 6276 3150 l 6198 3147 l 6123 3144 l 6051 3139 l 5982 3134 l 5917 3128 l 5854 3122 l 5793 3114 l 5735 3106 l 5679 3098 l 5625 3089 l 5573 3080 l 5523 3071 l 5474 3061 l 5427 3051 l 5381 3041 l 5337 3030 l 5294 3020 l 5253 3010 l 5214 3000 l 5177 2990 l 5143 2981 l 5111 2972 l 5082 2964 l 5055 2956 l 5032 2950 l 5012 2944 l 4995 2939 l 4981 2935 l 4970 2931 l 4962 2929 l 4950 2925 l gs col0 s gr gr % arrowhead 0 slj n 5227 2953 m 4981 2935 l 5189 3067 l col0 s % Polyline 2 slj gs clippath 6169 3927 m 6286 3902 l 6226 3620 l 6218 3868 l 6109 3645 l cp eoclip n 6225 1800 m 6225 1801 l 6224 1803 l 6223 1806 l 6221 1812 l 6218 1819 l 6214 1829 l 6209 1842 l 6204 1858 l 6198 1875 l 6191 1896 l 6183 1918 l 6176 1942 l 6168 1969 l 6159 1997 l 6151 2027 l 6143 2058 l 6135 2091 l 6127 2126 l 6120 2163 l 6113 2203 l 6106 2244 l 6100 2289 l 6094 2336 l 6089 2388 l 6084 2443 l 6080 2502 l 6077 2565 l 6076 2631 l 6075 2700 l 6076 2762 l 6077 2824 l 6079 2885 l 6082 2945 l 6086 3002 l 6090 3058 l 6095 3112 l 6100 3164 l 6106 3214 l 6111 3263 l 6118 3311 l 6124 3357 l 6131 3402 l 6138 3446 l 6145 3489 l 6152 3531 l 6159 3572 l 6167 3611 l 6174 3649 l 6181 3685 l 6187 3719 l 6194 3750 l 6199 3779 l 6205 3805 l 6210 3828 l 6214 3847 l 6217 3863 l 6220 3876 l 6222 3886 l 6225 3900 l gs col0 s gr gr % arrowhead 0 slj n 6109 3645 m 6218 3868 l 6226 3620 l col0 s % Polyline 2 slj gs clippath 6241 3919 m 6361 3909 l 6336 3622 l 6297 3867 l 6217 3632 l cp eoclip n 6225 3000 m 6300 3900 l gs col0 s gr gr % arrowhead 0 slj n 6217 3632 m 6297 3867 l 6336 3622 l col0 s % Polyline 2 slj gs clippath 6280 2866 m 6289 2986 l 6577 2962 l 6333 2922 l 6567 2843 l cp eoclip n 8175 2775 m 6300 2925 l gs col0 s gr gr % arrowhead 0 slj n 6567 2843 m 6333 2922 l 6577 2962 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 6199 1706 m 6274 1612 l 6049 1432 l 6199 1629 l 5974 1525 l cp eoclip n 3000 1650 m 3001 1649 l 3002 1648 l 3005 1645 l 3010 1641 l 3018 1635 l 3027 1627 l 3039 1617 l 3054 1604 l 3072 1590 l 3092 1573 l 3116 1554 l 3142 1534 l 3170 1511 l 3201 1488 l 3235 1463 l 3270 1436 l 3307 1410 l 3346 1382 l 3387 1355 l 3429 1327 l 3472 1299 l 3517 1272 l 3563 1245 l 3611 1219 l 3660 1193 l 3710 1169 l 3763 1145 l 3817 1122 l 3873 1100 l 3932 1079 l 3992 1060 l 4056 1042 l 4122 1026 l 4192 1011 l 4264 999 l 4338 989 l 4416 981 l 4495 977 l 4575 975 l 4652 976 l 4728 981 l 4802 988 l 4875 997 l 4945 1008 l 5013 1022 l 5079 1036 l 5142 1053 l 5203 1071 l 5262 1090 l 5319 1110 l 5374 1131 l 5427 1154 l 5479 1177 l 5530 1201 l 5579 1225 l 5626 1250 l 5673 1276 l 5718 1302 l 5763 1328 l 5805 1355 l 5847 1381 l 5887 1407 l 5926 1433 l 5962 1458 l 5997 1482 l 6030 1505 l 6060 1526 l 6088 1547 l 6114 1565 l 6136 1582 l 6156 1597 l 6173 1610 l 6188 1621 l 6199 1630 l 6208 1637 l 6215 1642 l 6225 1650 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 5974 1525 m 6199 1629 l 6049 1432 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 9510 1680 m 9585 1586 l 9360 1406 l 9510 1603 l 9285 1499 l cp eoclip n 6311 1624 m 6312 1623 l 6313 1622 l 6316 1619 l 6321 1615 l 6329 1609 l 6338 1601 l 6350 1591 l 6365 1578 l 6383 1564 l 6403 1547 l 6427 1528 l 6453 1508 l 6481 1485 l 6512 1462 l 6546 1437 l 6581 1410 l 6618 1384 l 6657 1356 l 6698 1329 l 6740 1301 l 6783 1273 l 6828 1246 l 6874 1219 l 6922 1193 l 6971 1167 l 7021 1143 l 7074 1119 l 7128 1096 l 7184 1074 l 7243 1053 l 7303 1034 l 7367 1016 l 7433 1000 l 7503 985 l 7575 973 l 7649 963 l 7727 955 l 7806 951 l 7886 949 l 7963 950 l 8039 955 l 8113 962 l 8186 971 l 8256 982 l 8324 996 l 8390 1010 l 8453 1027 l 8514 1045 l 8573 1064 l 8630 1084 l 8685 1105 l 8738 1128 l 8790 1151 l 8841 1175 l 8890 1199 l 8937 1224 l 8984 1250 l 9029 1276 l 9074 1302 l 9116 1329 l 9158 1355 l 9198 1381 l 9237 1407 l 9273 1432 l 9308 1456 l 9341 1479 l 9371 1500 l 9399 1521 l 9425 1539 l 9447 1556 l 9467 1571 l 9484 1584 l 9499 1595 l 9510 1604 l 9519 1611 l 9526 1616 l 9536 1624 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 9285 1499 m 9510 1603 l 9360 1406 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 4898 2809 m 5011 2768 l 4914 2497 l 4939 2744 l 4801 2538 l cp eoclip n 1650 2775 m 1650 2774 l 1651 2772 l 1653 2767 l 1655 2760 l 1658 2750 l 1663 2736 l 1668 2718 l 1676 2696 l 1684 2669 l 1695 2638 l 1707 2602 l 1720 2561 l 1735 2516 l 1752 2467 l 1771 2413 l 1791 2356 l 1812 2295 l 1835 2231 l 1860 2164 l 1885 2094 l 1912 2023 l 1940 1950 l 1969 1876 l 1999 1801 l 2030 1725 l 2061 1649 l 2094 1574 l 2128 1498 l 2162 1424 l 2197 1350 l 2233 1278 l 2270 1207 l 2308 1138 l 2347 1070 l 2387 1004 l 2428 940 l 2470 878 l 2513 819 l 2558 762 l 2605 708 l 2653 657 l 2703 609 l 2754 564 l 2807 523 l 2862 487 l 2919 454 l 2978 427 l 3038 405 l 3099 389 l 3162 378 l 3225 375 l 3286 378 l 3347 388 l 3407 403 l 3467 423 l 3525 449 l 3582 479 l 3637 513 l 3691 552 l 3744 593 l 3795 639 l 3845 687 l 3894 738 l 3941 791 l 3987 847 l 4032 905 l 4076 966 l 4119 1028 l 4161 1092 l 4202 1158 l 4243 1225 l 4282 1294 l 4321 1364 l 4359 1435 l 4397 1507 l 4434 1579 l 4470 1652 l 4505 1725 l 4539 1798 l 4572 1870 l 4605 1942 l 4636 2012 l 4667 2081 l 4696 2148 l 4723 2214 l 4750 2276 l 4775 2336 l 4798 2392 l 4820 2445 l 4840 2495 l 4858 2540 l 4874 2581 l 4889 2618 l 4902 2651 l 4913 2679 l 4922 2703 l 4930 2723 l 4936 2740 l 4941 2752 l 4945 2761 l 4950 2775 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 4801 2538 m 4939 2744 l 4914 2497 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 6173 2809 m 6286 2768 l 6189 2497 l 6214 2744 l 6076 2538 l cp eoclip n 2925 2775 m 2925 2774 l 2926 2772 l 2928 2767 l 2930 2760 l 2933 2750 l 2938 2736 l 2943 2718 l 2951 2696 l 2959 2669 l 2970 2638 l 2982 2602 l 2995 2561 l 3010 2516 l 3027 2467 l 3046 2413 l 3066 2356 l 3087 2295 l 3110 2231 l 3135 2164 l 3160 2094 l 3187 2023 l 3215 1950 l 3244 1876 l 3274 1801 l 3305 1725 l 3336 1649 l 3369 1574 l 3403 1498 l 3437 1424 l 3472 1350 l 3508 1278 l 3545 1207 l 3583 1138 l 3622 1070 l 3662 1004 l 3703 940 l 3745 878 l 3788 819 l 3833 762 l 3880 708 l 3928 657 l 3978 609 l 4029 564 l 4082 523 l 4137 487 l 4194 454 l 4253 427 l 4313 405 l 4374 389 l 4437 378 l 4500 375 l 4561 378 l 4622 388 l 4682 403 l 4742 423 l 4800 449 l 4857 479 l 4912 513 l 4966 552 l 5019 593 l 5070 639 l 5120 687 l 5169 738 l 5216 791 l 5262 847 l 5307 905 l 5351 966 l 5394 1028 l 5436 1092 l 5477 1158 l 5518 1225 l 5557 1294 l 5596 1364 l 5634 1435 l 5672 1507 l 5709 1579 l 5745 1652 l 5780 1725 l 5814 1798 l 5847 1870 l 5880 1942 l 5911 2012 l 5942 2081 l 5971 2148 l 5998 2214 l 6025 2276 l 6050 2336 l 6073 2392 l 6095 2445 l 6115 2495 l 6133 2540 l 6149 2581 l 6164 2618 l 6177 2651 l 6188 2679 l 6197 2703 l 6205 2723 l 6211 2740 l 6216 2752 l 6220 2761 l 6225 2775 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 6076 2538 m 6214 2744 l 6189 2497 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 8198 2809 m 8311 2768 l 8214 2497 l 8239 2744 l 8101 2538 l cp eoclip n 4950 2775 m 4950 2774 l 4951 2772 l 4953 2767 l 4955 2760 l 4958 2750 l 4963 2736 l 4968 2718 l 4976 2696 l 4984 2669 l 4995 2638 l 5007 2602 l 5020 2561 l 5035 2516 l 5052 2467 l 5071 2413 l 5091 2356 l 5112 2295 l 5135 2231 l 5160 2164 l 5185 2094 l 5212 2023 l 5240 1950 l 5269 1876 l 5299 1801 l 5330 1725 l 5361 1649 l 5394 1574 l 5428 1498 l 5462 1424 l 5497 1350 l 5533 1278 l 5570 1207 l 5608 1138 l 5647 1070 l 5687 1004 l 5728 940 l 5770 878 l 5813 819 l 5858 762 l 5905 708 l 5953 657 l 6003 609 l 6054 564 l 6107 523 l 6162 487 l 6219 454 l 6278 427 l 6338 405 l 6399 389 l 6462 378 l 6525 375 l 6586 378 l 6647 388 l 6707 403 l 6767 423 l 6825 449 l 6882 479 l 6937 513 l 6991 552 l 7044 593 l 7095 639 l 7145 687 l 7194 738 l 7241 791 l 7287 847 l 7332 905 l 7376 966 l 7419 1028 l 7461 1092 l 7502 1158 l 7543 1225 l 7582 1294 l 7621 1364 l 7659 1435 l 7697 1507 l 7734 1579 l 7770 1652 l 7805 1725 l 7839 1798 l 7872 1870 l 7905 1942 l 7936 2012 l 7967 2081 l 7996 2148 l 8023 2214 l 8050 2276 l 8075 2336 l 8098 2392 l 8120 2445 l 8140 2495 l 8158 2540 l 8174 2581 l 8189 2618 l 8202 2651 l 8213 2679 l 8222 2703 l 8230 2723 l 8236 2740 l 8241 2752 l 8245 2761 l 8250 2775 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 8101 2538 m 8239 2744 l 8214 2497 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 9473 2809 m 9586 2768 l 9489 2497 l 9514 2744 l 9376 2538 l cp eoclip n 6225 2775 m 6225 2774 l 6226 2772 l 6228 2767 l 6230 2760 l 6233 2750 l 6238 2736 l 6243 2718 l 6251 2696 l 6259 2669 l 6270 2638 l 6282 2602 l 6295 2561 l 6310 2516 l 6327 2467 l 6346 2413 l 6366 2356 l 6387 2295 l 6410 2231 l 6435 2164 l 6460 2094 l 6487 2023 l 6515 1950 l 6544 1876 l 6574 1801 l 6605 1725 l 6636 1649 l 6669 1574 l 6703 1498 l 6737 1424 l 6772 1350 l 6808 1278 l 6845 1207 l 6883 1138 l 6922 1070 l 6962 1004 l 7003 940 l 7045 878 l 7088 819 l 7133 762 l 7180 708 l 7228 657 l 7278 609 l 7329 564 l 7382 523 l 7437 487 l 7494 454 l 7553 427 l 7613 405 l 7674 389 l 7737 378 l 7800 375 l 7861 378 l 7922 388 l 7982 403 l 8042 423 l 8100 449 l 8157 479 l 8212 513 l 8266 552 l 8319 593 l 8370 639 l 8420 687 l 8469 738 l 8516 791 l 8562 847 l 8607 905 l 8651 966 l 8694 1028 l 8736 1092 l 8777 1158 l 8818 1225 l 8857 1294 l 8896 1364 l 8934 1435 l 8972 1507 l 9009 1579 l 9045 1652 l 9080 1725 l 9114 1798 l 9147 1870 l 9180 1942 l 9211 2012 l 9242 2081 l 9271 2148 l 9298 2214 l 9325 2276 l 9350 2336 l 9373 2392 l 9395 2445 l 9415 2495 l 9433 2540 l 9449 2581 l 9464 2618 l 9477 2651 l 9488 2679 l 9497 2703 l 9505 2723 l 9511 2740 l 9516 2752 l 9520 2761 l 9525 2775 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 9376 2538 m 9514 2744 l 9489 2497 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 11498 2809 m 11611 2768 l 11514 2497 l 11539 2744 l 11401 2538 l cp eoclip n 8250 2775 m 8250 2774 l 8251 2772 l 8253 2767 l 8255 2760 l 8258 2750 l 8263 2736 l 8268 2718 l 8276 2696 l 8284 2669 l 8295 2638 l 8307 2602 l 8320 2561 l 8335 2516 l 8352 2467 l 8371 2413 l 8391 2356 l 8412 2295 l 8435 2231 l 8460 2164 l 8485 2094 l 8512 2023 l 8540 1950 l 8569 1876 l 8599 1801 l 8630 1725 l 8661 1649 l 8694 1574 l 8728 1498 l 8762 1424 l 8797 1350 l 8833 1278 l 8870 1207 l 8908 1138 l 8947 1070 l 8987 1004 l 9028 940 l 9070 878 l 9113 819 l 9158 762 l 9205 708 l 9253 657 l 9303 609 l 9354 564 l 9407 523 l 9462 487 l 9519 454 l 9578 427 l 9638 405 l 9699 389 l 9762 378 l 9825 375 l 9886 378 l 9947 388 l 10007 403 l 10067 423 l 10125 449 l 10182 479 l 10237 513 l 10291 552 l 10344 593 l 10395 639 l 10445 687 l 10494 738 l 10541 791 l 10587 847 l 10632 905 l 10676 966 l 10719 1028 l 10761 1092 l 10802 1158 l 10843 1225 l 10882 1294 l 10921 1364 l 10959 1435 l 10997 1507 l 11034 1579 l 11070 1652 l 11105 1725 l 11139 1798 l 11172 1870 l 11205 1942 l 11236 2012 l 11267 2081 l 11296 2148 l 11323 2214 l 11350 2276 l 11375 2336 l 11398 2392 l 11420 2445 l 11440 2495 l 11458 2540 l 11474 2581 l 11489 2618 l 11502 2651 l 11513 2679 l 11522 2703 l 11530 2723 l 11536 2740 l 11541 2752 l 11545 2761 l 11550 2775 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 11401 2538 m 11539 2744 l 11514 2497 l col0 s % Polyline 2 slj [15 68] 68 sd gs clippath 2974 1761 m 2898 1669 l 2675 1851 l 2899 1746 l 2751 1944 l cp eoclip n 2925 3975 m 2924 3974 l 2923 3972 l 2921 3967 l 2917 3961 l 2912 3951 l 2904 3938 l 2896 3922 l 2885 3903 l 2872 3880 l 2858 3853 l 2843 3824 l 2826 3791 l 2808 3756 l 2788 3719 l 2769 3679 l 2749 3638 l 2728 3595 l 2708 3551 l 2687 3506 l 2667 3460 l 2647 3413 l 2628 3364 l 2609 3315 l 2592 3265 l 2574 3214 l 2558 3161 l 2543 3107 l 2529 3052 l 2516 2995 l 2504 2936 l 2495 2876 l 2486 2814 l 2480 2751 l 2476 2688 l 2475 2625 l 2477 2556 l 2482 2490 l 2489 2427 l 2499 2368 l 2511 2314 l 2526 2263 l 2541 2216 l 2558 2172 l 2577 2131 l 2596 2093 l 2616 2058 l 2638 2024 l 2660 1992 l 2682 1963 l 2705 1934 l 2728 1908 l 2751 1883 l 2774 1859 l 2796 1838 l 2817 1818 l 2836 1800 l 2855 1783 l 2871 1769 l 2885 1757 l 2897 1747 l 2906 1740 l 2914 1734 l 2925 1725 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 2751 1944 m 2899 1746 l 2675 1851 l col0 s % Polyline 2 slj [15 68] 68 sd gs clippath 6274 1762 m 6199 1668 l 5974 1849 l 6199 1746 l 6049 1942 l cp eoclip n 6300 4050 m 6300 4049 l 6298 4047 l 6296 4043 l 6293 4037 l 6289 4028 l 6283 4016 l 6276 4001 l 6267 3983 l 6256 3961 l 6244 3936 l 6231 3908 l 6216 3878 l 6200 3844 l 6183 3808 l 6166 3770 l 6147 3730 l 6129 3688 l 6110 3645 l 6091 3600 l 6072 3555 l 6054 3508 l 6035 3461 l 6017 3413 l 6000 3364 l 5983 3314 l 5966 3263 l 5950 3211 l 5935 3158 l 5921 3103 l 5908 3048 l 5895 2991 l 5884 2932 l 5874 2872 l 5865 2811 l 5858 2749 l 5853 2687 l 5850 2625 l 5849 2554 l 5851 2485 l 5856 2421 l 5863 2361 l 5872 2306 l 5883 2254 l 5896 2207 l 5910 2162 l 5925 2122 l 5941 2084 l 5958 2048 l 5976 2015 l 5995 1984 l 6014 1954 l 6034 1927 l 6054 1901 l 6074 1876 l 6093 1854 l 6112 1833 l 6131 1814 l 6148 1796 l 6164 1781 l 6178 1767 l 6190 1756 l 6200 1746 l 6209 1739 l 6215 1733 l 6225 1725 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 6049 1942 m 6199 1746 l 5974 1849 l col0 s % Polyline 2 slj [15 68] 68 sd gs clippath 9654 1679 m 9565 1598 l 9371 1810 l 9578 1674 l 9460 1891 l cp eoclip n 9600 3900 m 9599 3899 l 9598 3897 l 9595 3893 l 9591 3886 l 9584 3877 l 9576 3865 l 9566 3850 l 9554 3831 l 9539 3810 l 9523 3785 l 9506 3758 l 9487 3727 l 9467 3695 l 9446 3660 l 9425 3624 l 9403 3586 l 9381 3546 l 9360 3506 l 9339 3464 l 9318 3420 l 9298 3376 l 9278 3330 l 9259 3283 l 9242 3234 l 9225 3183 l 9210 3130 l 9195 3075 l 9183 3018 l 9172 2958 l 9163 2896 l 9156 2832 l 9152 2766 l 9150 2700 l 9152 2630 l 9157 2562 l 9164 2497 l 9174 2435 l 9186 2376 l 9201 2321 l 9216 2269 l 9233 2219 l 9252 2172 l 9271 2128 l 9291 2085 l 9313 2045 l 9335 2006 l 9357 1969 l 9380 1933 l 9403 1898 l 9426 1866 l 9449 1835 l 9471 1806 l 9492 1779 l 9511 1754 l 9530 1732 l 9546 1712 l 9560 1696 l 9572 1682 l 9581 1671 l 9589 1662 l 9600 1650 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 9460 1891 m 9578 1674 l 9371 1810 l col0 s /Times-Roman ff 315.00 scf sf 4125 1725 m gs 1 -1 sc (Lbusy,1S) col0 sh gr /Times-Roman ff 315.00 scf sf 10725 1725 m gs 1 -1 sc (Lbusy,3S) col0 sh gr /Times-Roman ff 315.00 scf sf 900 4125 m gs 1 -1 sc (Lidle,0S) col0 sh gr /Times-Roman ff 315.00 scf sf 4200 4125 m gs 1 -1 sc (Lidle,1S) col0 sh gr /Times-Roman ff 315.00 scf sf 10875 4125 m gs 1 -1 sc (Lidle,3S) col0 sh gr /Times-Roman ff 315.00 scf sf 7425 1725 m gs 1 -1 sc (Lbusy,2S) col0 sh gr /Times-Roman ff 345.00 scf sf 7275 2550 m gs 1 -1 sc (+) col0 sh gr /Times-Roman ff 315.00 scf sf 7575 4125 m gs 1 -1 sc (Lidle,2S) col0 sh gr F2psBegin10setmiterlimit0.060000.06000scF2psEnd rs %%EndDocument endTexFig 1859 2223 a Fo(\(b\))120 2419 y FC(Figure)25 b(4:)k(MC)23 b(for)h(short)h(host.)31 b(\(a\))24 b(Where)h(job)f(sizes)h(are)f(e)o (xponentially-distr)q(ib)n(u)q(te)q(d.)35 b(\(b\))24 b(Where)h(job)f(sizes)120 2532 y(are)g(Coxian.)261 2791 y(W)-7 b(e)27 b(solv)o(e)i(the)f(Mark)o(o)o(v)g(chain)h(in)f(Figure)g (4\(b\))g(for)g(the)g(number)h(of)f(short)h(jobs)f(at)g(the)g(short)g (host)h(using)120 2903 y(Matrix)c(Geometric)g(methods.)33 b(Then)24 b(via)h(Little')-5 b(s)25 b(La)o(w)-6 b(,)23 b(we)g(obtain)j(the)e(mean)h(response)i(time)d(of)g(small)g(jobs)120 3016 y(which)g(serv)o(e)g(at)f(the)h(short)h(host.)k(Aggre)o(gating)d (short)e(jobs)g(at)g(both)g(hosts,)h(we)d(then)j(ha)n(v)o(e)f(by)f(P)-8 b(AST)g(A:)460 3221 y Fu(E)5 b Fs([)23 b FC(T)m(ime)g(for)h(short)g (jobs)g Fs(])i(=)626 3358 y(Pr)p Fr(f)p FC(Long)e(host)g(idle)q Fr(g)d(\001)f Fu(E)5 b Fs([)p Fu(X)1577 3372 y Ft(S)1629 3358 y Fs(])21 b(+)f(Pr)o Fr(f)p FC(Long)k(host)g(b)n(usy)r Fr(g)d(\001)f Fu(E)5 b Fs([)24 b FC(T)m(ime)e(at)i(short)g(host)r Fs(])120 3563 y FC(Observ)o(e)h(that)g(while)g(the)g(mean)g(response)h (time)f(for)g(long)g(jobs)g(is)g(e)o(xact,)g(the)g(mean)f(response)j (time)d(for)h(short)120 3676 y(jobs)31 b(depends)g(on)f(the)g(accurac)o (y)i(of)e(the)g(approximation)j(of)d(the)g(b)n(usy)h(period)g(of)f(the) g(long)g(host.)49 b(W)-7 b(e)29 b(ha)n(v)o(e)120 3788 y(matched)38 b(the)f(\002rst)f(three)i(moments)f(of)g(the)g(b)n(usy)h (period)g(of)f(the)g(long)g(host.)69 b(Greater)38 b(accurac)o(y)g(can)f (be)120 3901 y(achie)n(v)o(ed)e(by)e(matching)h(more)f(moments)g(of)g (the)g(b)n(usy)h(period,)j(using)d(a)e(higher)j(de)o(gree)f(Coxian,)h (until)f(in)120 4014 y(theory)25 b(the)f(results)h(are)f(arbitrarily)i (close)e(to)g(the)g(actual)h(quantities.)120 4307 y FG(4)119 b(Cycle)31 b(Stealing)f(under)i(Central)f(Queue)120 4514 y FC(The)h Fx(CS-Central-Queue)25 b FC(algorithm)35 b(is)d(sho)n(wn)i (in)e(Figure)i(2.)56 b(Under)33 b Fx(CS-Central-Queu)o(e)p FC(,)28 b(all)120 4627 y(jobs)22 b(are)g(k)o(ept)h(in)f(a)f(central)i (queue)g(in)f(the)g(order)h(the)o(y)f(arri)n(v)o(e.)28 b(When)22 b(the)g(short)h(host)g(is)e(free,)h(it)g(grabs)h(the)f(ne)o (xt)120 4740 y(short)i(job)g(and)g(runs)g(it.)k(When)c(the)f(long)h (host)g(is)g(free,)f(it)g(grabs)i(the)e(ne)o(xt)h(long)g(job)g(and)f (runs)h(it.)29 b(If)23 b(there)h(is)f(no)120 4853 y(long)h(job,)g(it)f (grabs)i(the)f(ne)o(xt)g(short)g(job)l(.)261 4966 y(Observ)o(e)g(that)g (the)g(technique)i(we)d(used)h(for)g(solving)h Fx(CS-Immediate-Dis)o (pa)o(tc)o(h)17 b FC(\(where)24 b(we)e(split)120 5078 y(the)j(problem)h(into)f(tw)o(o)f(chains)i(where)f(one)g(w)o(as)f(a)g (function)j(of)d(the)h(other\))h(will)e(not)h(w)o(ork)f(here.)33 b(The)24 b(reason)1897 5349 y(9)p eop %%Page: 10 12 10 11 bop 120 3 3961 4 v 118 103 4 100 v 170 73 a Fw(Notation)p 523 103 V 112 w(De\002nition)p 4079 103 V 120 106 3961 4 v 118 206 4 100 v 170 176 a Fl(B)233 188 y Fk(L)p 523 206 V 574 176 a Fw(Busy)21 b(period)e(consisting)g(of)h(only)f(long)h (jobs,)g(and)f(started)h(by)g(a)h(single)f(long)f(job)h(\(of)g(size)g Fl(X)3357 188 y Fk(L)3407 176 y Fw(\).)p 4079 206 V 120 209 3961 4 v 118 309 4 100 v 170 279 a Fl(E)p 523 309 V 343 w Fw(e)o(xponential)e(random)h(v)n(ariable)g(with)h(rate)g Fj(2)p Fl(\026)1947 291 y Fk(S)p 4079 309 V 120 312 3961 4 v 118 412 4 100 v 170 382 a Fl(B)233 394 y Fk(E)p 523 412 V 574 382 a Fw(Busy)h(period)e(consisting)g(of)h(only)f(long)h (jobs,)g(and)f(started)h(by)g(a)h(single)f(job)g(of)g(size)g Fl(E)5 b Fw(.)p 4079 412 V 120 415 3961 4 v 118 515 4 100 v 170 485 a Fl(B)233 497 y Fk(E)s Fi(+)p Fk(L)p 523 515 V 574 485 a Fw(Busy)21 b(period)e(consisting)g(of)h(only)f(long)h (jobs,)g(and)f(started)h(by)g(a)h(job)f(of)f(size)i Fl(X)2942 497 y Fk(L)3010 485 y Fj(+)d Fl(E)5 b Fw(.)p 4079 515 V 120 518 3961 4 v 118 618 4 100 v 170 588 a Fl(N)32 b Fj(=)22 b Fl(A)418 600 y Fk(E)p 523 618 V 574 588 a Fw(Number)d(of)h(long)f(jobs)h(which)g(arri)n(v)o(e)f(during)g Fl(E)p 4079 618 V 120 621 3961 4 v 118 721 4 100 v 170 691 a(B)233 703 y Fk(N)6 b Fi(+1)p 523 721 V 574 691 a Fw(Busy)21 b(period)e(consisting)g(of)h(only)f(long)h(jobs,)g(and)f (started)h(by)g(a)h(job)f(whose)f(size)i(is)g(the)g(sum)f(of)g Fl(N)27 b Fj(+)18 b(1)i Fw(long)g(jobs.)p 4079 721 V 120 724 3961 4 v 800 877 a FC(T)-7 b(able)24 b(2:)29 b Fv(Notation)19 b(necessary)h(for)h(analyzing)e Fh(CS-Central-Queue) 120 1152 y FC(is)25 b(that)h(the)g(decision)i(of)d(which)h(job)g(the)f (long)i(host)f(tak)o(es)g(depends)i(on)d(kno)n(wing)i(the)f(e)o(xact)g (number)g(of)f(long)120 1265 y(and)k(short)h(jobs)f(in)f(the)h(system:) 40 b(There)29 b(is)g(no)f(w)o(ay)h(to)f(decompose)j(the)e(system)g (into)g(tw)o(o)g(chains.)45 b(W)-7 b(e)28 b(will)120 1378 y(instead)f(look)f(for)f(a)f Fy(single)51 b FC(Mark)o(o)o(v)26 b(chain)g(which)f(represents)j(this)e(system)f(and)h(yet)f(is)g (in\002nite)h(in)f(only)h(one)120 1491 y(dimension.)261 1603 y(There)32 b(will)g(be)g(a)g(lot)g(of)g(notation)i(in)e(this)h (section.)56 b(W)-7 b(e)31 b(will)h(introduce)j(it)d(as)g(we)f(go)h (along.)56 b(F)o(or)31 b(the)120 1716 y(reader')-5 b(s)25 b(con)l(v)o(enience,)i(the)d(notation)i(is)d(summarized)i(in)f(T)-7 b(able)23 b(2)g(belo)n(w)-6 b(.)120 1966 y Fo(4.1)99 b(F)n(ormulating)24 b(the)i(Mark)o(o)o(v)f(chain)g(f)n(or)g Fg(CS-Central-Queue)120 2140 y FC(In)i(Figure)h(5\(a\))g(we)f(sho)n(w)g (a)g(chain)h(representing)j Fx(CS-Central-Que)o(ue)p FC(.)i(The)27 b(\002rst)g(entry)h(of)f(each)h(state)120 2253 y(denotes)23 b(the)f(number)g(of)f(small)g(jobs,)h(which)g(ranges) h(from)e(zero)g(to)h(in\002nity)-6 b(.)29 b(The)20 b(second)j(entry)f (of)f(each)h(state)120 2366 y(denotes)32 b(the)e(number)h(of)e(long)i (jobs.)48 b(This)30 b(is)g(either)h Fs(0)p Fu(L)p FC(,)f Fs(1)p Fu(L)p FC(,)h(or)f(a)f(special)i(state)g(denoted)h(by)e Fs(\()p Fu(N)35 b Fs(+)25 b(1\))p Fu(L)p FC(.)120 2479 y(The)f(third)i(entry)g(of)f(each)h(state,)f(when)h(present,)g(denotes) h(the)e(type)h(of)f(job)g(in)g(service)h(at)f(the)g(long)h(host.)34 b(The)120 2591 y(service)e(time)f(for)g(the)g(long)h(job)f(is)f (assumed)i(to)f(be)g(generally-distrib)n(ut)q(ed.)56 b(F)o(or)30 b(simplicity)j(in)d(specifying)120 2704 y(the)i(Mark)o(o)o (v)g(chain,)i(the)d(service)i(time)e(for)g(the)h(small)f(job)h(is)f (assumed)i(to)e(be)g(e)o(xponential,)36 b(with)31 b(rate)h Fu(\026)3647 2718 y Ft(S)3697 2704 y FC(,)120 2817 y(although)26 b(this)e(is)f(straightforw)o(ard)28 b(to)23 b(generalize.)261 2930 y(The)32 b(logic)g(behind)i(the)e(chain)h(is)f(as)f(follo)n(ws:)47 b(Let')-5 b(s)32 b(start)g(in)g(re)o(gion)h(1,)g(and)f(consider)i(a)e (long)h(arri)n(v)n(al.)120 3043 y(This)25 b(causes)i(a)f(transition)i (to)d(re)o(gion)i(3,)e(and)h(that)g(long)h(arri)n(v)n(al)f(starts)h(a)e (long)h(b)n(usy)h(period,)g(whose)f(length)h(is)120 3156 y(denoted)f(by)e Fu(B)614 3170 y Ft(L)666 3156 y FC(.)k(W)-7 b(e)23 b(will)h(return)h(to)e(re)o(gions)j(1)d(or)h(2)f(only)i(after)f (time)g Fu(B)2510 3170 y Ft(L)2562 3156 y FC(.)29 b(During)24 b(this)g(b)n(usy)h(period,)g(man)o(y)120 3269 y(smalls)e(can)f(arri)n (v)o(e.)29 b(These)22 b(will)g(only)h(be)f(serv)o(ed)i(at)d(rate)i Fu(\026)2028 3283 y Ft(S)2100 3269 y FC(since)g(the)g(long)f(host)h(is) f(occupied)j(by)d(a)g(long)h(job)l(.)261 3382 y(Ne)o(xt)30 b(consider)j(a)e(long)g(arri)n(v)n(al)h(into)f(re)o(gion)h(2.)50 b(This)31 b(causes)h(a)e(transition)j(into)f(re)o(gion)g(5.)50 b(Before)31 b(the)120 3495 y(long)g(arri)n(v)n(al)g(can)f(run,)i(it)d (must)h(\002rst)g(w)o(ait)f(for)i(one)f(of)g(the)g(small)g(jobs)h(to)f (\002nish,)h(since)g(the)f(small)g(jobs)h(are)120 3608 y(occup)o(ying)26 b(both)d(hosts.)30 b(When)23 b(one)g(of)f(the)h (small)g(jobs)g(completes,)i(the)e(long)g(job)g(will)f(mo)o(v)o(e)h(to) f(occup)o(y)j(that)120 3721 y(host)f(\(that)g(host)g(will)f(be)h (renamed)g(the)g(long)g(host\))h(and)f(we)e(mo)o(v)o(e)h(to)g(re)o (gion)i(4.)j(Thus,)23 b(we)g(sit)g(in)g(re)o(gion)i(5)e(for)120 3833 y(time)k Fu(E)37 b Fr(\030)32 b Fu(E)5 b(xp)p Fs(\(2)p Fu(\026)820 3847 y Ft(S)872 3833 y Fs(\))p FC(,)27 b(w)o(aiting)h(for)g (one)f(of)h(the)f(small)h(jobs)g(to)f(complete.)41 b(During)28 b(time)f Fu(E)5 b FC(,)27 b Fu(N)37 b FC(ne)n(w)26 b(long)120 3946 y(jobs)d(arri)n(v)o(e.)29 b(At)22 b(the)h(moment)g(one)g(of)g(the) g(short)h(jobs)f(completes)i(there)f(are)e Fu(N)28 b Fs(+)17 b(1)22 b FC(long)i(jobs)f(in)g(the)g(system,)120 4059 y(and)29 b(a)g(long)h(starts)g(service.)46 b(W)-7 b(e)28 b(no)n(w)g(enter)i(a)f(b)n(usy)h(period)g(consisting)i(of)d (long)g(jobs,)i(started)g(by)e(a)f(job)h(of)120 4185 y(size)282 4121 y Fq(P)369 4147 y Ft(N)7 b FE(+1)369 4211 y Ft(i)p FE(=1)542 4185 y Fu(X)624 4137 y FE(\()p Ft(i)p FE(\))617 4212 y Ft(L)707 4185 y FC(.)27 b(The)21 b(length)i(of)d(this)i(b)n(usy)g(period)h(is)e(denoted)i(by)e Fu(B)2426 4199 y Ft(N)7 b FE(+1)2583 4185 y FC(.)27 b(At)20 b(the)i(end)f(of)g(this)h(b)n(usy)g(period,)120 4298 y(we)i(return)j(to)e(re)o(gion)i(1)d(or)i(2.)33 b(During)26 b(our)g(time)f(in)g(re)o(gion)h(4,)g(small)f(jobs)h(can)g(of)f(course)i (arri)n(v)o(e)e(and)h(depart.)120 4411 y(Such)e(small)f(jobs)i(are)e (serv)o(ed)i(with)e(rate)h Fu(\026)1509 4425 y Ft(S)1583 4411 y FC(since)g(there)h(is)e(a)g(long)h(job)g(occup)o(ying)j(one)d (host.)261 4524 y(Observ)o(e)g(that)g(the)f(only)h(time)f(that)g(the)g (small)h(jobs)f(are)h(serv)o(ed)g(at)f(rate)g Fs(2)p Fu(\026)2667 4538 y Ft(S)2740 4524 y FC(is)g(when)g(there)h(are)g(zero) f(long)120 4637 y(jobs)h(in)g(the)g(system,)g(or)f(when)h(a)f(long)h (job)g(\002nds)g(that)g(there)g(are)g(already)h(2)e(small)h(jobs)g (serving.)261 4750 y(The)j(chain)h(in)f(Figure)h(5\(a\))g(uses)g(tw)o (o)e(types)j(of)e(b)n(usy)h(period)h(transitions,)h(denoted)g(by)d Fu(B)3235 4764 y Ft(L)3313 4750 y FC(and)h Fu(B)3540 4764 y Ft(N)7 b FE(+1)3697 4750 y FC(.)120 4862 y(W)-7 b(e)24 b(can)h(deri)n(v)o(e)h(all)f(the)g(moments)g(of)g(these)h(b)n (usy)g(periods)g(and)f(represent)j(the)d(b)n(usy)h(period)g (transitions)i(by)d(a)120 4975 y(Coxian)k(distrib)n(ution.)45 b(Figure)28 b(5\(b\))h(is)e(identical)j(to)e(Figure)g(5\(a\),)i(e)o (xcept)f(that)f(the)g(b)n(usy)h(period)g(transitions)120 5088 y(ha)n(v)o(e)36 b(been)f(replaced)i(by)e(tw)o(o-phase)i(Coxian)f (distrib)n(utions,)41 b(which)35 b(allo)n(ws)h(us)e(to)h(model)h(the)f (\002rst)f(three)1875 5349 y(10)p eop %%Page: 11 13 11 12 bop 120 91 a FC(moments)34 b(of)f(each)g(b)n(usy)i(period.)58 b(More)34 b(moments)f(could)h(be)g(modeled)g(using)g(a)f(higher)n(-de)o (gree)k(Coxian,)120 204 y(ho)n(we)n(v)o(er)24 b(we)f(will)g(see)h(that) g(three)g(moments)g(pro)o(vide)h(suf)n(\002cient)g(accurac)o(y)-6 b(.)261 317 y(There)31 b(is)g(still)h(one)g(problem:)46 b(The)30 b(chain)j(in)e(Figure)g(5)g(is)g(not)h(a)e(strict)j(Mark)o(o)o (v)f(chain.)52 b(The)31 b(problem)120 430 y(is)g(that)h Fu(E)5 b FC(,)32 b(the)f(time)g(required)i(to)e(transition)j(from)d(re) o(gion)h(5)f(to)g(re)o(gion)h(4,)h(is)e(not)g(independent)k(of)c Fu(B)3540 444 y Ft(N)7 b FE(+1)3697 430 y FC(,)120 543 y(the)28 b(time)g(required)i(to)e(transition)j(from)c(re)o(gion)i(4)f (to)g(re)o(gion)h(1)f(or)f(2.)42 b(This)28 b(is)g(because)h(the)g (number)f(of)g(long)120 656 y(arri)n(v)n(als)f(during)g Fu(E)5 b FC(,)25 b Fu(N)10 b FC(,)25 b(is)g(correlated)j(with)d Fu(E)30 b FC(and)c(with)f Fu(B)2093 670 y Ft(N)7 b FE(+1)2250 656 y FC(.)34 b(F)o(or)24 b(Figure)i(5)f(to)h(be)f(a)g(Mark)o(o)o(v)h (chain,)h(we)120 769 y(w)o(ould)d(need)g(to)g(ha)n(v)o(e)g Fu(E)k FC(and)c Fu(B)1166 783 y Ft(N)7 b FE(+1)1346 769 y FC(be)24 b(independent.)261 882 y(T)-7 b(o)31 b(address)j(this)f (problem,)j(we)31 b(de\002ne)i(a)e(ne)n(w)h(random)h(v)n(ariable,)j Fu(B)2581 896 y Ft(E)2641 882 y FC(.)54 b Fu(B)2787 896 y Ft(E)2878 882 y FC(is)32 b(the)g(length)i(of)e(a)g(b)n(usy)120 995 y(period)c(consisting)h(of)e(only)g(long)g(jobs,)h(started)g(by)f (a)f(job)h(of)f(size)h Fu(E)5 b FC(.)37 b(Ne)o(xt)26 b(de\002ne)h Fu(B)2960 1009 y Ft(E)t FE(+)p Ft(L)3148 995 y FC(to)f(be)h(the)g(length)120 1108 y(of)c(a)h(b)n(usy)g(period)h (consisting)i(of)c(only)h(long)h(jobs,)f(started)h(by)f(a)f(job)h(of)f (size)h Fu(E)i Fs(+)20 b Fu(X)2887 1122 y Ft(L)2939 1108 y FC(.)28 b(Observ)o(e)c(that)1502 1312 y Fu(B)1571 1326 y Ft(E)t FE(+)p Ft(L)1759 1312 y Fs(=)1830 1327 y Ft(dist)1977 1312 y Fu(B)2046 1326 y Ft(E)2126 1312 y Fs(+)c Fu(B)2286 1326 y Ft(L)120 1516 y FC(Observ)o(e)k(also)h(that)f Fu(B)842 1530 y Ft(E)t FE(+)p Ft(L)1027 1516 y FC(represents)j(the)c (total)i(time)e(required)j(to)e(transition)i(from)e(re)o(gion)g(5)g(to) f(re)o(gion)i(1)e(or)120 1629 y(2,)g(and)h(that)g Fu(B)593 1643 y Ft(E)t FE(+)p Ft(L)778 1629 y FC(is)g(e)o(xact)g(\226)f(the)h (dependencies)j(between)e Fu(E)j FC(and)c Fu(B)2433 1643 y Ft(N)7 b FE(+1)2613 1629 y FC(are)24 b(inherent)h(in)f(it.)261 1742 y(W)-7 b(e)23 b(could)j(imagine)f(creating)h(a)e(single)h (transition)i(from)d(re)o(gion)i(5)d(to)h(re)o(gion)i(1)e(or)g(2)f(of)h (duration)j Fu(B)3535 1756 y Ft(E)t FE(+)p Ft(L)3697 1742 y FC(.)120 1855 y(This)d(w)o(ould)i(not)e(suit)i(our)f(needs,)g (ho)n(we)n(v)o(er:)32 b(While)25 b(it)f(is)g(not)h(dif)n(\002cult)h(to) e(compute)i(the)f(moments)g(of)g Fu(B)3558 1869 y Ft(E)t FE(+)p Ft(L)120 1968 y FC(and)g(create)h(a)e(Coxian)h(random)g(v)n (ariable)h(representing)j Fu(B)2024 1982 y Ft(E)t FE(+)p Ft(L)2186 1968 y FC(,)24 b(using)h(a)f(single)i(transition)h(from)e(re) o(gion)g(5)f(to)120 2081 y(re)o(gion)i(1)f(or)g(2)f(w)o(ould)i(not)f (capture)i(the)e(f)o(act)h(that)g(the)f(rate)g(at)g(which)h(small)f (jobs)h(are)f(serv)o(ed)h(is)f(initially)i Fs(2)p Fu(\026)3669 2095 y Ft(S)120 2193 y FC(b)n(ut)d(later)g Fu(\026)496 2207 y Ft(S)547 2193 y FC(.)261 2306 y(Therefore)f(we)e(choose)i (instead)h(to)d(e)o(xpress)i Fu(B)1771 2320 y Ft(E)t FE(+)p Ft(L)1954 2306 y FC(as)f(a)f(sum)h(of)f(tw)o(o)g(independent)k (random)e(v)n(ariables)h Fu(E)120 2419 y FC(and)g Fu(U)33 b FC(where)1616 2532 y Fu(B)1685 2546 y Ft(E)t FE(+)p Ft(L)1873 2532 y Fs(=)25 b Fu(E)g Fs(+)20 b Fu(U)261 2699 y FC(Gi)n(v)o(en)h(the)g(moments)g(of)g Fu(B)1149 2713 y Ft(E)t FE(+)p Ft(L)1332 2699 y FC(and)g(the)g(moments)h(of)f Fu(E)5 b FC(,)20 b(we)g(will)h(be)g(able)g(to)g(then)h(deri)n(v)o(e)f (the)h(moments)120 2812 y(of)h Fu(U)33 b FC(as)24 b(follo)n(ws:)261 2925 y(W)-7 b(e)23 b(\002rst)g(write)g(out)h(the)g(follo)n(wing)h (equations,)h(which)e(assume)g Fu(E)k FC(and)c Fu(U)33 b FC(are)24 b(independent:)859 3129 y Fu(B)928 3143 y Ft(E)t FE(+)p Ft(L)1173 3129 y Fs(=)83 b Fu(E)25 b Fs(+)20 b Fu(U;)736 3267 y(E)5 b Fs([)p Fu(B)902 3281 y Ft(E)t FE(+)p Ft(L)1065 3267 y Fs(])83 b(=)g Fu(E)5 b Fs([)p Fu(E)g Fs(])21 b(+)f Fu(E)5 b Fs([)p Fu(U)10 b Fs(])p Fu(;)736 3405 y(E)5 b Fs([)p Fu(B)907 3367 y FE(2)902 3427 y Ft(E)t FE(+)p Ft(L)1065 3405 y Fs(])83 b(=)g Fu(E)5 b Fs([)p Fu(E)1496 3367 y FE(2)1536 3405 y Fs(])21 b(+)f(2)p Fu(E)5 b Fs([)p Fu(E)g Fs(])p Fu(E)g Fs([)p Fu(U)10 b Fs(])22 b(+)e Fu(E)5 b Fs([)p Fu(U)2388 3367 y FE(2)2428 3405 y Fs(])p Fu(;)736 3543 y(E)g Fs([)p Fu(B)907 3505 y FE(3)902 3565 y Ft(E)t FE(+)p Ft(L)1065 3543 y Fs(])83 b(=)g Fu(E)5 b Fs([)p Fu(E)1496 3505 y FE(3)1536 3543 y Fs(])21 b(+)f(3)p Fu(E)5 b Fs([)p Fu(E)1887 3505 y FE(2)1927 3543 y Fs(])p Fu(E)g Fs([)p Fu(U)10 b Fs(])22 b(+)e(3)p Fu(E)5 b Fs([)p Fu(E)g Fs(])p Fu(E)g Fs([)p Fu(U)2667 3505 y FE(2)2708 3543 y Fs(])21 b(+)f Fu(E)5 b Fs([)p Fu(U)3014 3505 y FE(3)3054 3543 y Fs(])p Fu(:)261 3747 y FC(Ne)o(xt)23 b(we)g(solv)o(e)h(these)h(equations)h(for)e(the)f (moments)i(of)e Fu(U)33 b FC(as)23 b(follo)n(ws:)775 3951 y Fu(E)5 b Fs([)p Fu(U)10 b Fs(])84 b(=)f Fu(E)5 b Fs([)p Fu(B)1373 3965 y Ft(E)t FE(+)p Ft(L)1536 3951 y Fs(])20 b Fr(\000)g Fu(E)5 b Fs([)p Fu(E)g Fs(])p Fu(;)736 4089 y(E)g Fs([)p Fu(U)905 4051 y FE(2)945 4089 y Fs(])83 b(=)g Fu(E)5 b Fs([)p Fu(B)1378 4051 y FE(2)1373 4111 y Ft(E)t FE(+)p Ft(L)1536 4089 y Fs(])20 b Fr(\000)g Fu(E)5 b Fs([)p Fu(E)1841 4051 y FE(2)1882 4089 y Fs(])20 b Fr(\000)g Fs(2)p Fu(E)5 b Fs([)p Fu(E)g Fs(])p Fu(E)g Fs([)p Fu(U)10 b Fs(])p Fu(;)736 4227 y(E)5 b Fs([)p Fu(U)905 4189 y FE(3)945 4227 y Fs(])83 b(=)g Fu(E)5 b Fs([)p Fu(B)1378 4189 y FE(3)1373 4249 y Ft(E)t FE(+)p Ft(L)1536 4227 y Fs(])20 b Fr(\000)g Fs(3)p Fu(E)5 b Fs([)p Fu(E)1886 4189 y FE(2)1927 4227 y Fs(])p Fu(E)g Fs([)p Fu(U)10 b Fs(])21 b Fr(\000)f Fs(3)p Fu(E)5 b Fs([)p Fu(E)g Fs(])p Fu(E)g Fs([)p Fu(U)2666 4189 y FE(2)2708 4227 y Fs(])20 b Fr(\000)g Fu(E)5 b Fs([)p Fu(E)3013 4189 y FE(3)3054 4227 y Fs(])p Fu(:)261 4431 y FC(W)-7 b(e)24 b(no)n(w)h(\002nd)g(a)g(tw)o(o-phase)i(Coxian)f(which)g(matches) g(these)g(\002rst)f(three)h(moments)g(of)f Fu(U)10 b FC(.)33 b(The)25 b(resulting)120 4544 y(Mark)o(o)o(v)34 b(chain,)h(sho)n(wn)f(in)e(Figure)i(6,)g(is)f(almost)g(identical)i(to)e (Figure)g(5,)i(e)o(xcept)f(that)f(the)g(Coxian)h Fu(B)3563 4558 y Ft(N)7 b FE(+1)120 4657 y FC(random)28 b(v)n(ariable)i(has)d (been)i(replaced)g(by)f(the)f(random)i(v)n(ariable)g Fu(U)37 b FC(where)27 b Fu(U)37 b FC(is)27 b(de\002ned)h(according)j (to)c(the)120 4770 y(abo)o(v)o(e)36 b(equations)h(and)f(is)e (independent)39 b(of)c Fu(E)52 b Fr(\030)46 b Fu(E)5 b(xp)p Fs(\(2)p Fu(\026)2141 4784 y Ft(S)2192 4770 y Fs(\))p FC(.)63 b(Thus)35 b(we)f(ha)n(v)o(e)h(a)g(well-de\002ned)h (Mark)o(o)o(v)120 4883 y(Chain.)g(Note:)e(Computationally)-6 b(,)29 b(performance-wise)h(the)c(chain)h(in)e(Figure)i(5)e(is)h Fy(virtually)i(identical)g FC(to)e(the)120 4995 y(chain)f(in)e(Figure)h (6.)1875 5349 y(11)p eop %%Page: 12 14 12 13 bop 462 84 a 23018352 14208860 0 0 50849300 31312117 startTexFig 462 84 a %%BeginDocument: ../figures/k1.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: k1.eps %%Creator: fig2dev Version 3.2 Patchlevel 3d %%CreationDate: Tue May 21 14:23:47 2002 %%For: harchol@mor.sp.cs.cmu.edu (Mor Harchol-Balter) %%BoundingBox: 0 0 773 476 %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def F2psDictbeginF2psDict begin F2psDictbeginF2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 476 moveto 0 0 lineto 773 0 lineto 773 476 lineto closepath clip newpath -12.2 545.8 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def F2psBegin10setmiterlimit0.060000.06000scF2psBegin 10 setmiterlimit 0.06000 0.06000 sc % % Fig objects follow % /Symbol ff 180.00 scf sf 6211 1363 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 180.00 scf sf 6320 1471 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 180.00 scf sf 9195 1363 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 180.00 scf sf 9303 1471 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 180.00 scf sf 3227 1363 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 180.00 scf sf 3336 1471 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 210.00 scf sf 3159 2489 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 210.00 scf sf 3296 2624 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 210.00 scf sf 3159 4727 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 210.00 scf sf 3296 4862 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 180.00 scf sf 3159 3601 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 180.00 scf sf 3268 3709 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 180.00 scf sf 6075 3601 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 180.00 scf sf 6184 3709 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 180.00 scf sf 9127 3533 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 180.00 scf sf 9236 3641 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 180.00 scf sf 9195 7873 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 180.00 scf sf 9303 7981 m gs 1 -1 sc (S) col0 sh gr 7.500 slw % Ellipse n 11772 1946 49 49 0 360 DrawEllipse gs col0 s gr % Ellipse n 12043 1946 49 49 0 360 DrawEllipse gs col0 s gr % Ellipse n 12314 1946 49 49 0 360 DrawEllipse gs col0 s gr % Ellipse n 11840 6218 49 49 0 360 DrawEllipse gs col0 s gr % Ellipse n 12111 6218 49 49 0 360 DrawEllipse gs col0 s gr % Ellipse n 12382 6218 49 49 0 360 DrawEllipse gs col0 s gr % Ellipse n 11840 4116 49 49 0 360 DrawEllipse gs col0 s gr % Ellipse n 12111 4116 49 49 0 360 DrawEllipse gs col0 s gr % Ellipse n 12382 4116 49 49 0 360 DrawEllipse gs col0 s gr % Ellipse n 11772 8456 49 49 0 360 DrawEllipse gs col0 s gr % Ellipse n 12043 8456 49 49 0 360 DrawEllipse gs col0 s gr % Ellipse n 12314 8456 49 49 0 360 DrawEllipse gs col0 s gr /Symbol ff 210.00 scf sf 6618 7425 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 210.00 scf sf 6754 7561 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 6482 7425 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 210.00 scf sf 9602 7357 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 210.00 scf sf 9737 7493 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 9466 7357 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 180.00 scf sf 3092 5771 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 180.00 scf sf 3200 5879 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 180.00 scf sf 6075 5771 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 180.00 scf sf 6184 5879 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 180.00 scf sf 9195 5771 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 180.00 scf sf 9303 5879 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 210.00 scf sf 9331 6762 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 210.00 scf sf 9467 6896 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 210.00 scf sf 6075 6829 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 210.00 scf sf 6212 6964 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 210.00 scf sf 3092 6762 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 210.00 scf sf 3228 6896 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 270.00 scf sf 1396 3082 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 270.00 scf sf 1566 3167 m gs 1 -1 sc (L) col0 sh gr /Times-Roman ff 285.00 scf sf 2413 3031 m gs 1 -1 sc (B) col0 sh gr /Times-Roman ff 255.00 scf sf 2617 3167 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 270.00 scf sf 4380 3082 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 270.00 scf sf 4550 3167 m gs 1 -1 sc (L) col0 sh gr /Times-Roman ff 285.00 scf sf 5533 2963 m gs 1 -1 sc (B) col0 sh gr /Times-Roman ff 255.00 scf sf 5736 3099 m gs 1 -1 sc (L) col0 sh gr /Times-Roman ff 285.00 scf sf 11501 2895 m gs 1 -1 sc (B) col0 sh gr /Times-Roman ff 255.00 scf sf 11704 3031 m gs 1 -1 sc (L) col0 sh gr /Times-Roman ff 285.00 scf sf 8246 2963 m gs 1 -1 sc (B) col0 sh gr /Times-Roman ff 255.00 scf sf 8449 3099 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 270.00 scf sf 8720 5320 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 270.00 scf sf 8890 5404 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 270.00 scf sf 11704 5252 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 270.00 scf sf 11874 5337 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 210.00 scf sf 6143 2489 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 210.00 scf sf 6280 2624 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 210.00 scf sf 6211 4713 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 210.00 scf sf 6347 4848 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 6075 4713 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 210.00 scf sf 9331 4645 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 210.00 scf sf 9466 4780 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 210.00 scf sf 9195 4645 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 210.00 scf sf 9263 2489 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 210.00 scf sf 9399 2624 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 255.00 scf sf 1600 5337 m gs 1 -1 sc (N+1) col0 sh gr /Times-Roman ff 285.00 scf sf 1396 5201 m gs 1 -1 sc (B) col0 sh gr /Times-Roman ff 255.00 scf sf 4516 5337 m gs 1 -1 sc (N+1) col0 sh gr /Times-Roman ff 285.00 scf sf 4312 5201 m gs 1 -1 sc (B) col0 sh gr /Times-Roman ff 255.00 scf sf 7432 5337 m gs 1 -1 sc (N+1) col0 sh gr /Times-Roman ff 285.00 scf sf 7228 5201 m gs 1 -1 sc (B) col0 sh gr /Times-Roman ff 255.00 scf sf 10551 5337 m gs 1 -1 sc (N+1) col0 sh gr /Times-Roman ff 285.00 scf sf 10348 5201 m gs 1 -1 sc (B) col0 sh gr % Ellipse n 4923 1946 678 271 0 360 DrawEllipse gs col0 s gr % Ellipse n 10890 1946 678 271 0 360 DrawEllipse gs col0 s gr % Ellipse n 10958 4116 678 271 0 360 DrawEllipse gs col0 s gr % Ellipse n 7906 4116 678 271 0 360 DrawEllipse gs col0 s gr % Ellipse n 4923 4116 678 271 0 360 DrawEllipse gs col0 s gr % Ellipse n 4923 6286 678 271 0 360 DrawEllipse gs col0 s gr % Ellipse n 10890 6286 678 271 0 360 DrawEllipse gs col0 s gr % Ellipse n 7906 8456 678 271 0 360 DrawEllipse gs col0 s gr % Ellipse n 10890 8456 678 271 0 360 DrawEllipse gs col0 s gr % Ellipse n 7906 6286 678 271 0 360 DrawEllipse gs col0 s gr % Ellipse n 1871 6286 678 271 0 360 DrawEllipse gs col0 s gr % Ellipse n 1939 1946 678 271 0 360 DrawEllipse gs col0 s gr % Ellipse n 1939 4116 678 271 0 360 DrawEllipse gs col0 s gr % Ellipse n 1939 1946 678 271 0 360 DrawEllipse gs col0 s gr % Ellipse n 7906 1946 678 271 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 4228 1932 m 4284 1839 l 4057 1702 l 4216 1861 l 4002 1795 l cp eoclip n 2617 1810 m 2618 1809 l 2621 1808 l 2625 1806 l 2632 1802 l 2642 1797 l 2655 1790 l 2671 1783 l 2690 1773 l 2711 1763 l 2736 1752 l 2762 1740 l 2790 1727 l 2821 1715 l 2852 1702 l 2885 1690 l 2920 1678 l 2956 1666 l 2993 1655 l 3032 1645 l 3073 1636 l 3117 1627 l 3163 1620 l 3211 1614 l 3263 1610 l 3317 1607 l 3373 1606 l 3431 1607 l 3489 1611 l 3545 1616 l 3599 1624 l 3651 1633 l 3699 1643 l 3745 1654 l 3789 1666 l 3830 1679 l 3869 1692 l 3906 1706 l 3942 1721 l 3976 1735 l 4009 1751 l 4041 1766 l 4071 1781 l 4099 1796 l 4126 1810 l 4150 1823 l 4171 1835 l 4190 1846 l 4206 1855 l 4219 1863 l 4229 1869 l 4244 1878 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 4002 1795 m 4216 1861 l 4057 1702 l col0 s % Polyline 2 slj 7.500 slw gs clippath 2638 1961 m 2572 2047 l 2781 2209 l 2643 2034 l 2848 2123 l cp eoclip n 4244 2014 m 4243 2015 l 4241 2016 l 4236 2018 l 4230 2022 l 4220 2027 l 4208 2034 l 4192 2043 l 4173 2052 l 4152 2064 l 4128 2076 l 4102 2089 l 4073 2103 l 4043 2118 l 4011 2133 l 3978 2147 l 3944 2162 l 3908 2176 l 3871 2191 l 3834 2204 l 3795 2217 l 3754 2229 l 3712 2240 l 3668 2251 l 3622 2260 l 3573 2269 l 3523 2275 l 3471 2281 l 3417 2284 l 3363 2285 l 3305 2284 l 3250 2280 l 3197 2274 l 3148 2266 l 3102 2257 l 3058 2247 l 3018 2235 l 2980 2222 l 2944 2209 l 2910 2194 l 2878 2180 l 2848 2164 l 2818 2148 l 2791 2133 l 2765 2117 l 2740 2101 l 2718 2086 l 2697 2072 l 2678 2059 l 2662 2048 l 2649 2038 l 2638 2030 l 2630 2024 l 2617 2014 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 2848 2123 m 2643 2034 l 2781 2209 l col0 s % Polyline 2 slj 7.500 slw gs clippath 7144 1932 m 7200 1839 l 6973 1702 l 7132 1861 l 6918 1795 l cp eoclip n 5533 1810 m 5534 1809 l 5537 1808 l 5541 1806 l 5548 1802 l 5558 1797 l 5571 1790 l 5587 1783 l 5606 1773 l 5627 1763 l 5652 1752 l 5678 1740 l 5706 1727 l 5737 1715 l 5768 1702 l 5801 1690 l 5836 1678 l 5872 1666 l 5909 1655 l 5948 1645 l 5989 1636 l 6033 1627 l 6079 1620 l 6127 1614 l 6179 1610 l 6233 1607 l 6289 1606 l 6347 1607 l 6405 1611 l 6461 1616 l 6515 1624 l 6567 1633 l 6615 1643 l 6661 1654 l 6705 1666 l 6746 1679 l 6785 1692 l 6822 1706 l 6858 1721 l 6892 1735 l 6925 1751 l 6957 1766 l 6987 1781 l 7015 1796 l 7042 1810 l 7066 1823 l 7087 1835 l 7106 1846 l 7122 1855 l 7135 1863 l 7145 1869 l 7160 1878 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 6918 1795 m 7132 1861 l 6973 1702 l col0 s % Polyline 2 slj 7.500 slw gs clippath 10196 1864 m 10252 1771 l 10025 1634 l 10184 1793 l 9970 1727 l cp eoclip n 8585 1742 m 8586 1741 l 8589 1740 l 8593 1738 l 8600 1734 l 8610 1729 l 8623 1722 l 8639 1715 l 8658 1705 l 8679 1695 l 8703 1684 l 8730 1672 l 8758 1659 l 8788 1647 l 8820 1634 l 8853 1622 l 8887 1610 l 8923 1598 l 8960 1587 l 8999 1577 l 9040 1568 l 9084 1559 l 9130 1552 l 9178 1546 l 9230 1542 l 9284 1539 l 9340 1538 l 9398 1539 l 9456 1543 l 9512 1548 l 9566 1556 l 9618 1565 l 9666 1575 l 9712 1586 l 9756 1598 l 9797 1611 l 9836 1624 l 9873 1638 l 9909 1653 l 9944 1667 l 9977 1683 l 10008 1698 l 10039 1713 l 10067 1728 l 10093 1742 l 10118 1755 l 10139 1767 l 10158 1778 l 10174 1787 l 10187 1795 l 10197 1801 l 10212 1810 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 9970 1727 m 10184 1793 l 10025 1634 l col0 s % Polyline 2 slj 7.500 slw gs clippath 4228 4102 m 4284 4009 l 4057 3872 l 4216 4031 l 4002 3965 l cp eoclip n 2617 3980 m 2618 3979 l 2621 3978 l 2625 3976 l 2632 3972 l 2642 3967 l 2655 3960 l 2671 3953 l 2690 3943 l 2711 3933 l 2736 3922 l 2762 3910 l 2790 3897 l 2821 3885 l 2852 3872 l 2885 3860 l 2920 3848 l 2956 3836 l 2993 3825 l 3032 3815 l 3073 3806 l 3117 3797 l 3163 3790 l 3211 3784 l 3263 3780 l 3317 3777 l 3373 3776 l 3431 3777 l 3489 3781 l 3545 3786 l 3599 3794 l 3651 3803 l 3699 3813 l 3745 3824 l 3789 3836 l 3830 3849 l 3869 3862 l 3906 3876 l 3942 3891 l 3976 3905 l 4009 3921 l 4041 3936 l 4071 3951 l 4099 3966 l 4126 3980 l 4150 3993 l 4171 4005 l 4190 4016 l 4206 4025 l 4219 4033 l 4229 4039 l 4244 4048 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 4002 3965 m 4216 4031 l 4057 3872 l col0 s % Polyline 2 slj 7.500 slw gs clippath 7144 4102 m 7200 4009 l 6973 3872 l 7132 4031 l 6918 3965 l cp eoclip n 5533 3980 m 5534 3979 l 5537 3978 l 5541 3976 l 5548 3972 l 5558 3967 l 5571 3960 l 5587 3953 l 5606 3943 l 5627 3933 l 5652 3922 l 5678 3910 l 5706 3897 l 5737 3885 l 5768 3872 l 5801 3860 l 5836 3848 l 5872 3836 l 5909 3825 l 5948 3815 l 5989 3806 l 6033 3797 l 6079 3790 l 6127 3784 l 6179 3780 l 6233 3777 l 6289 3776 l 6347 3777 l 6405 3781 l 6461 3786 l 6515 3794 l 6567 3803 l 6615 3813 l 6661 3824 l 6705 3836 l 6746 3849 l 6785 3862 l 6822 3876 l 6858 3891 l 6892 3905 l 6925 3921 l 6957 3936 l 6987 3951 l 7015 3966 l 7042 3980 l 7066 3993 l 7087 4005 l 7106 4016 l 7122 4025 l 7135 4033 l 7145 4039 l 7160 4048 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 6918 3965 m 7132 4031 l 6973 3872 l col0 s % Polyline 2 slj 7.500 slw gs clippath 10135 4014 m 10191 3921 l 9964 3784 l 10123 3943 l 9909 3877 l cp eoclip n 8523 3892 m 8524 3891 l 8527 3890 l 8531 3888 l 8538 3884 l 8548 3879 l 8561 3872 l 8577 3864 l 8596 3855 l 8617 3845 l 8642 3833 l 8668 3821 l 8696 3809 l 8727 3796 l 8758 3784 l 8791 3771 l 8826 3759 l 8861 3748 l 8899 3737 l 8938 3726 l 8979 3717 l 9023 3709 l 9068 3701 l 9117 3695 l 9168 3691 l 9223 3688 l 9279 3687 l 9337 3688 l 9395 3692 l 9451 3697 l 9506 3705 l 9557 3714 l 9606 3724 l 9651 3735 l 9695 3747 l 9736 3760 l 9775 3773 l 9813 3787 l 9848 3802 l 9883 3817 l 9916 3832 l 9948 3847 l 9978 3863 l 10006 3877 l 10032 3892 l 10057 3905 l 10078 3917 l 10097 3928 l 10113 3937 l 10126 3945 l 10136 3951 l 10151 3960 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 9909 3877 m 10123 3943 l 9964 3784 l col0 s % Polyline 2 slj 7.500 slw gs clippath 10202 8421 m 10258 8328 l 10031 8191 l 10190 8350 l 9976 8284 l cp eoclip n 8591 8300 m 8592 8299 l 8595 8298 l 8599 8296 l 8606 8292 l 8616 8287 l 8629 8280 l 8645 8272 l 8664 8263 l 8685 8253 l 8710 8241 l 8736 8229 l 8764 8217 l 8795 8204 l 8826 8192 l 8859 8179 l 8894 8167 l 8930 8156 l 8967 8145 l 9006 8135 l 9047 8125 l 9091 8117 l 9137 8109 l 9185 8103 l 9237 8099 l 9291 8096 l 9347 8095 l 9405 8096 l 9463 8100 l 9519 8105 l 9573 8113 l 9625 8121 l 9673 8132 l 9719 8143 l 9763 8155 l 9804 8167 l 9843 8181 l 9880 8195 l 9916 8209 l 9950 8224 l 9983 8240 l 10015 8255 l 10045 8270 l 10073 8285 l 10100 8299 l 10124 8312 l 10145 8324 l 10164 8335 l 10180 8344 l 10193 8352 l 10203 8358 l 10218 8367 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 9976 8284 m 10190 8350 l 10031 8191 l col0 s % Polyline 2 slj 7.500 slw gs clippath 2643 4218 m 2577 4304 l 2786 4466 l 2648 4291 l 2853 4380 l cp eoclip n 4250 4271 m 4249 4272 l 4247 4273 l 4242 4275 l 4236 4279 l 4226 4284 l 4213 4291 l 4198 4300 l 4179 4309 l 4158 4321 l 4134 4333 l 4107 4346 l 4079 4360 l 4049 4375 l 4017 4390 l 3984 4404 l 3949 4419 l 3914 4433 l 3877 4448 l 3839 4461 l 3800 4474 l 3759 4486 l 3717 4497 l 3673 4508 l 3627 4517 l 3579 4526 l 3528 4532 l 3476 4538 l 3422 4541 l 3368 4542 l 3310 4541 l 3255 4537 l 3202 4531 l 3153 4523 l 3106 4514 l 3063 4504 l 3023 4492 l 2985 4479 l 2949 4466 l 2915 4451 l 2883 4437 l 2852 4421 l 2823 4405 l 2796 4390 l 2770 4374 l 2745 4358 l 2722 4343 l 2702 4329 l 2683 4316 l 2667 4305 l 2654 4295 l 2643 4287 l 2635 4281 l 2622 4271 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 2853 4380 m 2648 4291 l 2786 4466 l col0 s % Polyline 2 slj 7.500 slw gs clippath 5627 4150 m 5561 4236 l 5770 4398 l 5632 4223 l 5837 4312 l cp eoclip n 7234 4203 m 7233 4204 l 7231 4205 l 7226 4207 l 7220 4211 l 7210 4216 l 7197 4223 l 7182 4232 l 7163 4241 l 7142 4253 l 7118 4265 l 7091 4278 l 7063 4292 l 7033 4307 l 7001 4322 l 6968 4336 l 6933 4351 l 6898 4365 l 6861 4380 l 6823 4393 l 6784 4406 l 6743 4418 l 6701 4429 l 6657 4440 l 6611 4449 l 6563 4458 l 6512 4464 l 6460 4470 l 6406 4473 l 6352 4474 l 6294 4473 l 6239 4469 l 6186 4463 l 6137 4455 l 6090 4446 l 6047 4436 l 6007 4424 l 5969 4411 l 5933 4398 l 5899 4383 l 5867 4369 l 5836 4353 l 5807 4337 l 5780 4322 l 5754 4306 l 5729 4290 l 5706 4275 l 5686 4261 l 5667 4248 l 5651 4237 l 5638 4227 l 5627 4219 l 5619 4213 l 5606 4203 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 5837 4312 m 5632 4223 l 5770 4398 l col0 s % Polyline 2 slj 7.500 slw gs clippath 5622 1961 m 5556 2047 l 5765 2209 l 5627 2034 l 5832 2123 l cp eoclip n 7228 2014 m 7227 2015 l 7225 2016 l 7220 2018 l 7214 2022 l 7204 2027 l 7192 2034 l 7176 2043 l 7157 2052 l 7136 2064 l 7112 2076 l 7086 2089 l 7057 2103 l 7027 2118 l 6995 2133 l 6962 2147 l 6928 2162 l 6892 2176 l 6855 2191 l 6818 2204 l 6779 2217 l 6738 2229 l 6696 2240 l 6652 2251 l 6606 2260 l 6557 2269 l 6507 2275 l 6455 2281 l 6401 2284 l 6347 2285 l 6289 2284 l 6234 2280 l 6181 2274 l 6132 2266 l 6086 2257 l 6042 2247 l 6002 2235 l 5964 2222 l 5928 2209 l 5894 2194 l 5862 2180 l 5832 2164 l 5802 2148 l 5775 2133 l 5749 2117 l 5724 2101 l 5702 2086 l 5681 2072 l 5662 2059 l 5646 2048 l 5633 2038 l 5622 2030 l 5614 2024 l 5601 2014 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 5832 2123 m 5627 2034 l 5765 2209 l col0 s % Polyline 2 slj 7.500 slw gs clippath 8606 1961 m 8540 2047 l 8749 2209 l 8611 2034 l 8816 2123 l cp eoclip n 10212 2014 m 10211 2015 l 10209 2016 l 10204 2018 l 10198 2022 l 10188 2027 l 10176 2034 l 10160 2043 l 10141 2052 l 10120 2064 l 10096 2076 l 10070 2089 l 10041 2103 l 10011 2118 l 9979 2133 l 9946 2147 l 9912 2162 l 9876 2176 l 9839 2191 l 9802 2204 l 9763 2217 l 9722 2229 l 9680 2240 l 9636 2251 l 9590 2260 l 9541 2269 l 9491 2275 l 9439 2281 l 9385 2284 l 9331 2285 l 9273 2284 l 9218 2280 l 9165 2274 l 9116 2266 l 9070 2257 l 9026 2247 l 8986 2235 l 8948 2222 l 8912 2209 l 8878 2194 l 8846 2180 l 8816 2164 l 8786 2148 l 8759 2133 l 8733 2117 l 8708 2101 l 8686 2086 l 8665 2072 l 8646 2059 l 8630 2048 l 8617 2038 l 8606 2030 l 8598 2024 l 8585 2014 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 8816 2123 m 8611 2034 l 8749 2209 l col0 s % Polyline 2 slj 7.500 slw gs clippath 8606 4063 m 8540 4149 l 8749 4311 l 8611 4136 l 8816 4225 l cp eoclip n 10212 4116 m 10211 4117 l 10209 4118 l 10204 4120 l 10198 4124 l 10188 4129 l 10176 4136 l 10160 4145 l 10141 4154 l 10120 4166 l 10096 4178 l 10070 4191 l 10041 4205 l 10011 4220 l 9979 4235 l 9946 4249 l 9912 4264 l 9876 4278 l 9839 4293 l 9802 4306 l 9763 4319 l 9722 4331 l 9680 4342 l 9636 4353 l 9590 4362 l 9541 4371 l 9491 4377 l 9439 4383 l 9385 4386 l 9331 4387 l 9273 4386 l 9218 4382 l 9165 4376 l 9116 4368 l 9070 4359 l 9026 4349 l 8986 4337 l 8948 4324 l 8912 4311 l 8878 4296 l 8846 4282 l 8816 4266 l 8786 4250 l 8759 4235 l 8733 4219 l 8708 4203 l 8686 4188 l 8665 4174 l 8646 4161 l 8630 4150 l 8617 4140 l 8606 4132 l 8598 4126 l 8585 4116 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 8816 4225 m 8611 4136 l 8749 4311 l col0 s % Polyline 2 slj 7.500 slw gs clippath 5215 6505 m 5148 6590 l 5357 6753 l 5220 6577 l 5424 6667 l cp eoclip n 7364 8252 m 5194 6557 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 5424 6667 m 5220 6577 l 5357 6753 l col0 s % Polyline 2 slj 7.500 slw gs clippath 8213 6487 m 8146 6572 l 8355 6735 l 8218 6559 l 8422 6649 l cp eoclip n 10362 8234 m 8192 6539 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 8422 6649 m 8218 6559 l 8355 6735 l col0 s % Polyline 2 slj 45.000 slw gs clippath 7560 4421 m 7460 4329 l 7178 4635 l 7412 4482 l 7277 4727 l cp eoclip n 7432 6015 m 7431 6014 l 7430 6012 l 7427 6007 l 7423 6001 l 7418 5991 l 7411 5978 l 7402 5963 l 7391 5944 l 7379 5923 l 7366 5899 l 7352 5872 l 7337 5844 l 7322 5814 l 7307 5782 l 7291 5749 l 7276 5714 l 7261 5679 l 7246 5642 l 7233 5604 l 7220 5565 l 7207 5524 l 7196 5482 l 7186 5438 l 7177 5392 l 7170 5344 l 7164 5293 l 7161 5241 l 7159 5187 l 7160 5133 l 7164 5075 l 7171 5020 l 7179 4967 l 7190 4918 l 7203 4871 l 7217 4828 l 7232 4788 l 7248 4750 l 7264 4714 l 7282 4680 l 7300 4648 l 7319 4617 l 7338 4588 l 7358 4561 l 7377 4535 l 7395 4510 l 7413 4487 l 7430 4467 l 7446 4448 l 7459 4432 l 7471 4419 l 7481 4408 l 7488 4400 l 7500 4387 l gs col0 s gr gr % arrowhead 0 slj 60.000 slw n 7277 4727 m 7412 4482 l 7178 4635 l 7277 4727 l cp gs 0.00 setgray ef gr col0 s % Polyline 2 slj 45.000 slw gs clippath 10679 4421 m 10579 4329 l 10297 4635 l 10531 4482 l 10396 4727 l cp eoclip n 10551 6015 m 10550 6014 l 10549 6012 l 10546 6007 l 10542 6001 l 10537 5991 l 10530 5978 l 10521 5963 l 10510 5944 l 10499 5923 l 10485 5899 l 10471 5872 l 10457 5844 l 10441 5814 l 10426 5782 l 10411 5749 l 10395 5714 l 10380 5679 l 10366 5642 l 10352 5604 l 10339 5565 l 10327 5524 l 10316 5482 l 10306 5438 l 10297 5392 l 10290 5344 l 10284 5293 l 10281 5241 l 10279 5187 l 10280 5133 l 10284 5075 l 10291 5020 l 10299 4967 l 10310 4918 l 10323 4871 l 10336 4828 l 10351 4788 l 10367 4750 l 10384 4714 l 10402 4680 l 10420 4648 l 10439 4617 l 10458 4588 l 10477 4561 l 10496 4535 l 10515 4510 l 10533 4487 l 10549 4467 l 10565 4448 l 10579 4432 l 10590 4419 l 10600 4408 l 10607 4400 l 10619 4387 l gs col0 s gr gr % arrowhead 0 slj 60.000 slw n 10396 4727 m 10531 4482 l 10297 4635 l 10396 4727 l cp gs 0.00 setgray ef gr col0 s % Polyline 2 slj 45.000 slw gs clippath 4630 4378 m 4530 4286 l 4248 4592 l 4482 4439 l 4347 4684 l cp eoclip n 4502 5971 m 4501 5970 l 4500 5968 l 4497 5963 l 4493 5957 l 4488 5947 l 4481 5935 l 4472 5919 l 4461 5900 l 4450 5879 l 4436 5855 l 4422 5829 l 4408 5800 l 4392 5770 l 4377 5738 l 4362 5705 l 4346 5671 l 4331 5635 l 4317 5598 l 4303 5561 l 4290 5522 l 4278 5481 l 4267 5439 l 4257 5395 l 4248 5349 l 4241 5300 l 4235 5250 l 4232 5198 l 4230 5144 l 4231 5090 l 4235 5032 l 4242 4977 l 4250 4924 l 4261 4875 l 4274 4829 l 4287 4785 l 4302 4745 l 4318 4707 l 4335 4671 l 4353 4637 l 4371 4605 l 4390 4575 l 4409 4545 l 4428 4518 l 4447 4492 l 4466 4467 l 4484 4445 l 4500 4424 l 4516 4405 l 4530 4389 l 4541 4376 l 4551 4365 l 4558 4357 l 4570 4344 l gs col0 s gr gr % arrowhead 0 slj 60.000 slw n 4347 4684 m 4482 4439 l 4248 4592 l 4347 4684 l cp gs 0.00 setgray ef gr col0 s % Polyline 2 slj 45.000 slw gs clippath 1728 4421 m 1628 4329 l 1346 4635 l 1580 4482 l 1445 4727 l cp eoclip n 1600 6015 m 1599 6014 l 1598 6012 l 1595 6007 l 1591 6001 l 1586 5991 l 1579 5978 l 1570 5963 l 1559 5944 l 1547 5923 l 1534 5899 l 1520 5872 l 1505 5844 l 1490 5814 l 1475 5782 l 1459 5749 l 1444 5714 l 1429 5679 l 1414 5642 l 1401 5604 l 1388 5565 l 1375 5524 l 1364 5482 l 1354 5438 l 1345 5392 l 1338 5344 l 1332 5293 l 1329 5241 l 1327 5187 l 1328 5133 l 1332 5075 l 1339 5020 l 1347 4967 l 1358 4918 l 1371 4871 l 1385 4828 l 1400 4788 l 1416 4750 l 1432 4714 l 1450 4680 l 1468 4648 l 1487 4617 l 1506 4588 l 1526 4561 l 1545 4535 l 1563 4510 l 1581 4487 l 1598 4467 l 1614 4448 l 1627 4432 l 1639 4419 l 1649 4408 l 1656 4400 l 1668 4387 l gs col0 s gr gr % arrowhead 0 slj 60.000 slw n 1445 4727 m 1580 4482 l 1346 4635 l 1445 4727 l cp gs 0.00 setgray ef gr col0 s % Polyline 2 slj 7.500 slw gs clippath 4167 6251 m 4223 6158 l 3996 6021 l 4155 6180 l 3941 6114 l cp eoclip n 2555 6130 m 2556 6129 l 2559 6128 l 2563 6126 l 2570 6122 l 2580 6117 l 2593 6110 l 2609 6102 l 2628 6093 l 2649 6083 l 2674 6071 l 2700 6059 l 2728 6047 l 2759 6034 l 2790 6022 l 2823 6009 l 2858 5997 l 2893 5986 l 2931 5975 l 2970 5965 l 3011 5955 l 3055 5947 l 3100 5939 l 3149 5933 l 3200 5929 l 3255 5926 l 3311 5925 l 3369 5926 l 3427 5930 l 3483 5935 l 3538 5943 l 3589 5951 l 3638 5962 l 3683 5973 l 3727 5985 l 3768 5997 l 3807 6011 l 3845 6025 l 3880 6039 l 3915 6054 l 3948 6070 l 3980 6085 l 4010 6100 l 4038 6115 l 4064 6129 l 4089 6142 l 4110 6154 l 4129 6165 l 4145 6174 l 4158 6182 l 4168 6188 l 4183 6197 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 3941 6114 m 4155 6180 l 3996 6021 l col0 s % Polyline 2 slj 7.500 slw gs clippath 7219 6251 m 7275 6158 l 7048 6021 l 7207 6180 l 6993 6114 l cp eoclip n 5607 6130 m 5608 6129 l 5611 6128 l 5615 6126 l 5622 6122 l 5632 6117 l 5645 6110 l 5661 6102 l 5680 6093 l 5701 6083 l 5726 6071 l 5752 6059 l 5780 6047 l 5811 6034 l 5842 6022 l 5875 6009 l 5910 5997 l 5945 5986 l 5983 5975 l 6022 5965 l 6063 5955 l 6107 5947 l 6152 5939 l 6201 5933 l 6252 5929 l 6307 5926 l 6363 5925 l 6421 5926 l 6479 5930 l 6535 5935 l 6590 5943 l 6641 5951 l 6690 5962 l 6735 5973 l 6779 5985 l 6820 5997 l 6859 6011 l 6897 6025 l 6932 6039 l 6967 6054 l 7000 6070 l 7032 6085 l 7062 6100 l 7090 6115 l 7116 6129 l 7141 6142 l 7162 6154 l 7181 6165 l 7197 6174 l 7210 6182 l 7220 6188 l 7235 6197 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 6993 6114 m 7207 6180 l 7048 6021 l col0 s % Polyline 2 slj 7.500 slw gs clippath 10202 6251 m 10258 6158 l 10031 6021 l 10190 6180 l 9976 6114 l cp eoclip n 8591 6130 m 8592 6129 l 8595 6128 l 8599 6126 l 8606 6122 l 8616 6117 l 8629 6110 l 8645 6102 l 8664 6093 l 8685 6083 l 8710 6071 l 8736 6059 l 8764 6047 l 8795 6034 l 8826 6022 l 8859 6009 l 8894 5997 l 8930 5986 l 8967 5975 l 9006 5965 l 9047 5955 l 9091 5947 l 9137 5939 l 9185 5933 l 9237 5929 l 9291 5926 l 9347 5925 l 9405 5926 l 9463 5930 l 9519 5935 l 9573 5943 l 9625 5951 l 9673 5962 l 9719 5973 l 9763 5985 l 9804 5997 l 9843 6011 l 9880 6025 l 9916 6039 l 9950 6054 l 9983 6070 l 10015 6085 l 10045 6100 l 10073 6115 l 10100 6129 l 10124 6142 l 10145 6154 l 10164 6165 l 10180 6174 l 10193 6182 l 10203 6188 l 10218 6197 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 9976 6114 m 10190 6180 l 10031 6021 l col0 s % Polyline 2 slj 7.500 slw gs clippath 2638 6301 m 2572 6387 l 2781 6549 l 2643 6374 l 2848 6463 l cp eoclip n 4244 6354 m 4243 6355 l 4241 6356 l 4236 6358 l 4230 6362 l 4220 6367 l 4208 6374 l 4192 6383 l 4173 6392 l 4152 6404 l 4128 6416 l 4102 6429 l 4073 6443 l 4043 6458 l 4011 6473 l 3978 6487 l 3944 6502 l 3908 6516 l 3871 6531 l 3834 6544 l 3795 6557 l 3754 6569 l 3712 6580 l 3668 6591 l 3622 6600 l 3573 6609 l 3523 6615 l 3471 6621 l 3417 6624 l 3363 6625 l 3305 6624 l 3250 6620 l 3197 6614 l 3148 6606 l 3102 6597 l 3058 6587 l 3018 6575 l 2980 6562 l 2944 6549 l 2910 6534 l 2878 6520 l 2848 6504 l 2818 6488 l 2791 6473 l 2765 6457 l 2740 6441 l 2718 6426 l 2697 6412 l 2678 6399 l 2662 6388 l 2649 6378 l 2638 6370 l 2630 6364 l 2617 6354 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 2848 6463 m 2643 6374 l 2781 6549 l col0 s % Polyline 2 slj 7.500 slw gs clippath 5614 6390 m 5548 6476 l 5757 6638 l 5619 6463 l 5824 6552 l cp eoclip n 7220 6443 m 7219 6444 l 7217 6445 l 7212 6447 l 7206 6451 l 7196 6456 l 7184 6463 l 7168 6472 l 7149 6482 l 7128 6493 l 7104 6505 l 7078 6519 l 7049 6533 l 7019 6547 l 6987 6562 l 6954 6577 l 6920 6592 l 6884 6606 l 6847 6620 l 6810 6634 l 6771 6647 l 6730 6659 l 6688 6670 l 6644 6681 l 6598 6690 l 6549 6698 l 6499 6705 l 6447 6711 l 6393 6714 l 6339 6715 l 6281 6714 l 6226 6710 l 6173 6704 l 6124 6696 l 6078 6687 l 6034 6676 l 5994 6665 l 5956 6652 l 5920 6638 l 5886 6624 l 5854 6609 l 5824 6594 l 5794 6578 l 5767 6562 l 5741 6546 l 5716 6531 l 5694 6516 l 5673 6502 l 5654 6489 l 5638 6477 l 5625 6467 l 5614 6459 l 5606 6453 l 5593 6443 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 5824 6552 m 5619 6463 l 5757 6638 l col0 s % Polyline 2 slj 7.500 slw gs clippath 8597 6322 m 8531 6408 l 8740 6570 l 8602 6395 l 8807 6484 l cp eoclip n 10204 6375 m 10203 6376 l 10201 6377 l 10196 6379 l 10190 6383 l 10180 6388 l 10167 6395 l 10152 6404 l 10133 6414 l 10112 6425 l 10088 6437 l 10061 6451 l 10033 6465 l 10003 6479 l 9971 6494 l 9938 6509 l 9903 6524 l 9868 6538 l 9831 6552 l 9793 6566 l 9754 6579 l 9713 6591 l 9671 6602 l 9627 6613 l 9581 6622 l 9533 6630 l 9482 6637 l 9430 6643 l 9376 6646 l 9322 6647 l 9264 6646 l 9209 6642 l 9156 6636 l 9107 6628 l 9060 6619 l 9017 6608 l 8977 6597 l 8939 6584 l 8903 6570 l 8869 6556 l 8837 6541 l 8806 6526 l 8777 6510 l 8750 6494 l 8724 6478 l 8699 6463 l 8676 6448 l 8656 6434 l 8637 6421 l 8621 6409 l 8608 6399 l 8597 6391 l 8589 6385 l 8576 6375 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 8807 6484 m 8602 6395 l 8740 6570 l col0 s % Polyline 2 slj 7.500 slw gs clippath 1718 2242 m 1638 2169 l 1458 2363 l 1646 2241 l 1538 2437 l cp eoclip n 1600 3845 m 1599 3844 l 1598 3842 l 1595 3837 l 1591 3831 l 1586 3821 l 1579 3808 l 1570 3793 l 1559 3774 l 1547 3753 l 1534 3729 l 1520 3702 l 1505 3674 l 1490 3644 l 1475 3612 l 1459 3579 l 1444 3544 l 1429 3509 l 1414 3472 l 1401 3434 l 1388 3395 l 1375 3354 l 1364 3312 l 1354 3268 l 1345 3222 l 1338 3174 l 1332 3123 l 1329 3071 l 1327 3017 l 1328 2963 l 1332 2905 l 1339 2850 l 1347 2797 l 1358 2748 l 1371 2701 l 1385 2658 l 1400 2618 l 1416 2580 l 1432 2544 l 1450 2510 l 1468 2478 l 1487 2447 l 1506 2418 l 1526 2391 l 1545 2365 l 1563 2340 l 1581 2317 l 1598 2297 l 1614 2278 l 1627 2262 l 1639 2249 l 1649 2238 l 1656 2230 l 1668 2217 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 1538 2437 m 1646 2241 l 1458 2363 l col0 s % Polyline 2 slj 45.000 slw gs clippath 2009 3819 m 2122 3895 l 2352 3548 l 2146 3737 l 2240 3473 l cp eoclip n 2074 2217 m 2075 2218 l 2076 2221 l 2079 2225 l 2084 2232 l 2090 2242 l 2098 2255 l 2108 2271 l 2120 2290 l 2133 2311 l 2147 2336 l 2162 2362 l 2177 2390 l 2193 2421 l 2209 2452 l 2225 2485 l 2240 2520 l 2255 2555 l 2269 2593 l 2283 2632 l 2296 2673 l 2307 2717 l 2318 2762 l 2327 2811 l 2335 2862 l 2341 2917 l 2345 2973 l 2346 3031 l 2345 3089 l 2341 3145 l 2335 3200 l 2327 3251 l 2318 3300 l 2307 3345 l 2296 3389 l 2283 3430 l 2269 3469 l 2255 3507 l 2240 3542 l 2225 3577 l 2209 3610 l 2193 3642 l 2177 3672 l 2162 3700 l 2147 3726 l 2133 3751 l 2120 3772 l 2108 3791 l 2098 3807 l 2090 3820 l 2084 3830 l 2074 3845 l gs col0 s gr gr % arrowhead 0 slj 60.000 slw n 2240 3473 m 2146 3737 l 2352 3548 l 2240 3473 l cp gs 0.00 setgray ef gr col0 s % Polyline 2 slj 45.000 slw gs clippath 5129 3819 m 5242 3895 l 5472 3548 l 5266 3737 l 5360 3473 l cp eoclip n 5194 2217 m 5195 2218 l 5196 2221 l 5199 2225 l 5204 2232 l 5210 2242 l 5218 2255 l 5228 2271 l 5239 2290 l 5252 2311 l 5266 2336 l 5281 2362 l 5297 2390 l 5313 2421 l 5328 2452 l 5344 2485 l 5360 2520 l 5374 2555 l 5389 2593 l 5402 2632 l 5415 2673 l 5427 2717 l 5437 2762 l 5446 2811 l 5454 2862 l 5460 2917 l 5464 2973 l 5465 3031 l 5464 3089 l 5460 3145 l 5454 3200 l 5446 3251 l 5437 3300 l 5427 3345 l 5415 3389 l 5402 3430 l 5389 3469 l 5374 3507 l 5360 3542 l 5344 3577 l 5328 3610 l 5313 3642 l 5297 3672 l 5281 3700 l 5266 3726 l 5252 3751 l 5239 3772 l 5228 3791 l 5218 3807 l 5210 3820 l 5204 3830 l 5194 3845 l gs col0 s gr gr % arrowhead 0 slj 60.000 slw n 5360 3473 m 5266 3737 l 5472 3548 l 5360 3473 l cp gs 0.00 setgray ef gr col0 s % Polyline 2 slj 7.500 slw gs clippath 4707 2245 m 4627 2172 l 4447 2366 l 4635 2244 l 4527 2440 l cp eoclip n 4589 3847 m 4588 3846 l 4587 3844 l 4584 3839 l 4580 3833 l 4575 3823 l 4568 3811 l 4559 3795 l 4548 3776 l 4537 3755 l 4523 3731 l 4509 3705 l 4495 3676 l 4479 3646 l 4464 3614 l 4449 3581 l 4433 3547 l 4418 3511 l 4404 3474 l 4390 3437 l 4377 3398 l 4365 3357 l 4354 3315 l 4344 3271 l 4335 3225 l 4328 3176 l 4322 3126 l 4319 3074 l 4317 3020 l 4318 2966 l 4322 2908 l 4329 2853 l 4337 2800 l 4348 2751 l 4361 2705 l 4374 2661 l 4389 2621 l 4405 2583 l 4422 2547 l 4440 2513 l 4458 2481 l 4477 2451 l 4496 2421 l 4515 2394 l 4534 2368 l 4553 2343 l 4571 2321 l 4587 2300 l 4603 2281 l 4617 2265 l 4628 2252 l 4638 2241 l 4645 2233 l 4657 2220 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 4527 2440 m 4635 2244 l 4447 2366 l col0 s % Polyline 2 slj 45.000 slw gs clippath 7841 3819 m 7954 3895 l 8184 3548 l 7978 3737 l 8072 3473 l cp eoclip n 7906 2217 m 7907 2218 l 7908 2221 l 7911 2225 l 7916 2232 l 7922 2242 l 7930 2255 l 7940 2271 l 7952 2290 l 7965 2311 l 7979 2336 l 7994 2362 l 8009 2390 l 8025 2421 l 8041 2452 l 8057 2485 l 8072 2520 l 8087 2555 l 8101 2593 l 8115 2632 l 8128 2673 l 8139 2717 l 8150 2762 l 8159 2811 l 8167 2862 l 8173 2917 l 8177 2973 l 8178 3031 l 8177 3089 l 8173 3145 l 8167 3200 l 8159 3251 l 8150 3300 l 8139 3345 l 8128 3389 l 8115 3430 l 8101 3469 l 8087 3507 l 8072 3542 l 8057 3577 l 8041 3610 l 8025 3642 l 8009 3672 l 7994 3700 l 7979 3726 l 7965 3751 l 7952 3772 l 7940 3791 l 7930 3807 l 7922 3820 l 7916 3830 l 7906 3845 l gs col0 s gr gr % arrowhead 0 slj 60.000 slw n 8072 3473 m 7978 3737 l 8184 3548 l 8072 3473 l cp gs 0.00 setgray ef gr col0 s % Polyline 2 slj 45.000 slw gs clippath 11116 3811 m 11229 3887 l 11459 3540 l 11253 3729 l 11347 3465 l cp eoclip n 11181 2210 m 11182 2211 l 11183 2214 l 11186 2218 l 11191 2225 l 11197 2235 l 11205 2248 l 11215 2264 l 11227 2283 l 11240 2304 l 11254 2329 l 11269 2355 l 11284 2383 l 11300 2414 l 11316 2445 l 11332 2478 l 11347 2513 l 11362 2549 l 11376 2586 l 11390 2625 l 11403 2666 l 11414 2710 l 11425 2756 l 11434 2804 l 11442 2856 l 11448 2910 l 11452 2966 l 11453 3024 l 11452 3082 l 11448 3138 l 11442 3192 l 11434 3244 l 11425 3292 l 11414 3338 l 11403 3382 l 11390 3423 l 11376 3462 l 11362 3499 l 11347 3535 l 11332 3569 l 11316 3602 l 11300 3634 l 11284 3664 l 11269 3692 l 11254 3719 l 11240 3743 l 11227 3764 l 11215 3783 l 11205 3799 l 11197 3812 l 11191 3822 l 11181 3837 l gs col0 s gr gr % arrowhead 0 slj 60.000 slw n 11347 3465 m 11253 3729 l 11459 3540 l 11347 3465 l cp gs 0.00 setgray ef gr col0 s % Polyline 2 slj 7.500 slw gs clippath 8258 8236 m 8351 8292 l 8488 8065 l 8330 8224 l 8395 8010 l cp eoclip n 8313 4319 m 8313 4320 l 8314 4321 l 8316 4324 l 8319 4329 l 8322 4336 l 8327 4345 l 8334 4357 l 8341 4372 l 8351 4390 l 8361 4411 l 8374 4434 l 8387 4461 l 8402 4490 l 8418 4523 l 8435 4557 l 8453 4595 l 8471 4634 l 8491 4676 l 8510 4719 l 8530 4764 l 8551 4811 l 8571 4859 l 8591 4909 l 8611 4960 l 8631 5012 l 8650 5066 l 8669 5121 l 8688 5178 l 8706 5236 l 8723 5296 l 8740 5358 l 8756 5421 l 8771 5487 l 8785 5556 l 8798 5627 l 8811 5700 l 8822 5777 l 8831 5856 l 8840 5938 l 8847 6022 l 8852 6109 l 8855 6197 l 8856 6286 l 8855 6375 l 8852 6463 l 8847 6550 l 8840 6634 l 8831 6716 l 8822 6795 l 8811 6872 l 8798 6945 l 8785 7016 l 8771 7084 l 8756 7150 l 8740 7214 l 8723 7276 l 8706 7336 l 8688 7394 l 8669 7451 l 8650 7506 l 8631 7559 l 8611 7612 l 8591 7663 l 8571 7712 l 8551 7761 l 8530 7807 l 8510 7852 l 8491 7896 l 8471 7937 l 8453 7977 l 8435 8014 l 8418 8049 l 8402 8081 l 8387 8110 l 8374 8137 l 8361 8160 l 8351 8181 l 8341 8199 l 8334 8214 l 8327 8226 l 8322 8235 l 8319 8242 l 8313 8252 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 8395 8010 m 8330 8224 l 8488 8065 l col0 s % Polyline 2 slj 7.500 slw gs clippath 11242 8236 m 11335 8292 l 11472 8065 l 11314 8224 l 11379 8010 l cp eoclip n 11297 4319 m 11297 4320 l 11298 4321 l 11300 4324 l 11303 4329 l 11306 4336 l 11311 4345 l 11318 4357 l 11325 4372 l 11335 4390 l 11345 4411 l 11358 4434 l 11371 4461 l 11386 4490 l 11402 4523 l 11419 4557 l 11437 4595 l 11455 4634 l 11475 4676 l 11494 4719 l 11514 4764 l 11535 4811 l 11555 4859 l 11575 4909 l 11595 4960 l 11615 5012 l 11634 5066 l 11653 5121 l 11672 5178 l 11690 5236 l 11707 5296 l 11724 5358 l 11740 5421 l 11755 5487 l 11769 5556 l 11782 5627 l 11795 5700 l 11806 5777 l 11815 5856 l 11824 5938 l 11831 6022 l 11836 6109 l 11839 6197 l 11840 6286 l 11839 6375 l 11836 6463 l 11831 6550 l 11824 6634 l 11815 6716 l 11806 6795 l 11795 6872 l 11782 6945 l 11769 7016 l 11755 7084 l 11740 7150 l 11724 7214 l 11707 7276 l 11690 7336 l 11672 7394 l 11653 7451 l 11634 7506 l 11615 7559 l 11595 7612 l 11575 7663 l 11555 7712 l 11535 7761 l 11514 7807 l 11494 7852 l 11475 7896 l 11455 7937 l 11437 7977 l 11419 8014 l 11402 8049 l 11386 8081 l 11371 8110 l 11358 8137 l 11345 8160 l 11335 8181 l 11325 8199 l 11318 8214 l 11311 8226 l 11306 8235 l 11303 8242 l 11297 8252 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 11379 8010 m 11314 8224 l 11472 8065 l col0 s /Times-Roman ff 285.00 scf sf 7432 8592 m gs 1 -1 sc (2S,1L,S) col0 sh gr /Times-Roman ff 285.00 scf sf 10416 8592 m gs 1 -1 sc (3S,1L,S) col0 sh gr /Times-Roman ff 285.00 scf sf 1464 4252 m gs 1 -1 sc (0S,0L) col0 sh gr /Times-Roman ff 285.00 scf sf 4448 4252 m gs 1 -1 sc (1S,0L) col0 sh gr /Times-Roman ff 285.00 scf sf 1532 2082 m gs 1 -1 sc (0S,1L) col0 sh gr /Times-Roman ff 285.00 scf sf 4448 2082 m gs 1 -1 sc (1S,lL) col0 sh gr /Times-Roman ff 285.00 scf sf 7432 4252 m gs 1 -1 sc (2S,0L,S) col0 sh gr /Times-Roman ff 285.00 scf sf 10483 4252 m gs 1 -1 sc (3S,0L,S) col0 sh gr /Times-Roman ff 255.00 scf sf 10348 6354 m gs 1 -1 sc (3S,\(N+1\)L) col0 sh gr /Times-Roman ff 255.00 scf sf 7364 6354 m gs 1 -1 sc (2S,\(N+1\)L) col0 sh gr /Times-Roman ff 255.00 scf sf 4380 6354 m gs 1 -1 sc (1S,\(N+1\)L) col0 sh gr /Times-Roman ff 255.00 scf sf 1261 6354 m gs 1 -1 sc (0S,\(N+1\)L) col0 sh gr /Times-Roman ff 285.00 scf sf 7432 2082 m gs 1 -1 sc (2S,1L,L) col0 sh gr /Times-Roman ff 285.00 scf sf 10416 2082 m gs 1 -1 sc (3S,1L,L) col0 sh gr % Polyline [15 68] 68 sd n 225 1200 m 12975 1200 l 12975 2475 l 225 2475 l cp gs col0 s gr [] 0 sd % Polyline [15 68] 68 sd n 225 3300 m 5925 3300 l 5925 4800 l 225 4800 l cp gs col0 s gr [] 0 sd % Polyline [15 68] 68 sd n 6975 3225 m 12975 3225 l 12975 4725 l 6975 4725 l cp gs col0 s gr [] 0 sd % Polyline [15 68] 68 sd n 225 5550 m 13050 5550 l 13050 7050 l 225 7050 l cp gs col0 s gr [] 0 sd % Polyline [15 68] 68 sd n 5775 7875 m 12675 7875 l 12675 9075 l 5775 9075 l cp gs col0 s gr [] 0 sd /Times-Roman ff 270.00 scf sf 375 3675 m gs 1 -1 sc (Region 1) col0 sh gr /Times-Roman ff 270.00 scf sf 11625 3600 m gs 1 -1 sc (Region 2) col0 sh gr /Times-Roman ff 270.00 scf sf 375 1575 m gs 1 -1 sc (Region 3) col0 sh gr /Times-Roman ff 270.00 scf sf 375 5925 m gs 1 -1 sc (Region 4) col0 sh gr /Times-Roman ff 270.00 scf sf 5925 8250 m gs 1 -1 sc (Region5) col0 sh gr F2psBegin10setmiterlimit0.060000.06000scF2psEnd rs %%EndDocument endTexFig 1822 1997 a Ff(\(a\))568 2211 y 21171196 14208860 0 0 49204756 32825098 startTexFig 568 2211 a %%BeginDocument: ../figures/k1expanded.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: k1expanded.eps %%Creator: fig2dev Version 3.2 Patchlevel 3d %%CreationDate: Tue Apr 30 12:51:37 2002 %%For: harchol@mor.sp.cs.cmu.edu (Mor Harchol-Balter) %%BoundingBox: 0 0 748 499 %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def F2psDictbeginF2psDict begin F2psDictbeginF2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 499 moveto 0 0 lineto 748 0 lineto 748 499 lineto closepath clip newpath -35.1 545.3 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def F2psBegin10setmiterlimit0.060000.06000scF2psBegin 10 setmiterlimit 0.06000 0.06000 sc % % Fig objects follow % /Symbol ff 195.00 scf sf 6150 930 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 6270 1050 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 9450 930 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 9570 1050 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 2775 3405 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 2895 3525 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 9375 3330 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 9495 3450 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 9450 8130 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 9570 8250 m gs 1 -1 sc (S) col0 sh gr 15.000 slw % Ellipse n 12300 1575 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12600 1575 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12900 1575 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12375 6300 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12675 6300 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12975 6300 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12375 3975 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12675 3975 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12975 3975 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12300 8775 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12600 8775 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12900 8775 54 54 0 360 DrawEllipse gs col0 s gr /Symbol ff 240.00 scf sf 6600 7635 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 6750 7785 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 240.00 scf sf 6450 7635 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 240.00 scf sf 9900 7560 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 10050 7710 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 240.00 scf sf 9750 7560 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 195.00 scf sf 2700 5805 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 2820 5925 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 6000 5805 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 6120 5925 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 9450 5805 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 9570 5925 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 9600 6901 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 9751 7050 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 6000 6976 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 6151 7125 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 2700 6901 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 2851 7050 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 300.00 scf sf 825 2832 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 1013 2925 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 4125 2832 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 4313 2925 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 8925 5307 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 9113 5400 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 12225 5232 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 12413 5325 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 255.00 scf sf 1200 2325 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 1275 2475 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 255.00 scf sf 1875 2325 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 1950 2475 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 255.00 scf sf 1200 3225 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 1275 3375 m gs 1 -1 sc (3) col0 sh gr % Ellipse n 1575 2775 168 168 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 1519 2651 m 1636 2627 l 1580 2345 l 1569 2593 l 1463 2369 l cp eoclip n 1425 1875 m 1575 2625 l gs col0 s gr gr % arrowhead 0 slj n 1463 2369 m 1569 2593 l 1580 2345 l col0 s % Polyline 2 slj gs clippath 1438 3683 m 1558 3695 l 1586 3409 l 1503 3642 l 1467 3397 l cp eoclip n 1575 2925 m 1500 3675 l gs col0 s gr gr % arrowhead 0 slj n 1467 3397 m 1503 3642 l 1586 3409 l col0 s % Polyline 2 slj gs clippath 1589 3661 m 1696 3715 l 1825 3457 l 1665 3645 l 1718 3403 l cp eoclip n 1650 1875 m 1650 1876 l 1652 1878 l 1654 1882 l 1657 1889 l 1661 1898 l 1667 1910 l 1674 1925 l 1682 1943 l 1691 1963 l 1701 1986 l 1712 2012 l 1724 2039 l 1736 2069 l 1748 2100 l 1761 2133 l 1773 2167 l 1785 2202 l 1797 2238 l 1808 2277 l 1818 2316 l 1829 2358 l 1838 2401 l 1847 2447 l 1855 2496 l 1861 2547 l 1867 2600 l 1871 2657 l 1874 2715 l 1875 2775 l 1874 2835 l 1871 2893 l 1867 2950 l 1861 3003 l 1855 3054 l 1847 3103 l 1838 3149 l 1829 3192 l 1818 3234 l 1808 3273 l 1797 3312 l 1785 3348 l 1773 3383 l 1761 3417 l 1748 3450 l 1736 3481 l 1724 3511 l 1712 3538 l 1701 3564 l 1691 3587 l 1682 3607 l 1674 3625 l 1667 3640 l 1661 3652 l 1657 3661 l 1650 3675 l gs col0 s gr gr % arrowhead 0 slj n 1718 3403 m 1665 3645 l 1825 3457 l col0 s /Times-Roman ff 315.00 scf sf 975 1725 m gs 1 -1 sc (0S,1L) col0 sh gr /Symbol ff 255.00 scf sf 4575 2325 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 4650 2475 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 255.00 scf sf 5250 2325 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 5325 2475 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 255.00 scf sf 4575 3225 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 4650 3375 m gs 1 -1 sc (3) col0 sh gr % Ellipse n 4950 2775 168 168 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 4894 2651 m 5011 2627 l 4955 2345 l 4944 2593 l 4838 2369 l cp eoclip n 4800 1875 m 4950 2625 l gs col0 s gr gr % arrowhead 0 slj n 4838 2369 m 4944 2593 l 4955 2345 l col0 s % Polyline 2 slj gs clippath 4813 3683 m 4933 3695 l 4961 3409 l 4878 3642 l 4842 3397 l cp eoclip n 4950 2925 m 4875 3675 l gs col0 s gr gr % arrowhead 0 slj n 4842 3397 m 4878 3642 l 4961 3409 l col0 s % Polyline 2 slj gs clippath 4964 3661 m 5071 3715 l 5200 3457 l 5040 3645 l 5093 3403 l cp eoclip n 5025 1875 m 5025 1876 l 5027 1878 l 5029 1882 l 5032 1889 l 5036 1898 l 5042 1910 l 5049 1925 l 5057 1943 l 5066 1963 l 5076 1986 l 5087 2012 l 5099 2039 l 5111 2069 l 5123 2100 l 5136 2133 l 5148 2167 l 5160 2202 l 5172 2238 l 5183 2277 l 5193 2316 l 5204 2358 l 5213 2401 l 5222 2447 l 5230 2496 l 5236 2547 l 5242 2600 l 5246 2657 l 5249 2715 l 5250 2775 l 5249 2835 l 5246 2893 l 5242 2950 l 5236 3003 l 5230 3054 l 5222 3103 l 5213 3149 l 5204 3192 l 5193 3234 l 5183 3273 l 5172 3312 l 5160 3348 l 5148 3383 l 5136 3417 l 5123 3450 l 5111 3481 l 5099 3511 l 5087 3538 l 5076 3564 l 5066 3587 l 5057 3607 l 5049 3625 l 5042 3640 l 5036 3652 l 5032 3661 l 5025 3675 l gs col0 s gr gr % arrowhead 0 slj n 5093 3403 m 5040 3645 l 5200 3457 l col0 s /Symbol ff 255.00 scf sf 7800 2325 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 7875 2475 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 255.00 scf sf 8475 2325 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 8550 2475 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 255.00 scf sf 7800 3225 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 7875 3375 m gs 1 -1 sc (3) col0 sh gr % Ellipse n 8175 2775 168 168 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 8119 2651 m 8236 2627 l 8180 2345 l 8169 2593 l 8063 2369 l cp eoclip n 8025 1875 m 8175 2625 l gs col0 s gr gr % arrowhead 0 slj n 8063 2369 m 8169 2593 l 8180 2345 l col0 s % Polyline 2 slj gs clippath 8038 3683 m 8158 3695 l 8186 3409 l 8103 3642 l 8067 3397 l cp eoclip n 8175 2925 m 8100 3675 l gs col0 s gr gr % arrowhead 0 slj n 8067 3397 m 8103 3642 l 8186 3409 l col0 s % Polyline 2 slj gs clippath 8189 3661 m 8296 3715 l 8425 3457 l 8265 3645 l 8318 3403 l cp eoclip n 8250 1875 m 8250 1876 l 8252 1878 l 8254 1882 l 8257 1889 l 8261 1898 l 8267 1910 l 8274 1925 l 8282 1943 l 8291 1963 l 8301 1986 l 8312 2012 l 8324 2039 l 8336 2069 l 8348 2100 l 8361 2133 l 8373 2167 l 8385 2202 l 8397 2238 l 8408 2277 l 8418 2316 l 8429 2358 l 8438 2401 l 8447 2447 l 8455 2496 l 8461 2547 l 8467 2600 l 8471 2657 l 8474 2715 l 8475 2775 l 8474 2835 l 8471 2893 l 8467 2950 l 8461 3003 l 8455 3054 l 8447 3103 l 8438 3149 l 8429 3192 l 8418 3234 l 8408 3273 l 8397 3312 l 8385 3348 l 8373 3383 l 8361 3417 l 8348 3450 l 8336 3481 l 8324 3511 l 8312 3538 l 8301 3564 l 8291 3587 l 8282 3607 l 8274 3625 l 8267 3640 l 8261 3652 l 8257 3661 l 8250 3675 l gs col0 s gr gr % arrowhead 0 slj n 8318 3403 m 8265 3645 l 8425 3457 l col0 s /Symbol ff 255.00 scf sf 11025 2325 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 11100 2475 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 255.00 scf sf 11700 2325 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 11775 2475 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 255.00 scf sf 11025 3225 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 11100 3375 m gs 1 -1 sc (3) col0 sh gr % Ellipse n 11400 2775 168 168 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 11344 2651 m 11461 2627 l 11405 2345 l 11394 2593 l 11288 2369 l cp eoclip n 11250 1875 m 11400 2625 l gs col0 s gr gr % arrowhead 0 slj n 11288 2369 m 11394 2593 l 11405 2345 l col0 s % Polyline 2 slj gs clippath 11263 3683 m 11383 3695 l 11411 3409 l 11328 3642 l 11292 3397 l cp eoclip n 11400 2925 m 11325 3675 l gs col0 s gr gr % arrowhead 0 slj n 11292 3397 m 11328 3642 l 11411 3409 l col0 s % Polyline 2 slj gs clippath 11414 3661 m 11521 3715 l 11650 3457 l 11490 3645 l 11543 3403 l cp eoclip n 11475 1875 m 11475 1876 l 11477 1878 l 11479 1882 l 11482 1889 l 11486 1898 l 11492 1910 l 11499 1925 l 11507 1943 l 11516 1963 l 11526 1986 l 11537 2012 l 11549 2039 l 11561 2069 l 11573 2100 l 11586 2133 l 11598 2167 l 11610 2202 l 11622 2238 l 11633 2277 l 11643 2316 l 11654 2358 l 11663 2401 l 11672 2447 l 11680 2496 l 11686 2547 l 11692 2600 l 11696 2657 l 11699 2715 l 11700 2775 l 11699 2835 l 11696 2893 l 11692 2950 l 11686 3003 l 11680 3054 l 11672 3103 l 11663 3149 l 11654 3192 l 11643 3234 l 11633 3273 l 11622 3312 l 11610 3348 l 11598 3383 l 11586 3417 l 11573 3450 l 11561 3481 l 11549 3511 l 11537 3538 l 11526 3564 l 11516 3587 l 11507 3607 l 11499 3625 l 11492 3640 l 11486 3652 l 11482 3661 l 11475 3675 l gs col0 s gr gr % arrowhead 0 slj n 11543 3403 m 11490 3645 l 11650 3457 l col0 s /Symbol ff 255.00 scf sf 1500 5850 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 360.00 scf sf 1350 5775 m gs 1 -1 sc (t) col0 sh gr /Symbol ff 255.00 scf sf 750 5775 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 360.00 scf sf 600 5700 m gs 1 -1 sc (t) col0 sh gr /Symbol ff 255.00 scf sf 1500 4875 m gs 1 -1 sc (3) col0 sh gr /Symbol ff 360.00 scf sf 1350 4800 m gs 1 -1 sc (t) col0 sh gr % Ellipse n 1200 5175 168 168 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 1255 5298 m 1138 5322 l 1194 5604 l 1206 5357 l 1311 5580 l cp eoclip n 1350 6075 m 1200 5325 l gs col0 s gr gr % arrowhead 0 slj n 1311 5580 m 1206 5357 l 1194 5604 l col0 s % Polyline 2 slj gs clippath 1336 4266 m 1216 4254 l 1188 4540 l 1272 4308 l 1307 4552 l cp eoclip n 1200 5025 m 1275 4275 l gs col0 s gr gr % arrowhead 0 slj n 1307 4552 m 1272 4308 l 1188 4540 l col0 s % Polyline 2 slj gs clippath 1185 4288 m 1078 4234 l 949 4492 l 1110 4305 l 1056 4546 l cp eoclip n 1125 6075 m 1125 6074 l 1123 6072 l 1121 6068 l 1118 6061 l 1114 6052 l 1108 6040 l 1101 6025 l 1093 6007 l 1084 5987 l 1074 5964 l 1063 5938 l 1051 5911 l 1039 5881 l 1027 5850 l 1014 5817 l 1002 5783 l 990 5748 l 978 5712 l 967 5673 l 957 5634 l 946 5592 l 937 5549 l 928 5503 l 920 5454 l 914 5403 l 908 5350 l 904 5293 l 901 5235 l 900 5175 l 901 5115 l 904 5057 l 908 5000 l 914 4947 l 920 4896 l 928 4847 l 937 4801 l 946 4758 l 957 4716 l 967 4677 l 978 4638 l 990 4602 l 1002 4567 l 1014 4533 l 1027 4500 l 1039 4469 l 1051 4439 l 1063 4412 l 1074 4386 l 1084 4363 l 1093 4343 l 1101 4325 l 1108 4310 l 1114 4298 l 1118 4289 l 1125 4275 l gs col0 s gr gr % arrowhead 0 slj n 1056 4546 m 1110 4305 l 949 4492 l col0 s /Symbol ff 255.00 scf sf 4950 5850 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 360.00 scf sf 4800 5775 m gs 1 -1 sc (t) col0 sh gr /Symbol ff 255.00 scf sf 4200 5775 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 360.00 scf sf 4050 5700 m gs 1 -1 sc (t) col0 sh gr /Symbol ff 255.00 scf sf 4950 4875 m gs 1 -1 sc (3) col0 sh gr /Symbol ff 360.00 scf sf 4800 4800 m gs 1 -1 sc (t) col0 sh gr % Ellipse n 4650 5175 168 168 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 4705 5298 m 4588 5322 l 4644 5604 l 4656 5357 l 4761 5580 l cp eoclip n 4800 6075 m 4650 5325 l gs col0 s gr gr % arrowhead 0 slj n 4761 5580 m 4656 5357 l 4644 5604 l col0 s % Polyline 2 slj gs clippath 4786 4266 m 4666 4254 l 4638 4540 l 4722 4308 l 4757 4552 l cp eoclip n 4650 5025 m 4725 4275 l gs col0 s gr gr % arrowhead 0 slj n 4757 4552 m 4722 4308 l 4638 4540 l col0 s % Polyline 2 slj gs clippath 4635 4288 m 4528 4234 l 4399 4492 l 4560 4305 l 4506 4546 l cp eoclip n 4575 6075 m 4575 6074 l 4573 6072 l 4571 6068 l 4568 6061 l 4564 6052 l 4558 6040 l 4551 6025 l 4543 6007 l 4534 5987 l 4524 5964 l 4513 5938 l 4501 5911 l 4489 5881 l 4477 5850 l 4464 5817 l 4452 5783 l 4440 5748 l 4428 5712 l 4417 5673 l 4407 5634 l 4396 5592 l 4387 5549 l 4378 5503 l 4370 5454 l 4364 5403 l 4358 5350 l 4354 5293 l 4351 5235 l 4350 5175 l 4351 5115 l 4354 5057 l 4358 5000 l 4364 4947 l 4370 4896 l 4378 4847 l 4387 4801 l 4396 4758 l 4407 4716 l 4417 4677 l 4428 4638 l 4440 4602 l 4452 4567 l 4464 4533 l 4477 4500 l 4489 4469 l 4501 4439 l 4513 4412 l 4524 4386 l 4534 4363 l 4543 4343 l 4551 4325 l 4558 4310 l 4564 4298 l 4568 4289 l 4575 4275 l gs col0 s gr gr % arrowhead 0 slj n 4506 4546 m 4560 4305 l 4399 4492 l col0 s /Symbol ff 255.00 scf sf 8325 5850 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 360.00 scf sf 8175 5775 m gs 1 -1 sc (t) col0 sh gr /Symbol ff 255.00 scf sf 7575 5775 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 360.00 scf sf 7425 5700 m gs 1 -1 sc (t) col0 sh gr /Symbol ff 255.00 scf sf 8325 4875 m gs 1 -1 sc (3) col0 sh gr /Symbol ff 360.00 scf sf 8175 4800 m gs 1 -1 sc (t) col0 sh gr % Ellipse n 8025 5175 168 168 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 8080 5298 m 7963 5322 l 8019 5604 l 8031 5357 l 8136 5580 l cp eoclip n 8175 6075 m 8025 5325 l gs col0 s gr gr % arrowhead 0 slj n 8136 5580 m 8031 5357 l 8019 5604 l col0 s % Polyline 2 slj gs clippath 8161 4266 m 8041 4254 l 8013 4540 l 8097 4308 l 8132 4552 l cp eoclip n 8025 5025 m 8100 4275 l gs col0 s gr gr % arrowhead 0 slj n 8132 4552 m 8097 4308 l 8013 4540 l col0 s % Polyline 2 slj gs clippath 8010 4288 m 7903 4234 l 7774 4492 l 7935 4305 l 7881 4546 l cp eoclip n 7950 6075 m 7950 6074 l 7948 6072 l 7946 6068 l 7943 6061 l 7939 6052 l 7933 6040 l 7926 6025 l 7918 6007 l 7909 5987 l 7899 5964 l 7888 5938 l 7876 5911 l 7864 5881 l 7852 5850 l 7839 5817 l 7827 5783 l 7815 5748 l 7803 5712 l 7792 5673 l 7782 5634 l 7771 5592 l 7762 5549 l 7753 5503 l 7745 5454 l 7739 5403 l 7733 5350 l 7729 5293 l 7726 5235 l 7725 5175 l 7726 5115 l 7729 5057 l 7733 5000 l 7739 4947 l 7745 4896 l 7753 4847 l 7762 4801 l 7771 4758 l 7782 4716 l 7792 4677 l 7803 4638 l 7815 4602 l 7827 4567 l 7839 4533 l 7852 4500 l 7864 4469 l 7876 4439 l 7888 4412 l 7899 4386 l 7909 4363 l 7918 4343 l 7926 4325 l 7933 4310 l 7939 4298 l 7943 4289 l 7950 4275 l gs col0 s gr gr % arrowhead 0 slj n 7881 4546 m 7935 4305 l 7774 4492 l col0 s /Symbol ff 255.00 scf sf 11700 5775 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 360.00 scf sf 11550 5700 m gs 1 -1 sc (t) col0 sh gr /Symbol ff 255.00 scf sf 10950 5700 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 360.00 scf sf 10800 5625 m gs 1 -1 sc (t) col0 sh gr /Symbol ff 255.00 scf sf 11700 4800 m gs 1 -1 sc (3) col0 sh gr /Symbol ff 360.00 scf sf 11550 4725 m gs 1 -1 sc (t) col0 sh gr % Ellipse n 11400 5100 168 168 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 11455 5223 m 11338 5247 l 11394 5529 l 11406 5282 l 11511 5505 l cp eoclip n 11550 6000 m 11400 5250 l gs col0 s gr gr % arrowhead 0 slj n 11511 5505 m 11406 5282 l 11394 5529 l col0 s % Polyline 2 slj gs clippath 11536 4191 m 11416 4179 l 11388 4465 l 11472 4233 l 11507 4477 l cp eoclip n 11400 4950 m 11475 4200 l gs col0 s gr gr % arrowhead 0 slj n 11507 4477 m 11472 4233 l 11388 4465 l col0 s % Polyline 2 slj gs clippath 11385 4213 m 11278 4159 l 11149 4417 l 11310 4230 l 11256 4471 l cp eoclip n 11325 6000 m 11325 5999 l 11323 5997 l 11321 5993 l 11318 5986 l 11314 5977 l 11308 5965 l 11301 5950 l 11293 5932 l 11284 5912 l 11274 5889 l 11263 5863 l 11251 5836 l 11239 5806 l 11227 5775 l 11214 5742 l 11202 5708 l 11190 5673 l 11178 5637 l 11167 5598 l 11157 5559 l 11146 5517 l 11137 5474 l 11128 5428 l 11120 5379 l 11114 5328 l 11108 5275 l 11104 5218 l 11101 5160 l 11100 5100 l 11101 5040 l 11104 4982 l 11108 4925 l 11114 4872 l 11120 4821 l 11128 4772 l 11137 4726 l 11146 4683 l 11157 4641 l 11167 4602 l 11178 4563 l 11190 4527 l 11202 4492 l 11214 4458 l 11227 4425 l 11239 4394 l 11251 4364 l 11263 4337 l 11274 4311 l 11284 4288 l 11293 4268 l 11301 4250 l 11308 4235 l 11314 4223 l 11318 4214 l 11325 4200 l gs col0 s gr gr % arrowhead 0 slj n 11256 4471 m 11310 4230 l 11149 4417 l col0 s /Symbol ff 240.00 scf sf 2700 3076 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 2851 3225 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 2700 1005 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 2820 1125 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 2700 1801 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 2851 1950 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 2700 2280 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 2820 2400 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 9450 3001 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 9601 3150 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 9450 5401 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 9601 5550 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 6000 5401 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 6151 5550 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 2625 5401 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 2776 5550 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 2700 4276 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 2851 4425 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 6075 4185 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 6225 4335 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 240.00 scf sf 5925 4185 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 240.00 scf sf 9525 4110 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 9675 4260 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 240.00 scf sf 9375 4110 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 240.00 scf sf 9375 1801 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 9526 1950 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 6075 1801 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 6226 1950 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 9375 2280 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 9495 2400 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 9375 4755 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 9495 4875 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 5925 4755 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 6045 4875 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 2625 4755 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 2745 4875 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 6075 3405 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 6195 3525 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 6000 3001 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 6151 3150 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 6000 2280 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 6120 2400 m gs 1 -1 sc (S) col0 sh gr % Ellipse n 4725 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 11325 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 8025 3975 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 4725 3975 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 4725 6375 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 11325 6375 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 8025 8775 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 11325 8775 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 8025 6375 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 1350 6375 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 1425 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 1425 3975 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 1425 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 8025 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 11391 3940 750 300 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 3958 1559 m 4017 1455 l 3767 1312 l 3946 1484 l 3707 1417 l cp eoclip n 2175 1425 m 2176 1424 l 2178 1423 l 2182 1421 l 2189 1418 l 2198 1413 l 2210 1407 l 2225 1399 l 2243 1391 l 2263 1381 l 2286 1370 l 2312 1358 l 2339 1345 l 2369 1333 l 2400 1320 l 2433 1307 l 2467 1294 l 2502 1281 l 2538 1269 l 2577 1258 l 2616 1247 l 2658 1237 l 2701 1228 l 2747 1219 l 2796 1212 l 2847 1206 l 2900 1202 l 2957 1199 l 3015 1199 l 3075 1200 l 3135 1204 l 3193 1209 l 3250 1217 l 3303 1225 l 3354 1236 l 3403 1247 l 3449 1259 l 3492 1272 l 3534 1285 l 3573 1299 l 3612 1314 l 3648 1329 l 3683 1344 l 3717 1360 l 3750 1376 l 3781 1391 l 3811 1407 l 3838 1421 l 3864 1435 l 3887 1448 l 3907 1460 l 3925 1470 l 3940 1479 l 3952 1486 l 3961 1492 l 3975 1500 l gs col0 s gr gr % arrowhead 0 slj n 3707 1417 m 3946 1484 l 3767 1312 l col0 s % Polyline 2 slj gs clippath 2200 1593 m 2126 1687 l 2352 1865 l 2201 1670 l 2426 1771 l cp eoclip n 3975 1650 m 3974 1651 l 3971 1652 l 3966 1655 l 3959 1659 l 3948 1665 l 3935 1672 l 3917 1682 l 3897 1692 l 3873 1705 l 3847 1719 l 3817 1733 l 3786 1749 l 3752 1765 l 3717 1781 l 3680 1798 l 3642 1814 l 3603 1830 l 3563 1845 l 3521 1860 l 3478 1875 l 3433 1888 l 3386 1901 l 3337 1912 l 3286 1923 l 3233 1932 l 3177 1939 l 3119 1945 l 3060 1949 l 3000 1950 l 2936 1949 l 2875 1944 l 2817 1938 l 2762 1929 l 2711 1919 l 2663 1907 l 2618 1895 l 2576 1881 l 2537 1866 l 2499 1850 l 2464 1833 l 2430 1816 l 2398 1799 l 2367 1781 l 2338 1764 l 2311 1747 l 2286 1730 l 2263 1715 l 2243 1700 l 2225 1688 l 2210 1677 l 2198 1668 l 2189 1661 l 2175 1650 l gs col0 s gr gr % arrowhead 0 slj n 2426 1771 m 2201 1670 l 2352 1865 l col0 s % Polyline 2 slj gs clippath 7183 1559 m 7242 1455 l 6992 1312 l 7171 1484 l 6932 1417 l cp eoclip n 5400 1425 m 5401 1424 l 5403 1423 l 5407 1421 l 5414 1418 l 5423 1413 l 5435 1407 l 5450 1399 l 5468 1391 l 5488 1381 l 5511 1370 l 5537 1358 l 5564 1345 l 5594 1333 l 5625 1320 l 5658 1307 l 5692 1294 l 5727 1281 l 5763 1269 l 5802 1258 l 5841 1247 l 5883 1237 l 5926 1228 l 5972 1219 l 6021 1212 l 6072 1206 l 6125 1202 l 6182 1199 l 6240 1199 l 6300 1200 l 6360 1204 l 6418 1209 l 6475 1217 l 6528 1225 l 6579 1236 l 6628 1247 l 6674 1259 l 6717 1272 l 6759 1285 l 6798 1299 l 6837 1314 l 6873 1329 l 6908 1344 l 6942 1360 l 6975 1376 l 7006 1391 l 7036 1407 l 7063 1421 l 7089 1435 l 7112 1448 l 7132 1460 l 7150 1470 l 7165 1479 l 7177 1486 l 7186 1492 l 7200 1500 l gs col0 s gr gr % arrowhead 0 slj n 6932 1417 m 7171 1484 l 6992 1312 l col0 s % Polyline 2 slj gs clippath 10558 1484 m 10617 1380 l 10367 1237 l 10546 1409 l 10307 1342 l cp eoclip n 8775 1350 m 8776 1349 l 8778 1348 l 8782 1346 l 8789 1343 l 8798 1338 l 8810 1332 l 8825 1324 l 8843 1316 l 8863 1306 l 8886 1295 l 8912 1283 l 8939 1270 l 8969 1258 l 9000 1245 l 9033 1232 l 9067 1219 l 9102 1206 l 9138 1194 l 9177 1183 l 9216 1172 l 9258 1162 l 9301 1153 l 9347 1144 l 9396 1137 l 9447 1131 l 9500 1127 l 9557 1124 l 9615 1124 l 9675 1125 l 9735 1129 l 9793 1134 l 9850 1142 l 9903 1150 l 9954 1161 l 10003 1172 l 10049 1184 l 10092 1197 l 10134 1210 l 10173 1224 l 10212 1239 l 10248 1254 l 10283 1269 l 10317 1285 l 10350 1301 l 10381 1316 l 10411 1332 l 10438 1346 l 10464 1360 l 10487 1373 l 10507 1385 l 10525 1395 l 10540 1404 l 10552 1411 l 10561 1417 l 10575 1425 l gs col0 s gr gr % arrowhead 0 slj n 10307 1342 m 10546 1409 l 10367 1237 l col0 s % Polyline 2 slj gs clippath 3958 3959 m 4017 3855 l 3767 3712 l 3946 3884 l 3707 3817 l cp eoclip n 2175 3825 m 2176 3824 l 2178 3823 l 2182 3821 l 2189 3818 l 2198 3813 l 2210 3807 l 2225 3799 l 2243 3791 l 2263 3781 l 2286 3770 l 2312 3758 l 2339 3745 l 2369 3733 l 2400 3720 l 2433 3707 l 2467 3694 l 2502 3681 l 2538 3669 l 2577 3658 l 2616 3647 l 2658 3637 l 2701 3628 l 2747 3619 l 2796 3612 l 2847 3606 l 2900 3602 l 2957 3599 l 3015 3599 l 3075 3600 l 3135 3604 l 3193 3609 l 3250 3617 l 3303 3625 l 3354 3636 l 3403 3647 l 3449 3659 l 3492 3672 l 3534 3685 l 3573 3699 l 3612 3714 l 3648 3729 l 3683 3744 l 3717 3760 l 3750 3776 l 3781 3791 l 3811 3807 l 3838 3821 l 3864 3835 l 3887 3848 l 3907 3860 l 3925 3870 l 3940 3879 l 3952 3886 l 3961 3892 l 3975 3900 l gs col0 s gr gr % arrowhead 0 slj n 3707 3817 m 3946 3884 l 3767 3712 l col0 s % Polyline 2 slj gs clippath 7183 3959 m 7242 3855 l 6992 3712 l 7171 3884 l 6932 3817 l cp eoclip n 5400 3825 m 5401 3824 l 5403 3823 l 5407 3821 l 5414 3818 l 5423 3813 l 5435 3807 l 5450 3799 l 5468 3791 l 5488 3781 l 5511 3770 l 5537 3758 l 5564 3745 l 5594 3733 l 5625 3720 l 5658 3707 l 5692 3694 l 5727 3681 l 5763 3669 l 5802 3658 l 5841 3647 l 5883 3637 l 5926 3628 l 5972 3619 l 6021 3612 l 6072 3606 l 6125 3602 l 6182 3599 l 6240 3599 l 6300 3600 l 6360 3604 l 6418 3609 l 6475 3617 l 6528 3625 l 6579 3636 l 6628 3647 l 6674 3659 l 6717 3672 l 6759 3685 l 6798 3699 l 6837 3714 l 6873 3729 l 6908 3744 l 6942 3760 l 6975 3776 l 7006 3791 l 7036 3807 l 7063 3821 l 7089 3835 l 7112 3848 l 7132 3860 l 7150 3870 l 7165 3879 l 7177 3886 l 7186 3892 l 7200 3900 l gs col0 s gr gr % arrowhead 0 slj n 6932 3817 m 7171 3884 l 6992 3712 l col0 s % Polyline 2 slj gs clippath 10490 3861 m 10549 3757 l 10299 3614 l 10478 3786 l 10239 3719 l cp eoclip n 8707 3727 m 8708 3726 l 8710 3725 l 8714 3723 l 8721 3720 l 8730 3715 l 8742 3709 l 8757 3701 l 8775 3693 l 8795 3683 l 8818 3672 l 8844 3660 l 8871 3647 l 8901 3635 l 8932 3622 l 8965 3609 l 8999 3596 l 9034 3583 l 9070 3571 l 9109 3560 l 9148 3549 l 9190 3539 l 9233 3530 l 9279 3521 l 9328 3514 l 9379 3508 l 9432 3504 l 9489 3501 l 9547 3501 l 9607 3502 l 9667 3506 l 9725 3511 l 9782 3519 l 9835 3527 l 9886 3538 l 9935 3549 l 9981 3561 l 10024 3574 l 10066 3587 l 10105 3601 l 10144 3616 l 10180 3631 l 10215 3646 l 10249 3662 l 10282 3678 l 10313 3693 l 10343 3709 l 10370 3723 l 10396 3737 l 10419 3750 l 10439 3762 l 10457 3772 l 10472 3781 l 10484 3788 l 10493 3794 l 10507 3802 l gs col0 s gr gr % arrowhead 0 slj n 10239 3719 m 10478 3786 l 10299 3614 l col0 s % Polyline 2 slj gs clippath 10565 8736 m 10624 8632 l 10374 8489 l 10553 8661 l 10314 8594 l cp eoclip n 8782 8602 m 8783 8601 l 8785 8600 l 8789 8598 l 8796 8595 l 8805 8590 l 8817 8584 l 8832 8576 l 8850 8568 l 8870 8558 l 8893 8547 l 8919 8535 l 8946 8522 l 8976 8510 l 9007 8497 l 9040 8484 l 9074 8471 l 9109 8458 l 9145 8446 l 9184 8435 l 9223 8424 l 9265 8414 l 9308 8405 l 9354 8396 l 9403 8389 l 9454 8383 l 9507 8379 l 9564 8376 l 9622 8376 l 9682 8377 l 9742 8381 l 9800 8386 l 9857 8394 l 9910 8402 l 9961 8413 l 10010 8424 l 10056 8436 l 10099 8449 l 10141 8462 l 10180 8476 l 10219 8491 l 10255 8506 l 10290 8521 l 10324 8537 l 10357 8553 l 10388 8568 l 10418 8584 l 10445 8598 l 10471 8612 l 10494 8625 l 10514 8637 l 10532 8647 l 10547 8656 l 10559 8663 l 10568 8669 l 10582 8677 l gs col0 s gr gr % arrowhead 0 slj n 10314 8594 m 10553 8661 l 10374 8489 l col0 s % Polyline 2 slj gs clippath 2206 4089 m 2132 4183 l 2358 4361 l 2207 4166 l 2432 4267 l cp eoclip n 3981 4146 m 3980 4147 l 3977 4148 l 3972 4151 l 3965 4155 l 3954 4161 l 3941 4168 l 3923 4178 l 3903 4188 l 3879 4201 l 3853 4215 l 3823 4229 l 3792 4245 l 3758 4261 l 3723 4277 l 3686 4294 l 3648 4310 l 3609 4326 l 3569 4341 l 3527 4356 l 3484 4371 l 3439 4384 l 3392 4397 l 3343 4408 l 3292 4419 l 3239 4428 l 3183 4435 l 3125 4441 l 3066 4445 l 3006 4446 l 2942 4445 l 2881 4440 l 2823 4434 l 2768 4425 l 2717 4415 l 2669 4403 l 2624 4391 l 2582 4377 l 2543 4362 l 2505 4346 l 2470 4329 l 2436 4312 l 2404 4295 l 2373 4277 l 2344 4260 l 2317 4243 l 2292 4226 l 2269 4211 l 2249 4196 l 2231 4184 l 2216 4173 l 2204 4164 l 2195 4157 l 2181 4146 l gs col0 s gr gr % arrowhead 0 slj n 2432 4267 m 2207 4166 l 2358 4361 l col0 s % Polyline 2 slj gs clippath 5506 4014 m 5432 4108 l 5658 4286 l 5507 4091 l 5732 4192 l cp eoclip n 7281 4071 m 7280 4072 l 7277 4073 l 7272 4076 l 7265 4080 l 7254 4086 l 7241 4093 l 7223 4103 l 7203 4113 l 7179 4126 l 7153 4140 l 7123 4154 l 7092 4170 l 7058 4186 l 7023 4202 l 6986 4219 l 6948 4235 l 6909 4251 l 6869 4266 l 6827 4281 l 6784 4296 l 6739 4309 l 6692 4322 l 6643 4333 l 6592 4344 l 6539 4353 l 6483 4360 l 6425 4366 l 6366 4370 l 6306 4371 l 6242 4370 l 6181 4365 l 6123 4359 l 6068 4350 l 6017 4340 l 5969 4328 l 5924 4316 l 5882 4302 l 5843 4287 l 5805 4271 l 5770 4254 l 5736 4237 l 5704 4220 l 5673 4202 l 5644 4185 l 5617 4168 l 5592 4151 l 5569 4136 l 5549 4121 l 5531 4109 l 5516 4098 l 5504 4089 l 5495 4082 l 5481 4071 l gs col0 s gr gr % arrowhead 0 slj n 5732 4192 m 5507 4091 l 5658 4286 l col0 s % Polyline 2 slj gs clippath 5500 1593 m 5426 1687 l 5652 1865 l 5501 1670 l 5726 1771 l cp eoclip n 7275 1650 m 7274 1651 l 7271 1652 l 7266 1655 l 7259 1659 l 7248 1665 l 7235 1672 l 7217 1682 l 7197 1692 l 7173 1705 l 7147 1719 l 7117 1733 l 7086 1749 l 7052 1765 l 7017 1781 l 6980 1798 l 6942 1814 l 6903 1830 l 6863 1845 l 6821 1860 l 6778 1875 l 6733 1888 l 6686 1901 l 6637 1912 l 6586 1923 l 6533 1932 l 6477 1939 l 6419 1945 l 6360 1949 l 6300 1950 l 6236 1949 l 6175 1944 l 6117 1938 l 6062 1929 l 6011 1919 l 5963 1907 l 5918 1895 l 5876 1881 l 5837 1866 l 5799 1850 l 5764 1833 l 5730 1816 l 5698 1799 l 5667 1781 l 5638 1764 l 5611 1747 l 5586 1730 l 5563 1715 l 5543 1700 l 5525 1688 l 5510 1677 l 5498 1668 l 5489 1661 l 5475 1650 l gs col0 s gr gr % arrowhead 0 slj n 5726 1771 m 5501 1670 l 5652 1865 l col0 s % Polyline 2 slj gs clippath 8800 1593 m 8726 1687 l 8952 1865 l 8801 1670 l 9026 1771 l cp eoclip n 10575 1650 m 10574 1651 l 10571 1652 l 10566 1655 l 10559 1659 l 10548 1665 l 10535 1672 l 10517 1682 l 10497 1692 l 10473 1705 l 10447 1719 l 10417 1733 l 10386 1749 l 10352 1765 l 10317 1781 l 10280 1798 l 10242 1814 l 10203 1830 l 10163 1845 l 10121 1860 l 10078 1875 l 10033 1888 l 9986 1901 l 9937 1912 l 9886 1923 l 9833 1932 l 9777 1939 l 9719 1945 l 9660 1949 l 9600 1950 l 9536 1949 l 9475 1944 l 9417 1938 l 9362 1929 l 9311 1919 l 9263 1907 l 9218 1895 l 9176 1881 l 9137 1866 l 9099 1850 l 9064 1833 l 9030 1816 l 8998 1799 l 8967 1781 l 8938 1764 l 8911 1747 l 8886 1730 l 8863 1715 l 8843 1700 l 8825 1688 l 8810 1677 l 8798 1668 l 8789 1661 l 8775 1650 l gs col0 s gr gr % arrowhead 0 slj n 9026 1771 m 8801 1670 l 8952 1865 l col0 s % Polyline 2 slj gs clippath 8800 3918 m 8726 4012 l 8952 4190 l 8801 3995 l 9026 4096 l cp eoclip n 10575 3975 m 10574 3976 l 10571 3977 l 10566 3980 l 10559 3984 l 10548 3990 l 10535 3997 l 10517 4007 l 10497 4017 l 10473 4030 l 10447 4044 l 10417 4058 l 10386 4074 l 10352 4090 l 10317 4106 l 10280 4123 l 10242 4139 l 10203 4155 l 10163 4170 l 10121 4185 l 10078 4200 l 10033 4213 l 9986 4226 l 9937 4237 l 9886 4248 l 9833 4257 l 9777 4264 l 9719 4270 l 9660 4274 l 9600 4275 l 9536 4274 l 9475 4269 l 9417 4263 l 9362 4254 l 9311 4244 l 9263 4232 l 9218 4220 l 9176 4206 l 9137 4191 l 9099 4175 l 9064 4158 l 9030 4141 l 8998 4124 l 8967 4106 l 8938 4089 l 8911 4072 l 8886 4055 l 8863 4040 l 8843 4025 l 8825 4013 l 8810 4002 l 8798 3993 l 8789 3986 l 8775 3975 l gs col0 s gr gr % arrowhead 0 slj n 9026 4096 m 8801 3995 l 8952 4190 l col0 s % Polyline 2 slj gs clippath 5050 6618 m 4976 6713 l 5203 6890 l 5051 6695 l 5277 6795 l cp eoclip n 7425 8550 m 5025 6675 l gs col0 s gr gr % arrowhead 0 slj n 5277 6795 m 5051 6695 l 5203 6890 l col0 s % Polyline 2 slj gs clippath 8366 6598 m 8292 6693 l 8519 6870 l 8367 6675 l 8593 6775 l cp eoclip n 10741 8530 m 8341 6655 l gs col0 s gr gr % arrowhead 0 slj n 8593 6775 m 8367 6675 l 8519 6870 l col0 s % Polyline 2 slj gs clippath 3890 6336 m 3949 6232 l 3699 6089 l 3878 6261 l 3639 6194 l cp eoclip n 2107 6202 m 2108 6201 l 2110 6200 l 2114 6198 l 2121 6195 l 2130 6190 l 2142 6184 l 2157 6176 l 2175 6168 l 2195 6158 l 2218 6147 l 2244 6135 l 2271 6122 l 2301 6110 l 2332 6097 l 2365 6084 l 2399 6071 l 2434 6058 l 2470 6046 l 2509 6035 l 2548 6024 l 2590 6014 l 2633 6005 l 2679 5996 l 2728 5989 l 2779 5983 l 2832 5979 l 2889 5976 l 2947 5976 l 3007 5977 l 3067 5981 l 3125 5986 l 3182 5994 l 3235 6002 l 3286 6013 l 3335 6024 l 3381 6036 l 3424 6049 l 3466 6062 l 3505 6076 l 3544 6091 l 3580 6106 l 3615 6121 l 3649 6137 l 3682 6153 l 3713 6168 l 3743 6184 l 3770 6198 l 3796 6212 l 3819 6225 l 3839 6237 l 3857 6247 l 3872 6256 l 3884 6263 l 3893 6269 l 3907 6277 l gs col0 s gr gr % arrowhead 0 slj n 3639 6194 m 3878 6261 l 3699 6089 l col0 s % Polyline 2 slj gs clippath 7265 6336 m 7324 6232 l 7074 6089 l 7253 6261 l 7014 6194 l cp eoclip n 5482 6202 m 5483 6201 l 5485 6200 l 5489 6198 l 5496 6195 l 5505 6190 l 5517 6184 l 5532 6176 l 5550 6168 l 5570 6158 l 5593 6147 l 5619 6135 l 5646 6122 l 5676 6110 l 5707 6097 l 5740 6084 l 5774 6071 l 5809 6058 l 5845 6046 l 5884 6035 l 5923 6024 l 5965 6014 l 6008 6005 l 6054 5996 l 6103 5989 l 6154 5983 l 6207 5979 l 6264 5976 l 6322 5976 l 6382 5977 l 6442 5981 l 6500 5986 l 6557 5994 l 6610 6002 l 6661 6013 l 6710 6024 l 6756 6036 l 6799 6049 l 6841 6062 l 6880 6076 l 6919 6091 l 6955 6106 l 6990 6121 l 7024 6137 l 7057 6153 l 7088 6168 l 7118 6184 l 7145 6198 l 7171 6212 l 7194 6225 l 7214 6237 l 7232 6247 l 7247 6256 l 7259 6263 l 7268 6269 l 7282 6277 l gs col0 s gr gr % arrowhead 0 slj n 7014 6194 m 7253 6261 l 7074 6089 l col0 s % Polyline 2 slj gs clippath 10565 6336 m 10624 6232 l 10374 6089 l 10553 6261 l 10314 6194 l cp eoclip n 8782 6202 m 8783 6201 l 8785 6200 l 8789 6198 l 8796 6195 l 8805 6190 l 8817 6184 l 8832 6176 l 8850 6168 l 8870 6158 l 8893 6147 l 8919 6135 l 8946 6122 l 8976 6110 l 9007 6097 l 9040 6084 l 9074 6071 l 9109 6058 l 9145 6046 l 9184 6035 l 9223 6024 l 9265 6014 l 9308 6005 l 9354 5996 l 9403 5989 l 9454 5983 l 9507 5979 l 9564 5976 l 9622 5976 l 9682 5977 l 9742 5981 l 9800 5986 l 9857 5994 l 9910 6002 l 9961 6013 l 10010 6024 l 10056 6036 l 10099 6049 l 10141 6062 l 10180 6076 l 10219 6091 l 10255 6106 l 10290 6121 l 10324 6137 l 10357 6153 l 10388 6168 l 10418 6184 l 10445 6198 l 10471 6212 l 10494 6225 l 10514 6237 l 10532 6247 l 10547 6256 l 10559 6263 l 10568 6269 l 10582 6277 l gs col0 s gr gr % arrowhead 0 slj n 10314 6194 m 10553 6261 l 10374 6089 l col0 s % Polyline 2 slj gs clippath 2200 6393 m 2126 6487 l 2352 6665 l 2201 6470 l 2426 6571 l cp eoclip n 3975 6450 m 3974 6451 l 3971 6452 l 3966 6455 l 3959 6459 l 3948 6465 l 3935 6472 l 3917 6482 l 3897 6492 l 3873 6505 l 3847 6519 l 3817 6533 l 3786 6549 l 3752 6565 l 3717 6581 l 3680 6598 l 3642 6614 l 3603 6630 l 3563 6645 l 3521 6660 l 3478 6675 l 3433 6688 l 3386 6701 l 3337 6712 l 3286 6723 l 3233 6732 l 3177 6739 l 3119 6745 l 3060 6749 l 3000 6750 l 2936 6749 l 2875 6744 l 2817 6738 l 2762 6729 l 2711 6719 l 2663 6707 l 2618 6695 l 2576 6681 l 2537 6666 l 2499 6650 l 2464 6633 l 2430 6616 l 2398 6599 l 2367 6581 l 2338 6564 l 2311 6547 l 2286 6530 l 2263 6515 l 2243 6500 l 2225 6488 l 2210 6477 l 2198 6468 l 2189 6461 l 2175 6450 l gs col0 s gr gr % arrowhead 0 slj n 2426 6571 m 2201 6470 l 2352 6665 l col0 s % Polyline 2 slj gs clippath 5491 6492 m 5417 6586 l 5643 6764 l 5492 6569 l 5717 6670 l cp eoclip n 7266 6549 m 7265 6550 l 7262 6551 l 7257 6554 l 7250 6558 l 7239 6564 l 7226 6571 l 7208 6581 l 7188 6591 l 7164 6604 l 7138 6618 l 7108 6632 l 7077 6648 l 7043 6664 l 7008 6680 l 6971 6697 l 6933 6713 l 6894 6729 l 6854 6744 l 6812 6759 l 6769 6774 l 6724 6787 l 6677 6800 l 6628 6811 l 6577 6822 l 6524 6831 l 6468 6838 l 6410 6844 l 6351 6848 l 6291 6849 l 6227 6848 l 6166 6843 l 6108 6837 l 6053 6828 l 6002 6818 l 5954 6806 l 5909 6794 l 5867 6780 l 5828 6765 l 5790 6749 l 5755 6732 l 5721 6715 l 5689 6698 l 5658 6680 l 5629 6663 l 5602 6646 l 5577 6629 l 5554 6614 l 5534 6599 l 5516 6587 l 5501 6576 l 5489 6567 l 5480 6560 l 5466 6549 l gs col0 s gr gr % arrowhead 0 slj n 5717 6670 m 5492 6569 l 5643 6764 l col0 s % Polyline 2 slj gs clippath 8791 6417 m 8717 6511 l 8943 6689 l 8792 6494 l 9017 6595 l cp eoclip n 10566 6474 m 10565 6475 l 10562 6476 l 10557 6479 l 10550 6483 l 10539 6489 l 10526 6496 l 10508 6506 l 10488 6516 l 10464 6529 l 10438 6543 l 10408 6557 l 10377 6573 l 10343 6589 l 10308 6605 l 10271 6622 l 10233 6638 l 10194 6654 l 10154 6669 l 10112 6684 l 10069 6699 l 10024 6712 l 9977 6725 l 9928 6736 l 9877 6747 l 9824 6756 l 9768 6763 l 9710 6769 l 9651 6773 l 9591 6774 l 9527 6773 l 9466 6768 l 9408 6762 l 9353 6753 l 9302 6743 l 9254 6731 l 9209 6719 l 9167 6705 l 9128 6690 l 9090 6674 l 9055 6657 l 9021 6640 l 8989 6623 l 8958 6605 l 8929 6588 l 8902 6571 l 8877 6554 l 8854 6539 l 8834 6524 l 8816 6512 l 8801 6501 l 8789 6492 l 8780 6485 l 8766 6474 l gs col0 s gr gr % arrowhead 0 slj n 9017 6595 m 8792 6494 l 8943 6689 l col0 s % Polyline 2 slj gs clippath 1179 1904 m 1090 1823 l 896 2035 l 1103 1899 l 985 2116 l cp eoclip n 1050 3675 m 1049 3674 l 1048 3671 l 1045 3666 l 1041 3659 l 1034 3648 l 1026 3635 l 1017 3617 l 1005 3597 l 992 3573 l 977 3547 l 962 3517 l 946 3486 l 929 3452 l 912 3417 l 895 3380 l 878 3342 l 861 3303 l 845 3263 l 830 3221 l 816 3178 l 802 3133 l 790 3086 l 779 3037 l 769 2986 l 761 2933 l 755 2877 l 751 2819 l 749 2760 l 750 2700 l 754 2641 l 760 2583 l 769 2528 l 780 2476 l 792 2427 l 806 2382 l 821 2339 l 837 2298 l 854 2260 l 872 2224 l 890 2190 l 909 2157 l 928 2126 l 948 2096 l 968 2067 l 988 2040 l 1007 2015 l 1026 1991 l 1043 1969 l 1060 1949 l 1074 1932 l 1087 1917 l 1098 1904 l 1107 1894 l 1114 1887 l 1125 1875 l gs col0 s gr gr % arrowhead 0 slj n 985 2116 m 1103 1899 l 896 2035 l col0 s % Polyline 2 slj gs clippath 4485 1907 m 4396 1826 l 4202 2038 l 4409 1902 l 4291 2119 l cp eoclip n 4356 3678 m 4355 3677 l 4354 3674 l 4351 3669 l 4347 3662 l 4340 3651 l 4332 3638 l 4323 3620 l 4311 3600 l 4298 3576 l 4283 3550 l 4268 3520 l 4252 3489 l 4235 3455 l 4218 3420 l 4201 3383 l 4184 3345 l 4167 3306 l 4151 3266 l 4136 3224 l 4122 3181 l 4108 3136 l 4096 3089 l 4085 3040 l 4075 2989 l 4067 2936 l 4061 2880 l 4057 2822 l 4055 2763 l 4056 2703 l 4060 2644 l 4066 2586 l 4075 2531 l 4086 2479 l 4098 2430 l 4112 2385 l 4127 2342 l 4143 2301 l 4160 2263 l 4178 2227 l 4196 2193 l 4215 2160 l 4234 2129 l 4254 2099 l 4274 2070 l 4294 2043 l 4313 2018 l 4332 1994 l 4349 1972 l 4366 1952 l 4380 1935 l 4393 1920 l 4404 1907 l 4413 1897 l 4420 1890 l 4431 1878 l gs col0 s gr gr % arrowhead 0 slj n 4291 2119 m 4409 1902 l 4202 2038 l col0 s % Polyline 2 slj gs clippath 8414 8536 m 8521 8590 l 8650 8332 l 8490 8520 l 8543 8278 l cp eoclip n 8475 4200 m 8475 4201 l 8476 4202 l 8478 4205 l 8480 4210 l 8484 4217 l 8489 4226 l 8495 4238 l 8503 4252 l 8512 4269 l 8523 4290 l 8535 4313 l 8548 4340 l 8563 4369 l 8579 4402 l 8596 4436 l 8615 4474 l 8634 4514 l 8654 4556 l 8674 4600 l 8695 4646 l 8716 4694 l 8738 4744 l 8759 4795 l 8780 4847 l 8801 4901 l 8822 4956 l 8843 5013 l 8863 5071 l 8883 5130 l 8902 5191 l 8921 5254 l 8939 5318 l 8956 5385 l 8972 5453 l 8988 5524 l 9002 5598 l 9016 5674 l 9029 5753 l 9040 5834 l 9050 5919 l 9059 6006 l 9066 6095 l 9071 6187 l 9074 6281 l 9075 6375 l 9074 6469 l 9071 6563 l 9066 6655 l 9059 6744 l 9050 6831 l 9040 6916 l 9029 6997 l 9016 7076 l 9002 7152 l 8988 7226 l 8972 7297 l 8956 7365 l 8939 7432 l 8921 7496 l 8902 7559 l 8883 7620 l 8863 7679 l 8843 7737 l 8822 7794 l 8801 7849 l 8780 7903 l 8759 7955 l 8737 8006 l 8716 8056 l 8695 8104 l 8674 8150 l 8654 8194 l 8634 8236 l 8615 8276 l 8596 8314 l 8579 8348 l 8563 8381 l 8548 8410 l 8535 8437 l 8523 8460 l 8512 8481 l 8503 8498 l 8495 8512 l 8489 8524 l 8484 8533 l 8480 8540 l 8475 8550 l gs col0 s gr gr % arrowhead 0 slj n 8543 8278 m 8490 8520 l 8650 8332 l col0 s % Polyline 2 slj gs clippath 11714 8536 m 11821 8590 l 11950 8332 l 11790 8520 l 11843 8278 l cp eoclip n 11775 4200 m 11775 4201 l 11776 4202 l 11778 4205 l 11780 4210 l 11784 4217 l 11789 4226 l 11795 4238 l 11803 4252 l 11812 4269 l 11823 4290 l 11835 4313 l 11848 4340 l 11863 4369 l 11879 4402 l 11896 4436 l 11915 4474 l 11934 4514 l 11954 4556 l 11974 4600 l 11995 4646 l 12016 4694 l 12038 4744 l 12059 4795 l 12080 4847 l 12101 4901 l 12122 4956 l 12143 5013 l 12163 5071 l 12183 5130 l 12202 5191 l 12221 5254 l 12239 5318 l 12256 5385 l 12272 5453 l 12288 5524 l 12302 5598 l 12316 5674 l 12329 5753 l 12340 5834 l 12350 5919 l 12359 6006 l 12366 6095 l 12371 6187 l 12374 6281 l 12375 6375 l 12374 6469 l 12371 6563 l 12366 6655 l 12359 6744 l 12350 6831 l 12340 6916 l 12329 6997 l 12316 7076 l 12302 7152 l 12288 7226 l 12272 7297 l 12256 7365 l 12239 7432 l 12221 7496 l 12202 7559 l 12183 7620 l 12163 7679 l 12143 7737 l 12122 7794 l 12101 7849 l 12080 7903 l 12059 7955 l 12037 8006 l 12016 8056 l 11995 8104 l 11974 8150 l 11954 8194 l 11934 8236 l 11915 8276 l 11896 8314 l 11879 8348 l 11863 8381 l 11848 8410 l 11835 8437 l 11823 8460 l 11812 8481 l 11803 8498 l 11795 8512 l 11789 8524 l 11784 8533 l 11780 8540 l 11775 8550 l gs col0 s gr gr % arrowhead 0 slj n 11843 8278 m 11790 8520 l 11950 8332 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 4796 2836 m 4831 2722 l 4556 2637 l 4768 2765 l 4520 2751 l cp eoclip n 1725 2700 m 1726 2700 l 1727 2699 l 1731 2698 l 1736 2696 l 1743 2693 l 1753 2689 l 1765 2684 l 1780 2678 l 1798 2672 l 1818 2664 l 1841 2656 l 1867 2647 l 1895 2637 l 1925 2627 l 1957 2616 l 1991 2605 l 2027 2595 l 2065 2584 l 2104 2573 l 2145 2562 l 2188 2552 l 2233 2542 l 2280 2533 l 2328 2524 l 2380 2515 l 2434 2507 l 2491 2500 l 2551 2493 l 2615 2487 l 2682 2482 l 2754 2478 l 2829 2476 l 2908 2474 l 2990 2474 l 3075 2475 l 3152 2478 l 3229 2481 l 3305 2486 l 3380 2492 l 3453 2498 l 3523 2505 l 3592 2513 l 3658 2522 l 3723 2531 l 3786 2540 l 3846 2550 l 3906 2560 l 3964 2571 l 4020 2581 l 4075 2593 l 4129 2604 l 4182 2616 l 4234 2627 l 4284 2639 l 4334 2651 l 4381 2662 l 4428 2674 l 4472 2685 l 4514 2696 l 4554 2707 l 4592 2717 l 4626 2726 l 4658 2735 l 4687 2743 l 4712 2750 l 4733 2756 l 4752 2761 l 4767 2765 l 4778 2769 l 4787 2771 l 4800 2775 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 4520 2751 m 4768 2765 l 4556 2637 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 1710 2790 m 1710 2910 l 1998 2910 l 1758 2850 l 1998 2790 l cp eoclip n 4800 2850 m 4799 2850 l 4797 2850 l 4793 2850 l 4787 2850 l 4778 2850 l 4766 2850 l 4751 2850 l 4733 2850 l 4711 2850 l 4685 2850 l 4656 2850 l 4623 2850 l 4588 2850 l 4549 2850 l 4508 2850 l 4464 2850 l 4417 2850 l 4369 2850 l 4319 2850 l 4268 2850 l 4215 2850 l 4161 2850 l 4106 2850 l 4051 2850 l 3994 2850 l 3936 2850 l 3877 2850 l 3818 2850 l 3757 2850 l 3695 2850 l 3632 2850 l 3567 2850 l 3501 2850 l 3433 2850 l 3364 2850 l 3293 2850 l 3221 2850 l 3147 2850 l 3073 2850 l 2999 2850 l 2925 2850 l 2836 2850 l 2751 2850 l 2670 2850 l 2594 2850 l 2523 2850 l 2457 2850 l 2396 2850 l 2339 2850 l 2285 2850 l 2236 2850 l 2189 2850 l 2146 2850 l 2105 2850 l 2066 2850 l 2029 2850 l 1994 2850 l 1962 2850 l 1931 2850 l 1902 2850 l 1875 2850 l 1850 2850 l 1828 2850 l 1807 2850 l 1789 2850 l 1773 2850 l 1760 2850 l 1749 2850 l 1741 2850 l 1734 2850 l 1725 2850 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 1998 2790 m 1758 2850 l 1998 2910 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 8105 2782 m 8140 2668 l 7865 2583 l 8077 2711 l 7829 2697 l cp eoclip n 5034 2646 m 5035 2646 l 5036 2645 l 5040 2644 l 5045 2642 l 5052 2639 l 5062 2635 l 5074 2630 l 5089 2624 l 5107 2618 l 5127 2610 l 5150 2602 l 5176 2593 l 5204 2583 l 5234 2573 l 5266 2562 l 5300 2551 l 5336 2541 l 5374 2530 l 5413 2519 l 5454 2508 l 5497 2498 l 5542 2488 l 5589 2479 l 5637 2470 l 5689 2461 l 5743 2453 l 5800 2446 l 5860 2439 l 5924 2433 l 5991 2428 l 6063 2424 l 6138 2422 l 6217 2420 l 6299 2420 l 6384 2421 l 6461 2424 l 6538 2427 l 6614 2432 l 6689 2438 l 6762 2444 l 6832 2451 l 6901 2459 l 6967 2468 l 7032 2477 l 7095 2486 l 7155 2496 l 7215 2506 l 7273 2517 l 7329 2527 l 7384 2539 l 7438 2550 l 7491 2562 l 7543 2573 l 7593 2585 l 7643 2597 l 7690 2608 l 7737 2620 l 7781 2631 l 7823 2642 l 7863 2653 l 7901 2663 l 7935 2672 l 7967 2681 l 7996 2689 l 8021 2696 l 8042 2702 l 8061 2707 l 8076 2711 l 8087 2715 l 8096 2717 l 8109 2721 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 7829 2697 m 8077 2711 l 7865 2583 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 11330 2782 m 11365 2668 l 11090 2583 l 11302 2711 l 11054 2697 l cp eoclip n 8259 2646 m 8260 2646 l 8261 2645 l 8265 2644 l 8270 2642 l 8277 2639 l 8287 2635 l 8299 2630 l 8314 2624 l 8332 2618 l 8352 2610 l 8375 2602 l 8401 2593 l 8429 2583 l 8459 2573 l 8491 2562 l 8525 2551 l 8561 2541 l 8599 2530 l 8638 2519 l 8679 2508 l 8722 2498 l 8767 2488 l 8814 2479 l 8862 2470 l 8914 2461 l 8968 2453 l 9025 2446 l 9085 2439 l 9149 2433 l 9216 2428 l 9288 2424 l 9363 2422 l 9442 2420 l 9524 2420 l 9609 2421 l 9686 2424 l 9763 2427 l 9839 2432 l 9914 2438 l 9987 2444 l 10057 2451 l 10126 2459 l 10192 2468 l 10257 2477 l 10320 2486 l 10380 2496 l 10440 2506 l 10498 2517 l 10554 2527 l 10609 2539 l 10663 2550 l 10716 2562 l 10768 2573 l 10818 2585 l 10868 2597 l 10915 2608 l 10962 2620 l 11006 2631 l 11048 2642 l 11088 2653 l 11126 2663 l 11160 2672 l 11192 2681 l 11221 2689 l 11246 2696 l 11267 2702 l 11286 2707 l 11301 2711 l 11312 2715 l 11321 2717 l 11334 2721 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 11054 2697 m 11302 2711 l 11090 2583 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 4430 5257 m 4465 5143 l 4190 5058 l 4402 5186 l 4154 5172 l cp eoclip n 1359 5121 m 1360 5121 l 1361 5120 l 1365 5119 l 1370 5117 l 1377 5114 l 1387 5110 l 1399 5105 l 1414 5099 l 1432 5093 l 1452 5085 l 1475 5077 l 1501 5068 l 1529 5058 l 1559 5048 l 1591 5037 l 1625 5026 l 1661 5016 l 1699 5005 l 1738 4994 l 1779 4983 l 1822 4973 l 1867 4963 l 1914 4954 l 1962 4945 l 2014 4936 l 2068 4928 l 2125 4921 l 2185 4914 l 2249 4908 l 2316 4903 l 2388 4899 l 2463 4897 l 2542 4895 l 2624 4895 l 2709 4896 l 2786 4899 l 2863 4902 l 2939 4907 l 3014 4913 l 3087 4919 l 3157 4926 l 3226 4934 l 3292 4943 l 3357 4952 l 3420 4961 l 3480 4971 l 3540 4981 l 3598 4992 l 3654 5002 l 3709 5014 l 3763 5025 l 3816 5037 l 3868 5048 l 3918 5060 l 3968 5072 l 4015 5083 l 4062 5095 l 4106 5106 l 4148 5117 l 4188 5128 l 4226 5138 l 4260 5147 l 4292 5156 l 4321 5164 l 4346 5171 l 4367 5177 l 4386 5182 l 4401 5186 l 4412 5190 l 4421 5192 l 4434 5196 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 4154 5172 m 4402 5186 l 4190 5058 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 7880 5257 m 7915 5143 l 7640 5058 l 7852 5186 l 7604 5172 l cp eoclip n 4809 5121 m 4810 5121 l 4811 5120 l 4815 5119 l 4820 5117 l 4827 5114 l 4837 5110 l 4849 5105 l 4864 5099 l 4882 5093 l 4902 5085 l 4925 5077 l 4951 5068 l 4979 5058 l 5009 5048 l 5041 5037 l 5075 5026 l 5111 5016 l 5149 5005 l 5188 4994 l 5229 4983 l 5272 4973 l 5317 4963 l 5364 4954 l 5412 4945 l 5464 4936 l 5518 4928 l 5575 4921 l 5635 4914 l 5699 4908 l 5766 4903 l 5838 4899 l 5913 4897 l 5992 4895 l 6074 4895 l 6159 4896 l 6236 4899 l 6313 4902 l 6389 4907 l 6464 4913 l 6537 4919 l 6607 4926 l 6676 4934 l 6742 4943 l 6807 4952 l 6870 4961 l 6930 4971 l 6990 4981 l 7048 4992 l 7104 5002 l 7159 5014 l 7213 5025 l 7266 5037 l 7318 5048 l 7368 5060 l 7418 5072 l 7465 5083 l 7512 5095 l 7556 5106 l 7598 5117 l 7638 5128 l 7676 5138 l 7710 5147 l 7742 5156 l 7771 5164 l 7796 5171 l 7817 5177 l 7836 5182 l 7851 5186 l 7862 5190 l 7871 5192 l 7884 5196 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 7604 5172 m 7852 5186 l 7640 5058 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 11255 5257 m 11290 5143 l 11015 5058 l 11227 5186 l 10979 5172 l cp eoclip n 8184 5121 m 8185 5121 l 8186 5120 l 8190 5119 l 8195 5117 l 8202 5114 l 8212 5110 l 8224 5105 l 8239 5099 l 8257 5093 l 8277 5085 l 8300 5077 l 8326 5068 l 8354 5058 l 8384 5048 l 8416 5037 l 8450 5026 l 8486 5016 l 8524 5005 l 8563 4994 l 8604 4983 l 8647 4973 l 8692 4963 l 8739 4954 l 8787 4945 l 8839 4936 l 8893 4928 l 8950 4921 l 9010 4914 l 9074 4908 l 9141 4903 l 9213 4899 l 9288 4897 l 9367 4895 l 9449 4895 l 9534 4896 l 9611 4899 l 9688 4902 l 9764 4907 l 9839 4913 l 9912 4919 l 9982 4926 l 10051 4934 l 10117 4943 l 10182 4952 l 10245 4961 l 10305 4971 l 10365 4981 l 10423 4992 l 10479 5002 l 10534 5014 l 10588 5025 l 10641 5037 l 10693 5048 l 10743 5060 l 10793 5072 l 10840 5083 l 10887 5095 l 10931 5106 l 10973 5117 l 11013 5128 l 11051 5138 l 11085 5147 l 11117 5156 l 11146 5164 l 11171 5171 l 11192 5177 l 11211 5182 l 11226 5186 l 11237 5190 l 11246 5192 l 11259 5196 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 10979 5172 m 11227 5186 l 11015 5058 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 1410 5190 m 1410 5310 l 1698 5310 l 1458 5250 l 1698 5190 l cp eoclip n 4500 5250 m 4499 5250 l 4497 5250 l 4493 5250 l 4487 5250 l 4478 5250 l 4466 5250 l 4451 5250 l 4433 5250 l 4411 5250 l 4385 5250 l 4356 5250 l 4323 5250 l 4288 5250 l 4249 5250 l 4208 5250 l 4164 5250 l 4117 5250 l 4069 5250 l 4019 5250 l 3968 5250 l 3915 5250 l 3861 5250 l 3806 5250 l 3751 5250 l 3694 5250 l 3636 5250 l 3577 5250 l 3518 5250 l 3457 5250 l 3395 5250 l 3332 5250 l 3267 5250 l 3201 5250 l 3133 5250 l 3064 5250 l 2993 5250 l 2921 5250 l 2847 5250 l 2773 5250 l 2699 5250 l 2625 5250 l 2536 5250 l 2451 5250 l 2370 5250 l 2294 5250 l 2223 5250 l 2157 5250 l 2096 5250 l 2039 5250 l 1985 5250 l 1936 5250 l 1889 5250 l 1846 5250 l 1805 5250 l 1766 5250 l 1729 5250 l 1694 5250 l 1662 5250 l 1631 5250 l 1602 5250 l 1575 5250 l 1550 5250 l 1528 5250 l 1507 5250 l 1489 5250 l 1473 5250 l 1460 5250 l 1449 5250 l 1441 5250 l 1434 5250 l 1425 5250 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 1698 5190 m 1458 5250 l 1698 5310 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 4785 5190 m 4785 5310 l 5073 5310 l 4833 5250 l 5073 5190 l cp eoclip n 7875 5250 m 7874 5250 l 7872 5250 l 7868 5250 l 7862 5250 l 7853 5250 l 7841 5250 l 7826 5250 l 7808 5250 l 7786 5250 l 7760 5250 l 7731 5250 l 7698 5250 l 7663 5250 l 7624 5250 l 7583 5250 l 7539 5250 l 7492 5250 l 7444 5250 l 7394 5250 l 7343 5250 l 7290 5250 l 7236 5250 l 7181 5250 l 7126 5250 l 7069 5250 l 7011 5250 l 6952 5250 l 6893 5250 l 6832 5250 l 6770 5250 l 6707 5250 l 6642 5250 l 6576 5250 l 6508 5250 l 6439 5250 l 6368 5250 l 6296 5250 l 6222 5250 l 6148 5250 l 6074 5250 l 6000 5250 l 5911 5250 l 5826 5250 l 5745 5250 l 5669 5250 l 5598 5250 l 5532 5250 l 5471 5250 l 5414 5250 l 5360 5250 l 5311 5250 l 5264 5250 l 5221 5250 l 5180 5250 l 5141 5250 l 5104 5250 l 5069 5250 l 5037 5250 l 5006 5250 l 4977 5250 l 4950 5250 l 4925 5250 l 4903 5250 l 4882 5250 l 4864 5250 l 4848 5250 l 4835 5250 l 4824 5250 l 4816 5250 l 4809 5250 l 4800 5250 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 5073 5190 m 4833 5250 l 5073 5310 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 8160 5190 m 8160 5310 l 8448 5310 l 8208 5250 l 8448 5190 l cp eoclip n 11250 5250 m 11249 5250 l 11247 5250 l 11243 5250 l 11237 5250 l 11228 5250 l 11216 5250 l 11201 5250 l 11183 5250 l 11161 5250 l 11135 5250 l 11106 5250 l 11073 5250 l 11038 5250 l 10999 5250 l 10958 5250 l 10914 5250 l 10867 5250 l 10819 5250 l 10769 5250 l 10718 5250 l 10665 5250 l 10611 5250 l 10556 5250 l 10501 5250 l 10444 5250 l 10386 5250 l 10327 5250 l 10268 5250 l 10207 5250 l 10145 5250 l 10082 5250 l 10017 5250 l 9951 5250 l 9883 5250 l 9814 5250 l 9743 5250 l 9671 5250 l 9597 5250 l 9523 5250 l 9449 5250 l 9375 5250 l 9286 5250 l 9201 5250 l 9120 5250 l 9044 5250 l 8973 5250 l 8907 5250 l 8846 5250 l 8789 5250 l 8735 5250 l 8686 5250 l 8639 5250 l 8596 5250 l 8555 5250 l 8516 5250 l 8479 5250 l 8444 5250 l 8412 5250 l 8381 5250 l 8352 5250 l 8325 5250 l 8300 5250 l 8278 5250 l 8257 5250 l 8239 5250 l 8223 5250 l 8210 5250 l 8199 5250 l 8191 5250 l 8184 5250 l 8175 5250 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 8448 5190 m 8208 5250 l 8448 5310 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 8310 2790 m 8310 2910 l 8598 2910 l 8358 2850 l 8598 2790 l cp eoclip n 11400 2850 m 11399 2850 l 11397 2850 l 11393 2850 l 11387 2850 l 11378 2850 l 11366 2850 l 11351 2850 l 11333 2850 l 11311 2850 l 11285 2850 l 11256 2850 l 11223 2850 l 11188 2850 l 11149 2850 l 11108 2850 l 11064 2850 l 11017 2850 l 10969 2850 l 10919 2850 l 10868 2850 l 10815 2850 l 10761 2850 l 10706 2850 l 10651 2850 l 10594 2850 l 10536 2850 l 10477 2850 l 10418 2850 l 10357 2850 l 10295 2850 l 10232 2850 l 10167 2850 l 10101 2850 l 10033 2850 l 9964 2850 l 9893 2850 l 9821 2850 l 9747 2850 l 9673 2850 l 9599 2850 l 9525 2850 l 9436 2850 l 9351 2850 l 9270 2850 l 9194 2850 l 9123 2850 l 9057 2850 l 8996 2850 l 8939 2850 l 8885 2850 l 8836 2850 l 8789 2850 l 8746 2850 l 8705 2850 l 8666 2850 l 8629 2850 l 8594 2850 l 8562 2850 l 8531 2850 l 8502 2850 l 8475 2850 l 8450 2850 l 8428 2850 l 8407 2850 l 8389 2850 l 8373 2850 l 8360 2850 l 8349 2850 l 8341 2850 l 8334 2850 l 8325 2850 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 8598 2790 m 8358 2850 l 8598 2910 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 5085 2790 m 5085 2910 l 5373 2910 l 5133 2850 l 5373 2790 l cp eoclip n 8175 2850 m 8174 2850 l 8172 2850 l 8168 2850 l 8162 2850 l 8153 2850 l 8141 2850 l 8126 2850 l 8108 2850 l 8086 2850 l 8060 2850 l 8031 2850 l 7998 2850 l 7963 2850 l 7924 2850 l 7883 2850 l 7839 2850 l 7792 2850 l 7744 2850 l 7694 2850 l 7643 2850 l 7590 2850 l 7536 2850 l 7481 2850 l 7426 2850 l 7369 2850 l 7311 2850 l 7252 2850 l 7193 2850 l 7132 2850 l 7070 2850 l 7007 2850 l 6942 2850 l 6876 2850 l 6808 2850 l 6739 2850 l 6668 2850 l 6596 2850 l 6522 2850 l 6448 2850 l 6374 2850 l 6300 2850 l 6211 2850 l 6126 2850 l 6045 2850 l 5969 2850 l 5898 2850 l 5832 2850 l 5771 2850 l 5714 2850 l 5660 2850 l 5611 2850 l 5564 2850 l 5521 2850 l 5480 2850 l 5441 2850 l 5404 2850 l 5369 2850 l 5337 2850 l 5306 2850 l 5277 2850 l 5250 2850 l 5225 2850 l 5203 2850 l 5182 2850 l 5164 2850 l 5148 2850 l 5135 2850 l 5124 2850 l 5116 2850 l 5109 2850 l 5100 2850 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 5373 2790 m 5133 2850 l 5373 2910 l col0 s /Times-Roman ff 315.00 scf sf 7500 8925 m gs 1 -1 sc (2S,1L,S) col0 sh gr /Times-Roman ff 315.00 scf sf 10800 8925 m gs 1 -1 sc (3S,1L,S) col0 sh gr /Times-Roman ff 315.00 scf sf 900 4125 m gs 1 -1 sc (0S,0L) col0 sh gr /Times-Roman ff 315.00 scf sf 4200 4125 m gs 1 -1 sc (1S,0L) col0 sh gr /Times-Roman ff 315.00 scf sf 4200 1725 m gs 1 -1 sc (1S,lL) col0 sh gr /Times-Roman ff 315.00 scf sf 7500 4125 m gs 1 -1 sc (2S,0L,S) col0 sh gr /Times-Roman ff 315.00 scf sf 10875 4125 m gs 1 -1 sc (3S,0L,S) col0 sh gr /Times-Roman ff 285.00 scf sf 10725 6450 m gs 1 -1 sc (3S,\(N+1\)L) col0 sh gr /Times-Roman ff 285.00 scf sf 7425 6450 m gs 1 -1 sc (2S,\(N+1\)L) col0 sh gr /Times-Roman ff 285.00 scf sf 4125 6450 m gs 1 -1 sc (1S,\(N+1\)L) col0 sh gr /Times-Roman ff 285.00 scf sf 675 6450 m gs 1 -1 sc (0S,\(N+1\)L) col0 sh gr /Times-Roman ff 315.00 scf sf 7500 1725 m gs 1 -1 sc (2S,1L,L) col0 sh gr /Times-Roman ff 315.00 scf sf 10800 1725 m gs 1 -1 sc (3S,1L,L) col0 sh gr F2psBegin10setmiterlimit0.060000.06000scF2psEnd rs %%EndDocument endTexFig 1836 4124 a Ff(\(b\))120 4320 y FC(Figure)34 b(5:)48 b Fy(\(a\))33 b(Chain)h(corr)m(esponding)j(to)c Fx(CS-Central-Queu)o(e) p Fy(.)51 b(The)32 b(notation)k Fu(iS;)15 b(j)5 b(L)33 b Fy(r)m(epr)m(esents)j Fu(i)120 4433 y Fy(short)27 b(jobs)g(and)g Fu(j)k Fy(long)c(jobs.)37 b(The)26 b(thir)m(d)h(\002eld)f(in)h(the)f (state)h(denotes)h(whether)f(a)f(short)h(job)g(or)f(a)g(long)h(job)f (is)120 4545 y(in)i(service)j(at)d(the)h(long)g(host.)45 b(Light)29 b(arr)l(ows)g(r)m(epr)m(esent)h(e)n(xponential)j(r)o(ates.) 44 b(Bold)28 b(arr)l(ows)i(r)m(epr)m(esent)g(b)n(usy)120 4658 y(periods.)g Fu(B)512 4672 y Ft(L)586 4658 y Fy(is)22 b(a)g(b)n(usy)h(period)h(consisting)i(of)c(only)h(long)g(jobs,)g(and)g (started)h(by)f(a)f(single)h(long)g(job)l(.)29 b Fu(B)3480 4672 y Ft(N)7 b FE(+1)3659 4658 y Fy(is)120 4771 y(a)25 b(b)n(usy)h(period)h(consisting)h(of)d(only)h(long)g(jobs)g(and)g (started)h(by)e Fu(N)31 b Fs(+)21 b(1)k Fy(long)h(jobs,)g(wher)m(e)f Fu(N)35 b Fy(is)25 b(the)g(number)120 4884 y(of)i(long)h(arrivals)i (during)f Fu(E)5 b(xp)p Fs(\(2)p Fu(\026)1294 4898 y Ft(S)1345 4884 y Fs(\))p Fy(.)40 b(\(b\))27 b(Expanded)i(ver)o(sion)g (of)f(c)o(hain)g(in)f(\(a\))h(wher)m(e)f(b)n(usy)h(periods)h(have)120 4997 y(been)24 b(r)m(eplaced)i(by)d(Coxian)i(distrib)n(utions.)1875 5349 y FC(12)p eop %%Page: 13 15 13 14 bop 489 253 a 22592082 14208860 0 0 47560212 29799137 startTexFig 489 253 a %%BeginDocument: ../figures/k1indpt.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: k1indpt.eps %%Creator: fig2dev Version 3.2 Patchlevel 3d %%CreationDate: Tue May 21 14:26:02 2002 %%For: harchol@mor.sp.cs.cmu.edu (Mor Harchol-Balter) %%BoundingBox: 0 0 723 453 %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def F2psDictbeginF2psDict begin F2psDictbeginF2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 453 moveto 0 0 lineto 723 0 lineto 723 453 lineto closepath clip newpath -43.7 527.8 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def F2psBegin10setmiterlimit0.060000.06000scF2psBegin 10 setmiterlimit 0.06000 0.06000 sc % % Fig objects follow % /Symbol ff 165.00 scf sf 6714 1721 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 165.00 scf sf 6813 1818 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 165.00 scf sf 9422 1721 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 165.00 scf sf 9520 1818 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 165.00 scf sf 4007 1721 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 165.00 scf sf 4106 1818 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 3946 2731 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 195.00 scf sf 4070 2852 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 3946 4737 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 195.00 scf sf 4070 4858 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 165.00 scf sf 3946 3727 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 165.00 scf sf 4044 3824 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 165.00 scf sf 6592 3727 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 165.00 scf sf 6690 3824 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 165.00 scf sf 9360 3666 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 165.00 scf sf 9458 3764 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 165.00 scf sf 9422 7557 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 165.00 scf sf 9520 7654 m gs 1 -1 sc (S) col0 sh gr 7.500 slw % Ellipse n 11760 2244 45 44 0 360 DrawEllipse gs col0 s gr % Ellipse n 12006 2244 45 44 0 360 DrawEllipse gs col0 s gr % Ellipse n 12252 2244 45 44 0 360 DrawEllipse gs col0 s gr % Ellipse n 11821 6074 45 44 0 360 DrawEllipse gs col0 s gr % Ellipse n 12068 6074 45 44 0 360 DrawEllipse gs col0 s gr % Ellipse n 12313 6074 45 44 0 360 DrawEllipse gs col0 s gr % Ellipse n 11821 4189 45 44 0 360 DrawEllipse gs col0 s gr % Ellipse n 12068 4189 45 44 0 360 DrawEllipse gs col0 s gr % Ellipse n 12313 4189 45 44 0 360 DrawEllipse gs col0 s gr % Ellipse n 11760 8080 45 44 0 360 DrawEllipse gs col0 s gr % Ellipse n 12006 8080 45 44 0 360 DrawEllipse gs col0 s gr % Ellipse n 12252 8080 45 44 0 360 DrawEllipse gs col0 s gr /Symbol ff 195.00 scf sf 7084 7156 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 195.00 scf sf 7207 7278 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 195.00 scf sf 6961 7156 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 195.00 scf sf 9791 7095 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 195.00 scf sf 9914 7217 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 195.00 scf sf 9667 7095 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 165.00 scf sf 3884 5673 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 165.00 scf sf 3982 5770 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 165.00 scf sf 6592 5673 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 165.00 scf sf 6690 5770 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 165.00 scf sf 9422 5673 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 165.00 scf sf 9520 5770 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 9545 6561 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 195.00 scf sf 9668 6682 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 6592 6622 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 195.00 scf sf 6715 6743 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 3884 6561 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 195.00 scf sf 4008 6682 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 2346 3263 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 240.00 scf sf 2500 3338 m gs 1 -1 sc (L) col0 sh gr /Times-Roman ff 255.00 scf sf 3269 3216 m gs 1 -1 sc (B) col0 sh gr /Times-Roman ff 225.00 scf sf 3454 3338 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 240.00 scf sf 5053 3263 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 240.00 scf sf 5207 3338 m gs 1 -1 sc (L) col0 sh gr /Times-Roman ff 255.00 scf sf 6099 3156 m gs 1 -1 sc (B) col0 sh gr /Times-Roman ff 225.00 scf sf 6284 3277 m gs 1 -1 sc (L) col0 sh gr /Times-Roman ff 255.00 scf sf 11513 3095 m gs 1 -1 sc (B) col0 sh gr /Times-Roman ff 225.00 scf sf 11698 3216 m gs 1 -1 sc (L) col0 sh gr /Times-Roman ff 255.00 scf sf 8560 3156 m gs 1 -1 sc (B) col0 sh gr /Times-Roman ff 225.00 scf sf 8745 3277 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 195.00 scf sf 6653 2731 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 195.00 scf sf 6777 2852 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 6714 4724 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 195.00 scf sf 6837 4846 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 195.00 scf sf 6592 4724 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 195.00 scf sf 9545 4663 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 195.00 scf sf 9667 4785 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 195.00 scf sf 9422 4663 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 195.00 scf sf 9483 2731 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 195.00 scf sf 9607 2852 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 255.00 scf sf 2346 5223 m gs 1 -1 sc (U) col0 sh gr /Times-Roman ff 255.00 scf sf 4992 5162 m gs 1 -1 sc (U) col0 sh gr /Times-Roman ff 255.00 scf sf 7638 5162 m gs 1 -1 sc (U) col0 sh gr /Times-Roman ff 255.00 scf sf 10468 5162 m gs 1 -1 sc (U) col0 sh gr /Symbol ff 240.00 scf sf 8991 5086 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 240.00 scf sf 9145 5162 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 240.00 scf sf 11698 5086 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 240.00 scf sf 11852 5162 m gs 1 -1 sc (L) col0 sh gr % Ellipse n 5545 2244 615 243 0 360 DrawEllipse gs col0 s gr % Ellipse n 10960 2244 615 243 0 360 DrawEllipse gs col0 s gr % Ellipse n 11021 4189 615 243 0 360 DrawEllipse gs col0 s gr % Ellipse n 8253 4189 615 243 0 360 DrawEllipse gs col0 s gr % Ellipse n 5545 4189 615 243 0 360 DrawEllipse gs col0 s gr % Ellipse n 5545 6135 615 243 0 360 DrawEllipse gs col0 s gr % Ellipse n 10960 6135 615 243 0 360 DrawEllipse gs col0 s gr % Ellipse n 8253 8080 615 243 0 360 DrawEllipse gs col0 s gr % Ellipse n 10960 8080 615 243 0 360 DrawEllipse gs col0 s gr % Ellipse n 8253 6135 615 243 0 360 DrawEllipse gs col0 s gr % Ellipse n 2777 6135 615 243 0 360 DrawEllipse gs col0 s gr % Ellipse n 2839 2244 615 243 0 360 DrawEllipse gs col0 s gr % Ellipse n 2839 4189 615 243 0 360 DrawEllipse gs col0 s gr % Ellipse n 2839 2244 615 243 0 360 DrawEllipse gs col0 s gr % Ellipse n 8253 2244 615 243 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 4918 2232 m 4967 2148 l 4757 2024 l 4901 2166 l 4707 2108 l cp eoclip n 3454 2122 m 3455 2121 l 3458 2120 l 3463 2117 l 3471 2113 l 3482 2108 l 3496 2101 l 3513 2092 l 3533 2083 l 3556 2072 l 3582 2061 l 3609 2049 l 3639 2037 l 3669 2025 l 3702 2013 l 3736 2001 l 3771 1990 l 3808 1980 l 3847 1970 l 3888 1962 l 3932 1954 l 3979 1948 l 4028 1943 l 4081 1940 l 4136 1939 l 4192 1940 l 4248 1944 l 4303 1949 l 4356 1957 l 4405 1966 l 4452 1976 l 4496 1987 l 4537 1999 l 4576 2012 l 4613 2025 l 4648 2039 l 4682 2053 l 4715 2068 l 4746 2082 l 4775 2097 l 4802 2111 l 4828 2125 l 4851 2137 l 4871 2149 l 4888 2158 l 4902 2167 l 4913 2173 l 4930 2183 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 4707 2108 m 4901 2166 l 4757 2024 l col0 s % Polyline 2 slj 7.500 slw gs clippath 3472 2257 m 3411 2334 l 3603 2484 l 3480 2325 l 3664 2407 l cp eoclip n 4930 2305 m 4929 2306 l 4926 2307 l 4922 2310 l 4914 2314 l 4904 2319 l 4890 2327 l 4874 2335 l 4854 2346 l 4831 2357 l 4806 2370 l 4779 2383 l 4750 2397 l 4719 2411 l 4687 2426 l 4653 2440 l 4618 2453 l 4583 2467 l 4545 2480 l 4507 2492 l 4467 2503 l 4425 2514 l 4381 2523 l 4335 2531 l 4286 2538 l 4236 2543 l 4184 2547 l 4131 2548 l 4075 2547 l 4021 2543 l 3970 2537 l 3923 2529 l 3878 2519 l 3837 2509 l 3799 2497 l 3763 2484 l 3730 2471 l 3698 2457 l 3668 2442 l 3639 2427 l 3612 2411 l 3586 2396 l 3563 2381 l 3541 2367 l 3521 2354 l 3504 2342 l 3489 2331 l 3477 2323 l 3468 2316 l 3454 2305 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 3664 2407 m 3480 2325 l 3603 2484 l col0 s % Polyline 2 slj 7.500 slw gs clippath 7564 2232 m 7613 2148 l 7403 2024 l 7547 2166 l 7353 2108 l cp eoclip n 6099 2122 m 6100 2121 l 6103 2120 l 6108 2117 l 6116 2113 l 6127 2108 l 6141 2101 l 6158 2092 l 6178 2083 l 6201 2072 l 6227 2061 l 6254 2049 l 6283 2037 l 6314 2025 l 6347 2013 l 6381 2001 l 6416 1990 l 6453 1980 l 6492 1970 l 6533 1962 l 6577 1954 l 6624 1948 l 6673 1943 l 6726 1940 l 6780 1939 l 6837 1940 l 6894 1944 l 6948 1949 l 7001 1957 l 7050 1966 l 7097 1976 l 7141 1987 l 7182 1999 l 7221 2012 l 7258 2025 l 7294 2039 l 7328 2053 l 7360 2068 l 7391 2082 l 7421 2097 l 7448 2111 l 7474 2125 l 7497 2137 l 7517 2149 l 7534 2158 l 7548 2167 l 7559 2173 l 7576 2183 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 7353 2108 m 7547 2166 l 7403 2024 l col0 s % Polyline 2 slj 7.500 slw gs clippath 10332 2171 m 10381 2087 l 10171 1963 l 10315 2105 l 10121 2047 l cp eoclip n 8868 2061 m 8869 2060 l 8872 2059 l 8877 2056 l 8885 2052 l 8896 2047 l 8910 2040 l 8927 2031 l 8947 2022 l 8971 2011 l 8996 2000 l 9024 1988 l 9053 1976 l 9084 1964 l 9116 1952 l 9150 1940 l 9186 1929 l 9223 1919 l 9262 1909 l 9303 1901 l 9347 1893 l 9394 1887 l 9443 1882 l 9496 1879 l 9551 1878 l 9607 1879 l 9663 1883 l 9718 1888 l 9771 1896 l 9820 1905 l 9867 1915 l 9910 1926 l 9952 1938 l 9991 1951 l 10028 1964 l 10063 1978 l 10097 1992 l 10129 2007 l 10160 2021 l 10189 2036 l 10217 2050 l 10242 2064 l 10265 2076 l 10285 2088 l 10302 2097 l 10316 2106 l 10327 2112 l 10344 2122 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 10121 2047 m 10315 2105 l 10171 1963 l col0 s % Polyline 2 slj 7.500 slw gs clippath 4918 4177 m 4967 4093 l 4757 3969 l 4901 4111 l 4707 4053 l cp eoclip n 3454 4068 m 3455 4067 l 3458 4066 l 3463 4063 l 3471 4059 l 3482 4054 l 3496 4047 l 3513 4038 l 3533 4029 l 3556 4018 l 3582 4006 l 3609 3994 l 3639 3982 l 3669 3970 l 3702 3958 l 3736 3947 l 3771 3936 l 3808 3925 l 3847 3916 l 3888 3907 l 3932 3899 l 3979 3893 l 4028 3888 l 4081 3885 l 4136 3884 l 4192 3885 l 4248 3889 l 4303 3894 l 4356 3902 l 4405 3910 l 4452 3921 l 4496 3932 l 4537 3944 l 4576 3956 l 4613 3970 l 4648 3984 l 4682 3998 l 4715 4013 l 4746 4027 l 4775 4042 l 4802 4056 l 4828 4070 l 4851 4082 l 4871 4093 l 4888 4103 l 4902 4111 l 4913 4118 l 4930 4128 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 4707 4053 m 4901 4111 l 4757 3969 l col0 s % Polyline 2 slj 7.500 slw gs clippath 7564 4177 m 7613 4093 l 7403 3969 l 7547 4111 l 7353 4053 l cp eoclip n 6099 4068 m 6100 4067 l 6103 4066 l 6108 4063 l 6116 4059 l 6127 4054 l 6141 4047 l 6158 4038 l 6178 4029 l 6201 4018 l 6227 4006 l 6254 3994 l 6283 3982 l 6314 3970 l 6347 3958 l 6381 3947 l 6416 3936 l 6453 3925 l 6492 3916 l 6533 3907 l 6577 3899 l 6624 3893 l 6673 3888 l 6726 3885 l 6780 3884 l 6837 3885 l 6894 3889 l 6948 3894 l 7001 3902 l 7050 3910 l 7097 3921 l 7141 3932 l 7182 3944 l 7221 3956 l 7258 3970 l 7294 3984 l 7328 3998 l 7360 4013 l 7391 4027 l 7421 4042 l 7448 4056 l 7474 4070 l 7497 4082 l 7517 4093 l 7534 4103 l 7548 4111 l 7559 4118 l 7576 4128 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 7353 4053 m 7547 4111 l 7403 3969 l col0 s % Polyline 2 slj 7.500 slw gs clippath 10277 4098 m 10326 4014 l 10116 3890 l 10260 4032 l 10066 3974 l cp eoclip n 8812 3988 m 8813 3987 l 8816 3986 l 8821 3983 l 8829 3979 l 8840 3974 l 8854 3967 l 8871 3958 l 8891 3949 l 8914 3938 l 8940 3927 l 8967 3915 l 8997 3903 l 9028 3891 l 9060 3879 l 9094 3867 l 9130 3856 l 9167 3846 l 9206 3836 l 9247 3828 l 9291 3820 l 9338 3814 l 9387 3809 l 9440 3806 l 9494 3805 l 9551 3806 l 9608 3810 l 9662 3815 l 9715 3823 l 9764 3832 l 9811 3842 l 9855 3853 l 9896 3865 l 9935 3878 l 9972 3891 l 10007 3905 l 10041 3919 l 10074 3934 l 10105 3948 l 10134 3963 l 10161 3977 l 10187 3991 l 10210 4003 l 10230 4015 l 10247 4024 l 10261 4033 l 10272 4039 l 10289 4049 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 10066 3974 m 10260 4032 l 10116 3890 l col0 s % Polyline 2 slj 7.500 slw gs clippath 10338 8050 m 10387 7966 l 10177 7842 l 10321 7984 l 10127 7926 l cp eoclip n 8874 7940 m 8875 7939 l 8878 7938 l 8883 7935 l 8891 7931 l 8902 7926 l 8916 7919 l 8933 7910 l 8953 7901 l 8976 7890 l 9002 7878 l 9029 7866 l 9059 7854 l 9089 7842 l 9122 7830 l 9156 7818 l 9191 7807 l 9228 7797 l 9267 7788 l 9308 7779 l 9352 7771 l 9399 7765 l 9448 7760 l 9501 7757 l 9556 7756 l 9612 7757 l 9668 7761 l 9723 7766 l 9776 7774 l 9825 7783 l 9872 7793 l 9916 7804 l 9957 7816 l 9996 7829 l 10033 7842 l 10068 7856 l 10102 7871 l 10135 7885 l 10166 7900 l 10195 7915 l 10222 7929 l 10248 7942 l 10271 7955 l 10291 7966 l 10308 7976 l 10322 7984 l 10333 7991 l 10350 8001 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 10127 7926 m 10321 7984 l 10177 7842 l col0 s % Polyline 2 slj 7.500 slw gs clippath 3477 4280 m 3416 4357 l 3608 4507 l 3485 4348 l 3669 4430 l cp eoclip n 4935 4328 m 4934 4329 l 4931 4330 l 4927 4333 l 4919 4337 l 4909 4342 l 4895 4350 l 4879 4358 l 4859 4369 l 4836 4380 l 4811 4393 l 4784 4406 l 4755 4420 l 4724 4434 l 4692 4449 l 4658 4463 l 4623 4476 l 4588 4490 l 4550 4503 l 4512 4515 l 4472 4526 l 4430 4537 l 4386 4546 l 4340 4554 l 4291 4561 l 4241 4566 l 4189 4570 l 4136 4571 l 4080 4570 l 4026 4566 l 3975 4560 l 3928 4552 l 3883 4542 l 3842 4532 l 3804 4520 l 3768 4507 l 3735 4494 l 3703 4480 l 3673 4465 l 3644 4450 l 3617 4434 l 3591 4419 l 3568 4404 l 3546 4390 l 3526 4377 l 3509 4365 l 3494 4354 l 3482 4346 l 3473 4339 l 3459 4328 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 3669 4430 m 3485 4348 l 3608 4507 l col0 s % Polyline 2 slj 7.500 slw gs clippath 6183 4219 m 6122 4296 l 6314 4446 l 6191 4287 l 6375 4369 l cp eoclip n 7642 4267 m 7641 4268 l 7638 4269 l 7633 4272 l 7626 4276 l 7616 4281 l 7602 4289 l 7585 4297 l 7566 4308 l 7543 4319 l 7518 4332 l 7491 4345 l 7461 4359 l 7430 4373 l 7398 4388 l 7365 4402 l 7330 4415 l 7294 4429 l 7257 4442 l 7218 4454 l 7178 4465 l 7136 4476 l 7092 4485 l 7046 4493 l 6997 4500 l 6947 4505 l 6895 4509 l 6842 4510 l 6786 4509 l 6732 4505 l 6681 4499 l 6633 4491 l 6589 4481 l 6548 4471 l 6510 4459 l 6474 4446 l 6440 4433 l 6409 4419 l 6378 4404 l 6350 4389 l 6323 4373 l 6297 4358 l 6273 4343 l 6252 4329 l 6232 4316 l 6215 4304 l 6200 4293 l 6188 4285 l 6179 4278 l 6165 4267 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 6375 4369 m 6191 4287 l 6314 4446 l col0 s % Polyline 2 slj 7.500 slw gs clippath 6179 2257 m 6118 2334 l 6310 2484 l 6187 2325 l 6371 2407 l cp eoclip n 7638 2305 m 7637 2306 l 7634 2307 l 7629 2310 l 7622 2314 l 7612 2319 l 7598 2327 l 7581 2335 l 7562 2346 l 7539 2357 l 7514 2370 l 7486 2383 l 7457 2397 l 7426 2411 l 7394 2426 l 7360 2440 l 7325 2453 l 7289 2467 l 7252 2480 l 7213 2492 l 7173 2503 l 7131 2514 l 7087 2523 l 7041 2531 l 6992 2538 l 6942 2543 l 6890 2547 l 6837 2548 l 6781 2547 l 6727 2543 l 6676 2537 l 6629 2529 l 6584 2519 l 6543 2509 l 6505 2497 l 6469 2484 l 6436 2471 l 6404 2457 l 6374 2442 l 6345 2427 l 6318 2411 l 6293 2396 l 6269 2381 l 6247 2367 l 6228 2354 l 6211 2342 l 6196 2331 l 6184 2323 l 6175 2316 l 6161 2305 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 6371 2407 m 6187 2325 l 6310 2484 l col0 s % Polyline 2 slj 7.500 slw gs clippath 8886 2257 m 8825 2334 l 9017 2484 l 8894 2325 l 9078 2407 l cp eoclip n 10344 2305 m 10343 2306 l 10340 2307 l 10336 2310 l 10328 2314 l 10318 2319 l 10304 2327 l 10288 2335 l 10268 2346 l 10245 2357 l 10220 2370 l 10193 2383 l 10164 2397 l 10133 2411 l 10101 2426 l 10067 2440 l 10032 2453 l 9997 2467 l 9959 2480 l 9921 2492 l 9881 2503 l 9839 2514 l 9795 2523 l 9749 2531 l 9700 2538 l 9650 2543 l 9598 2547 l 9545 2548 l 9489 2547 l 9435 2543 l 9384 2537 l 9337 2529 l 9292 2519 l 9251 2509 l 9213 2497 l 9177 2484 l 9144 2471 l 9112 2457 l 9082 2442 l 9053 2427 l 9026 2411 l 9000 2396 l 8977 2381 l 8955 2367 l 8935 2354 l 8918 2342 l 8903 2331 l 8891 2323 l 8882 2316 l 8868 2305 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 9078 2407 m 8894 2325 l 9017 2484 l col0 s % Polyline 2 slj 7.500 slw gs clippath 8886 4141 m 8825 4218 l 9017 4368 l 8894 4209 l 9078 4291 l cp eoclip n 10344 4189 m 10343 4190 l 10340 4191 l 10336 4194 l 10328 4198 l 10318 4203 l 10304 4211 l 10288 4219 l 10268 4230 l 10245 4241 l 10220 4254 l 10193 4267 l 10164 4281 l 10133 4295 l 10101 4310 l 10067 4324 l 10032 4337 l 9997 4351 l 9959 4364 l 9921 4376 l 9881 4387 l 9839 4398 l 9795 4407 l 9749 4415 l 9700 4422 l 9650 4427 l 9598 4431 l 9545 4432 l 9489 4431 l 9435 4427 l 9384 4421 l 9337 4413 l 9292 4403 l 9251 4393 l 9213 4381 l 9177 4368 l 9144 4355 l 9112 4341 l 9082 4326 l 9053 4311 l 9026 4295 l 9000 4280 l 8977 4265 l 8955 4251 l 8935 4238 l 8918 4226 l 8903 4215 l 8891 4207 l 8882 4200 l 8868 4189 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 9078 4291 m 8894 4209 l 9017 4368 l col0 s % Polyline 2 slj 7.500 slw gs clippath 5810 6330 m 5750 6407 l 5943 6556 l 5818 6398 l 6002 6478 l cp eoclip n 7761 7898 m 5792 6378 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 6002 6478 m 5818 6398 l 5943 6556 l col0 s % Polyline 2 slj 7.500 slw gs clippath 8530 6314 m 8470 6391 l 8663 6540 l 8538 6382 l 8722 6462 l cp eoclip n 10481 7881 m 8512 6362 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 8722 6462 m 8538 6382 l 8663 6540 l col0 s % Polyline 2 slj 45.000 slw gs clippath 7938 4462 m 7848 4379 l 7583 4664 l 7795 4527 l 7673 4747 l cp eoclip n 7822 5891 m 7821 5890 l 7820 5887 l 7817 5883 l 7813 5875 l 7807 5865 l 7799 5852 l 7789 5835 l 7778 5816 l 7766 5793 l 7753 5769 l 7738 5742 l 7724 5713 l 7709 5682 l 7694 5650 l 7679 5617 l 7664 5583 l 7651 5547 l 7637 5511 l 7625 5473 l 7614 5433 l 7603 5391 l 7594 5348 l 7587 5302 l 7581 5254 l 7577 5205 l 7575 5153 l 7576 5101 l 7580 5046 l 7587 4992 l 7596 4942 l 7607 4895 l 7619 4851 l 7633 4811 l 7648 4773 l 7664 4738 l 7681 4704 l 7699 4673 l 7717 4643 l 7736 4615 l 7754 4588 l 7773 4563 l 7791 4539 l 7808 4518 l 7824 4498 l 7839 4481 l 7851 4467 l 7862 4455 l 7870 4446 l 7883 4432 l gs col0 s gr gr % arrowhead 0 slj 60.000 slw n 7673 4747 m 7795 4527 l 7583 4664 l 7673 4747 l cp gs 0.00 setgray ef gr col0 s % Polyline 2 slj 45.000 slw gs clippath 10769 4462 m 10679 4379 l 10414 4664 l 10626 4527 l 10504 4747 l cp eoclip n 10652 5891 m 10651 5890 l 10650 5887 l 10647 5883 l 10643 5875 l 10637 5865 l 10629 5852 l 10619 5835 l 10608 5816 l 10596 5793 l 10583 5769 l 10568 5742 l 10554 5713 l 10539 5682 l 10524 5650 l 10509 5617 l 10494 5583 l 10480 5547 l 10467 5511 l 10455 5473 l 10444 5433 l 10433 5391 l 10424 5348 l 10417 5302 l 10411 5254 l 10407 5205 l 10405 5153 l 10406 5101 l 10410 5046 l 10417 4992 l 10426 4942 l 10437 4895 l 10449 4851 l 10463 4811 l 10479 4773 l 10495 4738 l 10512 4704 l 10529 4673 l 10548 4643 l 10566 4615 l 10585 4588 l 10604 4563 l 10622 4539 l 10639 4518 l 10655 4498 l 10670 4481 l 10682 4467 l 10693 4455 l 10701 4446 l 10714 4432 l gs col0 s gr gr % arrowhead 0 slj 60.000 slw n 10504 4747 m 10626 4527 l 10414 4664 l 10504 4747 l cp gs 0.00 setgray ef gr col0 s % Polyline 2 slj 45.000 slw gs clippath 5281 4423 m 5191 4340 l 4926 4625 l 5138 4488 l 5016 4708 l cp eoclip n 5164 5853 m 5163 5852 l 5162 5849 l 5159 5845 l 5155 5837 l 5149 5827 l 5141 5814 l 5131 5797 l 5120 5778 l 5108 5755 l 5095 5730 l 5080 5703 l 5066 5674 l 5051 5644 l 5036 5612 l 5021 5579 l 5006 5544 l 4992 5509 l 4979 5472 l 4967 5434 l 4956 5394 l 4945 5353 l 4936 5309 l 4929 5263 l 4923 5216 l 4919 5166 l 4917 5114 l 4918 5062 l 4922 5006 l 4929 4953 l 4938 4903 l 4949 4856 l 4961 4812 l 4975 4772 l 4991 4734 l 5007 4698 l 5024 4665 l 5041 4634 l 5060 4604 l 5078 4576 l 5097 4549 l 5116 4524 l 5134 4500 l 5151 4479 l 5167 4459 l 5182 4442 l 5194 4428 l 5205 4416 l 5213 4407 l 5226 4393 l gs col0 s gr gr % arrowhead 0 slj 60.000 slw n 5016 4708 m 5138 4488 l 4926 4625 l 5016 4708 l cp gs 0.00 setgray ef gr col0 s % Polyline 2 slj 7.500 slw gs clippath 4863 6104 m 4912 6020 l 4702 5896 l 4846 6038 l 4652 5980 l cp eoclip n 3398 5994 m 3399 5993 l 3402 5992 l 3407 5989 l 3415 5985 l 3426 5980 l 3440 5973 l 3457 5964 l 3477 5955 l 3500 5944 l 3526 5933 l 3553 5921 l 3582 5909 l 3613 5897 l 3646 5885 l 3680 5873 l 3715 5862 l 3752 5852 l 3791 5842 l 3832 5834 l 3876 5826 l 3923 5820 l 3972 5815 l 4025 5812 l 4079 5811 l 4136 5812 l 4193 5816 l 4247 5821 l 4300 5829 l 4349 5838 l 4396 5848 l 4440 5859 l 4481 5871 l 4520 5884 l 4557 5897 l 4593 5911 l 4627 5925 l 4659 5940 l 4690 5954 l 4720 5969 l 4747 5983 l 4773 5997 l 4796 6009 l 4816 6021 l 4833 6030 l 4847 6039 l 4858 6045 l 4875 6055 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 4652 5980 m 4846 6038 l 4702 5896 l col0 s % Polyline 2 slj 7.500 slw gs clippath 7631 6104 m 7680 6020 l 7470 5896 l 7614 6038 l 7420 5980 l cp eoclip n 6166 5994 m 6167 5993 l 6170 5992 l 6175 5989 l 6183 5985 l 6194 5980 l 6208 5973 l 6225 5964 l 6245 5955 l 6268 5944 l 6294 5933 l 6321 5921 l 6351 5909 l 6382 5897 l 6414 5885 l 6448 5873 l 6484 5862 l 6521 5852 l 6560 5842 l 6601 5834 l 6645 5826 l 6692 5820 l 6741 5815 l 6794 5812 l 6848 5811 l 6905 5812 l 6962 5816 l 7016 5821 l 7069 5829 l 7118 5838 l 7165 5848 l 7209 5859 l 7250 5871 l 7289 5884 l 7326 5897 l 7361 5911 l 7395 5925 l 7428 5940 l 7459 5954 l 7488 5969 l 7515 5983 l 7541 5997 l 7564 6009 l 7584 6021 l 7601 6030 l 7615 6039 l 7626 6045 l 7643 6055 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 7420 5980 m 7614 6038 l 7470 5896 l col0 s % Polyline 2 slj 7.500 slw gs clippath 10338 6104 m 10387 6020 l 10177 5896 l 10321 6038 l 10127 5980 l cp eoclip n 8874 5994 m 8875 5993 l 8878 5992 l 8883 5989 l 8891 5985 l 8902 5980 l 8916 5973 l 8933 5964 l 8953 5955 l 8976 5944 l 9002 5933 l 9029 5921 l 9059 5909 l 9089 5897 l 9122 5885 l 9156 5873 l 9191 5862 l 9228 5852 l 9267 5842 l 9308 5834 l 9352 5826 l 9399 5820 l 9448 5815 l 9501 5812 l 9556 5811 l 9612 5812 l 9668 5816 l 9723 5821 l 9776 5829 l 9825 5838 l 9872 5848 l 9916 5859 l 9957 5871 l 9996 5884 l 10033 5897 l 10068 5911 l 10102 5925 l 10135 5940 l 10166 5954 l 10195 5969 l 10222 5983 l 10248 5997 l 10271 6009 l 10291 6021 l 10308 6030 l 10322 6039 l 10333 6045 l 10350 6055 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 10127 5980 m 10321 6038 l 10177 5896 l col0 s % Polyline 2 slj 7.500 slw gs clippath 3472 6147 m 3411 6224 l 3603 6374 l 3480 6215 l 3664 6297 l cp eoclip n 4930 6195 m 4929 6196 l 4926 6197 l 4922 6200 l 4914 6204 l 4904 6209 l 4890 6217 l 4874 6226 l 4854 6236 l 4831 6248 l 4806 6260 l 4779 6274 l 4750 6288 l 4719 6302 l 4687 6316 l 4653 6330 l 4618 6344 l 4583 6357 l 4545 6370 l 4507 6382 l 4467 6394 l 4425 6404 l 4381 6414 l 4335 6422 l 4286 6429 l 4236 6434 l 4184 6438 l 4131 6439 l 4075 6438 l 4021 6434 l 3970 6428 l 3923 6420 l 3878 6410 l 3837 6400 l 3799 6388 l 3763 6375 l 3730 6361 l 3698 6347 l 3668 6332 l 3639 6317 l 3612 6302 l 3586 6286 l 3563 6271 l 3541 6257 l 3521 6244 l 3504 6232 l 3489 6221 l 3477 6213 l 3468 6206 l 3454 6195 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 3664 6297 m 3480 6215 l 3603 6374 l col0 s % Polyline 2 slj 7.500 slw gs clippath 6171 6228 m 6110 6305 l 6302 6455 l 6179 6296 l 6363 6378 l cp eoclip n 7630 6276 m 7629 6277 l 7626 6278 l 7621 6281 l 7614 6285 l 7604 6290 l 7590 6298 l 7573 6306 l 7554 6317 l 7531 6328 l 7506 6341 l 7479 6354 l 7449 6368 l 7418 6382 l 7386 6397 l 7353 6411 l 7318 6424 l 7282 6438 l 7245 6451 l 7206 6463 l 7166 6474 l 7124 6485 l 7080 6494 l 7034 6502 l 6985 6509 l 6935 6514 l 6883 6518 l 6830 6519 l 6774 6518 l 6720 6514 l 6669 6508 l 6621 6500 l 6577 6490 l 6536 6480 l 6498 6468 l 6462 6455 l 6428 6442 l 6397 6428 l 6366 6413 l 6338 6398 l 6311 6382 l 6285 6367 l 6261 6352 l 6240 6338 l 6220 6325 l 6203 6313 l 6188 6302 l 6176 6294 l 6167 6287 l 6153 6276 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 6363 6378 m 6179 6296 l 6302 6455 l col0 s % Polyline 2 slj 7.500 slw gs clippath 8879 6167 m 8818 6244 l 9010 6394 l 8887 6235 l 9071 6317 l cp eoclip n 10337 6215 m 10336 6216 l 10333 6217 l 10329 6220 l 10321 6224 l 10311 6229 l 10297 6237 l 10281 6245 l 10261 6256 l 10238 6267 l 10213 6280 l 10186 6293 l 10157 6307 l 10126 6321 l 10094 6336 l 10060 6350 l 10025 6363 l 9990 6377 l 9952 6390 l 9914 6402 l 9874 6413 l 9832 6424 l 9788 6433 l 9742 6441 l 9693 6448 l 9643 6453 l 9591 6457 l 9538 6458 l 9482 6457 l 9428 6453 l 9377 6447 l 9330 6439 l 9285 6429 l 9244 6419 l 9206 6407 l 9170 6394 l 9137 6381 l 9105 6367 l 9075 6352 l 9046 6337 l 9019 6321 l 8993 6306 l 8970 6291 l 8948 6277 l 8928 6264 l 8911 6252 l 8896 6241 l 8884 6233 l 8875 6226 l 8861 6215 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 9071 6317 m 8887 6235 l 9010 6394 l col0 s % Polyline 2 slj 7.500 slw gs clippath 2638 2509 m 2566 2442 l 2399 2621 l 2569 2511 l 2471 2687 l cp eoclip n 2530 3946 m 2529 3945 l 2528 3942 l 2525 3938 l 2521 3930 l 2515 3920 l 2507 3907 l 2497 3890 l 2486 3871 l 2474 3848 l 2461 3824 l 2447 3797 l 2432 3768 l 2417 3737 l 2402 3705 l 2387 3672 l 2373 3638 l 2359 3602 l 2346 3566 l 2334 3528 l 2322 3488 l 2312 3446 l 2303 3403 l 2296 3357 l 2290 3309 l 2286 3260 l 2284 3208 l 2285 3156 l 2289 3101 l 2296 3047 l 2305 2997 l 2316 2950 l 2328 2906 l 2342 2866 l 2357 2828 l 2373 2793 l 2390 2759 l 2408 2728 l 2426 2698 l 2445 2670 l 2464 2643 l 2482 2618 l 2500 2594 l 2517 2573 l 2533 2553 l 2548 2536 l 2560 2522 l 2571 2510 l 2579 2501 l 2592 2487 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 2471 2687 m 2569 2511 l 2399 2621 l col0 s % Polyline 2 slj 45.000 slw gs clippath 2902 3925 m 3005 3991 l 3216 3664 l 3032 3837 l 3113 3598 l cp eoclip n 2962 2487 m 2963 2488 l 2965 2491 l 2968 2496 l 2973 2504 l 2980 2514 l 2988 2528 l 2999 2545 l 3011 2565 l 3024 2588 l 3039 2613 l 3054 2640 l 3069 2669 l 3085 2700 l 3100 2732 l 3115 2765 l 3129 2800 l 3143 2837 l 3156 2875 l 3167 2916 l 3178 2959 l 3188 3005 l 3196 3054 l 3202 3106 l 3206 3160 l 3207 3216 l 3206 3272 l 3202 3326 l 3196 3378 l 3188 3427 l 3178 3473 l 3167 3516 l 3156 3557 l 3143 3595 l 3129 3632 l 3115 3667 l 3100 3701 l 3085 3733 l 3069 3763 l 3054 3792 l 3039 3820 l 3024 3845 l 3011 3868 l 2999 3888 l 2988 3905 l 2980 3919 l 2973 3929 l 2962 3946 l gs col0 s gr gr % arrowhead 0 slj 60.000 slw n 3113 3598 m 3032 3837 l 3216 3664 l 3113 3598 l cp gs 0.00 setgray ef gr col0 s % Polyline 2 slj 45.000 slw gs clippath 5732 3925 m 5835 3991 l 6046 3664 l 5862 3837 l 5943 3598 l cp eoclip n 5792 2487 m 5793 2488 l 5795 2491 l 5798 2496 l 5803 2504 l 5810 2514 l 5818 2528 l 5829 2545 l 5841 2565 l 5854 2588 l 5869 2613 l 5884 2640 l 5899 2669 l 5915 2700 l 5930 2732 l 5945 2765 l 5959 2800 l 5973 2837 l 5986 2875 l 5997 2916 l 6008 2959 l 6018 3005 l 6026 3054 l 6032 3106 l 6036 3160 l 6037 3216 l 6036 3272 l 6032 3326 l 6026 3378 l 6018 3427 l 6008 3473 l 5997 3516 l 5986 3557 l 5973 3595 l 5959 3632 l 5945 3667 l 5930 3701 l 5915 3733 l 5899 3763 l 5884 3792 l 5869 3820 l 5854 3845 l 5841 3868 l 5829 3888 l 5818 3905 l 5810 3919 l 5803 3929 l 5792 3946 l gs col0 s gr gr % arrowhead 0 slj 60.000 slw n 5943 3598 m 5862 3837 l 6046 3664 l 5943 3598 l cp gs 0.00 setgray ef gr col0 s % Polyline 2 slj 7.500 slw gs clippath 5351 2511 m 5279 2444 l 5112 2623 l 5282 2513 l 5184 2689 l cp eoclip n 5243 3948 m 5242 3947 l 5241 3944 l 5238 3940 l 5234 3932 l 5227 3922 l 5220 3909 l 5210 3892 l 5199 3873 l 5187 3850 l 5173 3826 l 5159 3799 l 5144 3770 l 5129 3739 l 5114 3707 l 5099 3674 l 5085 3640 l 5071 3604 l 5058 3568 l 5045 3530 l 5034 3490 l 5023 3448 l 5014 3405 l 5007 3359 l 5001 3311 l 4997 3262 l 4995 3210 l 4996 3158 l 5000 3103 l 5007 3049 l 5016 2999 l 5027 2952 l 5040 2908 l 5054 2868 l 5069 2830 l 5085 2795 l 5102 2761 l 5120 2730 l 5138 2700 l 5157 2672 l 5176 2645 l 5194 2620 l 5213 2596 l 5230 2575 l 5246 2555 l 5261 2538 l 5273 2524 l 5284 2512 l 5292 2503 l 5305 2489 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 5184 2689 m 5282 2513 l 5112 2623 l col0 s % Polyline 2 slj 45.000 slw gs clippath 8193 3925 m 8296 3991 l 8507 3664 l 8323 3837 l 8404 3598 l cp eoclip n 8253 2487 m 8254 2488 l 8256 2491 l 8259 2496 l 8264 2504 l 8271 2514 l 8279 2528 l 8290 2545 l 8302 2565 l 8315 2588 l 8330 2613 l 8345 2640 l 8360 2669 l 8376 2700 l 8391 2732 l 8406 2765 l 8420 2800 l 8434 2837 l 8447 2875 l 8458 2916 l 8469 2959 l 8479 3005 l 8487 3054 l 8493 3106 l 8497 3160 l 8498 3216 l 8497 3272 l 8493 3326 l 8487 3378 l 8479 3427 l 8469 3473 l 8458 3516 l 8447 3557 l 8434 3595 l 8420 3632 l 8406 3667 l 8391 3701 l 8376 3733 l 8360 3763 l 8345 3792 l 8330 3820 l 8315 3845 l 8302 3868 l 8290 3888 l 8279 3905 l 8271 3919 l 8264 3929 l 8253 3946 l gs col0 s gr gr % arrowhead 0 slj 60.000 slw n 8404 3598 m 8323 3837 l 8507 3664 l 8404 3598 l cp gs 0.00 setgray ef gr col0 s % Polyline 2 slj 45.000 slw gs clippath 11164 3919 m 11267 3985 l 11478 3658 l 11294 3831 l 11375 3592 l cp eoclip n 11224 2480 m 11225 2481 l 11227 2484 l 11230 2489 l 11235 2497 l 11242 2507 l 11251 2521 l 11261 2538 l 11273 2558 l 11287 2581 l 11301 2606 l 11316 2633 l 11332 2663 l 11347 2693 l 11362 2725 l 11377 2759 l 11392 2794 l 11406 2830 l 11418 2869 l 11430 2910 l 11441 2953 l 11451 2999 l 11459 3048 l 11465 3100 l 11469 3154 l 11470 3210 l 11469 3266 l 11465 3320 l 11459 3372 l 11451 3421 l 11441 3467 l 11430 3510 l 11418 3551 l 11406 3590 l 11392 3626 l 11377 3661 l 11362 3695 l 11347 3727 l 11332 3758 l 11316 3787 l 11301 3814 l 11287 3839 l 11273 3862 l 11261 3882 l 11251 3899 l 11242 3913 l 11235 3923 l 11224 3940 l gs col0 s gr gr % arrowhead 0 slj 60.000 slw n 11375 3592 m 11294 3831 l 11478 3658 l 11375 3592 l cp gs 0.00 setgray ef gr col0 s % Polyline 2 slj 7.500 slw gs clippath 8572 7885 m 8656 7936 l 8781 7727 l 8639 7870 l 8697 7677 l cp eoclip n 8622 4372 m 8622 4373 l 8623 4374 l 8625 4377 l 8628 4382 l 8632 4389 l 8637 4399 l 8643 4411 l 8651 4426 l 8661 4444 l 8671 4465 l 8684 4489 l 8697 4515 l 8712 4545 l 8728 4576 l 8745 4611 l 8762 4647 l 8780 4686 l 8799 4727 l 8818 4769 l 8837 4813 l 8856 4858 l 8876 4905 l 8895 4953 l 8913 5002 l 8932 5053 l 8950 5105 l 8967 5159 l 8984 5214 l 9000 5271 l 9016 5330 l 9030 5391 l 9044 5454 l 9057 5520 l 9069 5588 l 9080 5659 l 9090 5732 l 9098 5809 l 9105 5887 l 9110 5968 l 9113 6051 l 9114 6135 l 9113 6219 l 9110 6302 l 9105 6383 l 9098 6461 l 9090 6538 l 9080 6611 l 9069 6682 l 9057 6750 l 9044 6816 l 9030 6879 l 9016 6940 l 9000 6999 l 8984 7056 l 8967 7111 l 8950 7165 l 8932 7217 l 8913 7268 l 8895 7317 l 8876 7365 l 8856 7412 l 8837 7457 l 8818 7501 l 8799 7543 l 8780 7584 l 8762 7623 l 8745 7659 l 8728 7694 l 8712 7725 l 8697 7755 l 8684 7781 l 8671 7805 l 8661 7826 l 8651 7844 l 8643 7859 l 8637 7871 l 8632 7881 l 8628 7888 l 8622 7898 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 8697 7677 m 8639 7870 l 8781 7727 l col0 s % Polyline 2 slj 7.500 slw gs clippath 11279 7885 m 11363 7936 l 11488 7727 l 11346 7870 l 11404 7677 l cp eoclip n 11329 4372 m 11329 4373 l 11330 4374 l 11332 4377 l 11335 4382 l 11339 4389 l 11344 4399 l 11350 4411 l 11358 4426 l 11368 4444 l 11378 4465 l 11391 4489 l 11404 4515 l 11419 4545 l 11435 4576 l 11452 4611 l 11469 4647 l 11487 4686 l 11506 4727 l 11525 4769 l 11544 4813 l 11563 4858 l 11583 4905 l 11602 4953 l 11620 5002 l 11639 5053 l 11657 5105 l 11674 5159 l 11691 5214 l 11707 5271 l 11723 5330 l 11737 5391 l 11751 5454 l 11764 5520 l 11776 5588 l 11787 5659 l 11797 5732 l 11805 5809 l 11812 5887 l 11817 5968 l 11820 6051 l 11821 6135 l 11820 6219 l 11817 6302 l 11812 6383 l 11805 6461 l 11797 6538 l 11787 6611 l 11776 6682 l 11764 6750 l 11751 6816 l 11737 6879 l 11723 6940 l 11707 6999 l 11691 7056 l 11674 7111 l 11657 7165 l 11639 7217 l 11620 7268 l 11602 7317 l 11583 7365 l 11563 7412 l 11544 7457 l 11525 7501 l 11506 7543 l 11487 7584 l 11469 7623 l 11452 7659 l 11435 7694 l 11419 7725 l 11404 7755 l 11391 7781 l 11378 7805 l 11368 7826 l 11358 7844 l 11350 7859 l 11344 7871 l 11339 7881 l 11335 7888 l 11329 7898 l gs col0 s gr gr % arrowhead 0 slj 15.000 slw n 11404 7677 m 11346 7870 l 11488 7727 l col0 s % Polyline 2 slj 45.000 slw gs clippath 2647 4462 m 2557 4379 l 2292 4664 l 2504 4527 l 2382 4747 l cp eoclip n 2530 5891 m 2529 5890 l 2528 5887 l 2525 5883 l 2521 5875 l 2515 5865 l 2507 5852 l 2497 5835 l 2486 5816 l 2474 5793 l 2461 5769 l 2447 5742 l 2432 5713 l 2417 5682 l 2402 5650 l 2387 5617 l 2373 5583 l 2359 5547 l 2346 5511 l 2334 5473 l 2322 5433 l 2312 5391 l 2303 5348 l 2296 5302 l 2290 5254 l 2286 5205 l 2284 5153 l 2285 5101 l 2289 5046 l 2296 4992 l 2305 4942 l 2316 4895 l 2328 4851 l 2342 4811 l 2357 4773 l 2373 4738 l 2390 4704 l 2408 4673 l 2426 4643 l 2445 4615 l 2464 4588 l 2482 4563 l 2500 4539 l 2517 4518 l 2533 4498 l 2548 4481 l 2560 4467 l 2571 4455 l 2579 4446 l 2592 4432 l gs col0 s gr gr % arrowhead 0 slj 60.000 slw n 2382 4747 m 2504 4527 l 2292 4664 l 2382 4747 l cp gs 0.00 setgray ef gr col0 s /Times-Roman ff 255.00 scf sf 7822 8202 m gs 1 -1 sc (2S,1L,S) col0 sh gr /Times-Roman ff 255.00 scf sf 10529 8202 m gs 1 -1 sc (3S,1L,S) col0 sh gr /Times-Roman ff 255.00 scf sf 2407 4311 m gs 1 -1 sc (0S,0L) col0 sh gr /Times-Roman ff 255.00 scf sf 5115 4311 m gs 1 -1 sc (1S,0L) col0 sh gr /Times-Roman ff 255.00 scf sf 2469 2365 m gs 1 -1 sc (0S,1L) col0 sh gr /Times-Roman ff 255.00 scf sf 5115 2365 m gs 1 -1 sc (1S,lL) col0 sh gr /Times-Roman ff 255.00 scf sf 7822 4311 m gs 1 -1 sc (2S,0L,S) col0 sh gr /Times-Roman ff 255.00 scf sf 10591 4311 m gs 1 -1 sc (3S,0L,S) col0 sh gr /Times-Roman ff 225.00 scf sf 10468 6195 m gs 1 -1 sc (3S,\(N+1\)L) col0 sh gr /Times-Roman ff 225.00 scf sf 7761 6195 m gs 1 -1 sc (2S,\(N+1\)L) col0 sh gr /Times-Roman ff 225.00 scf sf 5053 6195 m gs 1 -1 sc (1S,\(N+1\)L) col0 sh gr /Times-Roman ff 225.00 scf sf 2223 6195 m gs 1 -1 sc (0S,\(N+1\)L) col0 sh gr /Times-Roman ff 255.00 scf sf 7822 2365 m gs 1 -1 sc (2S,1L,L) col0 sh gr /Times-Roman ff 255.00 scf sf 10529 2365 m gs 1 -1 sc (3S,1L,L) col0 sh gr % Polyline 15.000 slw [15 68] 68 sd n 750 1275 m 12675 1275 l 12675 2925 l 750 2925 l cp gs col0 s gr [] 0 sd % Polyline [15 68] 68 sd n 750 3525 m 6375 3525 l 6375 5025 l 750 5025 l cp gs col0 s gr [] 0 sd % Polyline [15 68] 68 sd n 7125 3525 m 12675 3525 l 12675 5025 l 7125 5025 l cp gs col0 s gr [] 0 sd % Polyline [15 68] 68 sd n 750 5550 m 12675 5550 l 12675 6975 l 750 6975 l cp gs col0 s gr [] 0 sd % Polyline [15 68] 68 sd n 6675 7650 m 12750 7650 l 12750 8775 l 6675 8775 l cp gs col0 s gr [] 0 sd /Times-Roman ff 270.00 scf sf 975 1725 m gs 1 -1 sc (Region 3) col0 sh gr /Times-Roman ff 270.00 scf sf 900 6000 m gs 1 -1 sc (Region 4) col0 sh gr /Times-Roman ff 270.00 scf sf 825 3900 m gs 1 -1 sc (Region 1) col0 sh gr /Times-Roman ff 270.00 scf sf 11700 3900 m gs 1 -1 sc (Region 2) col0 sh gr /Times-Roman ff 270.00 scf sf 6825 8625 m gs 1 -1 sc (Region 5) col0 sh gr F2psBegin10setmiterlimit0.060000.06000scF2psEnd rs %%EndDocument endTexFig 1840 2166 a Ff(\(a\))579 2380 y 21171196 14208860 0 0 49204756 32825098 startTexFig 579 2380 a %%BeginDocument: ../figures/k1indptexpanded.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: k1indptexpanded.eps %%Creator: fig2dev Version 3.2 Patchlevel 3d %%CreationDate: Thu May 16 22:42:40 2002 %%For: harchol@mor.sp.cs.cmu.edu (Mor Harchol-Balter) %%BoundingBox: 0 0 748 499 %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def F2psDictbeginF2psDict begin F2psDictbeginF2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 499 moveto 0 0 lineto 748 0 lineto 748 499 lineto closepath clip newpath -35.1 545.3 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def F2psBegin10setmiterlimit0.060000.06000scF2psBegin 10 setmiterlimit 0.06000 0.06000 sc % % Fig objects follow % /Symbol ff 195.00 scf sf 6150 930 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 6270 1050 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 9450 930 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 9570 1050 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 2775 3405 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 2895 3525 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 9375 3330 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 9495 3450 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 9450 8130 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 9570 8250 m gs 1 -1 sc (S) col0 sh gr 15.000 slw % Ellipse n 12300 1575 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12600 1575 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12900 1575 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12375 6300 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12675 6300 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12975 6300 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12375 3975 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12675 3975 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12975 3975 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12300 8775 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12600 8775 54 54 0 360 DrawEllipse gs col0 s gr % Ellipse n 12900 8775 54 54 0 360 DrawEllipse gs col0 s gr /Symbol ff 240.00 scf sf 6600 7635 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 6750 7785 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 240.00 scf sf 6450 7635 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 240.00 scf sf 9900 7560 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 10050 7710 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 240.00 scf sf 9750 7560 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 195.00 scf sf 2700 5805 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 2820 5925 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 6000 5805 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 6120 5925 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 9450 5805 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 9570 5925 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 9600 6901 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 9751 7050 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 6000 6976 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 6151 7125 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 2700 6901 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 2851 7050 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 300.00 scf sf 825 2832 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 1013 2925 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 4125 2832 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 4313 2925 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 8925 5307 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 9113 5400 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 300.00 scf sf 12225 5232 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 300.00 scf sf 12413 5325 m gs 1 -1 sc (L) col0 sh gr /Symbol ff 255.00 scf sf 1200 2325 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 1275 2475 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 255.00 scf sf 1875 2325 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 1950 2475 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 255.00 scf sf 1200 3225 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 1275 3375 m gs 1 -1 sc (3) col0 sh gr % Ellipse n 1575 2775 168 168 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 1519 2651 m 1636 2627 l 1580 2345 l 1569 2593 l 1463 2369 l cp eoclip n 1425 1875 m 1575 2625 l gs col0 s gr gr % arrowhead 0 slj n 1463 2369 m 1569 2593 l 1580 2345 l col0 s % Polyline 2 slj gs clippath 1438 3683 m 1558 3695 l 1586 3409 l 1503 3642 l 1467 3397 l cp eoclip n 1575 2925 m 1500 3675 l gs col0 s gr gr % arrowhead 0 slj n 1467 3397 m 1503 3642 l 1586 3409 l col0 s % Polyline 2 slj gs clippath 1589 3661 m 1696 3715 l 1825 3457 l 1665 3645 l 1718 3403 l cp eoclip n 1650 1875 m 1650 1876 l 1652 1878 l 1654 1882 l 1657 1889 l 1661 1898 l 1667 1910 l 1674 1925 l 1682 1943 l 1691 1963 l 1701 1986 l 1712 2012 l 1724 2039 l 1736 2069 l 1748 2100 l 1761 2133 l 1773 2167 l 1785 2202 l 1797 2238 l 1808 2277 l 1818 2316 l 1829 2358 l 1838 2401 l 1847 2447 l 1855 2496 l 1861 2547 l 1867 2600 l 1871 2657 l 1874 2715 l 1875 2775 l 1874 2835 l 1871 2893 l 1867 2950 l 1861 3003 l 1855 3054 l 1847 3103 l 1838 3149 l 1829 3192 l 1818 3234 l 1808 3273 l 1797 3312 l 1785 3348 l 1773 3383 l 1761 3417 l 1748 3450 l 1736 3481 l 1724 3511 l 1712 3538 l 1701 3564 l 1691 3587 l 1682 3607 l 1674 3625 l 1667 3640 l 1661 3652 l 1657 3661 l 1650 3675 l gs col0 s gr gr % arrowhead 0 slj n 1718 3403 m 1665 3645 l 1825 3457 l col0 s /Times-Roman ff 315.00 scf sf 975 1725 m gs 1 -1 sc (0S,1L) col0 sh gr /Symbol ff 255.00 scf sf 4575 2325 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 4650 2475 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 255.00 scf sf 5250 2325 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 5325 2475 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 255.00 scf sf 4575 3225 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 4650 3375 m gs 1 -1 sc (3) col0 sh gr % Ellipse n 4950 2775 168 168 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 4894 2651 m 5011 2627 l 4955 2345 l 4944 2593 l 4838 2369 l cp eoclip n 4800 1875 m 4950 2625 l gs col0 s gr gr % arrowhead 0 slj n 4838 2369 m 4944 2593 l 4955 2345 l col0 s % Polyline 2 slj gs clippath 4813 3683 m 4933 3695 l 4961 3409 l 4878 3642 l 4842 3397 l cp eoclip n 4950 2925 m 4875 3675 l gs col0 s gr gr % arrowhead 0 slj n 4842 3397 m 4878 3642 l 4961 3409 l col0 s % Polyline 2 slj gs clippath 4964 3661 m 5071 3715 l 5200 3457 l 5040 3645 l 5093 3403 l cp eoclip n 5025 1875 m 5025 1876 l 5027 1878 l 5029 1882 l 5032 1889 l 5036 1898 l 5042 1910 l 5049 1925 l 5057 1943 l 5066 1963 l 5076 1986 l 5087 2012 l 5099 2039 l 5111 2069 l 5123 2100 l 5136 2133 l 5148 2167 l 5160 2202 l 5172 2238 l 5183 2277 l 5193 2316 l 5204 2358 l 5213 2401 l 5222 2447 l 5230 2496 l 5236 2547 l 5242 2600 l 5246 2657 l 5249 2715 l 5250 2775 l 5249 2835 l 5246 2893 l 5242 2950 l 5236 3003 l 5230 3054 l 5222 3103 l 5213 3149 l 5204 3192 l 5193 3234 l 5183 3273 l 5172 3312 l 5160 3348 l 5148 3383 l 5136 3417 l 5123 3450 l 5111 3481 l 5099 3511 l 5087 3538 l 5076 3564 l 5066 3587 l 5057 3607 l 5049 3625 l 5042 3640 l 5036 3652 l 5032 3661 l 5025 3675 l gs col0 s gr gr % arrowhead 0 slj n 5093 3403 m 5040 3645 l 5200 3457 l col0 s /Symbol ff 255.00 scf sf 7800 2325 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 7875 2475 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 255.00 scf sf 8475 2325 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 8550 2475 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 255.00 scf sf 7800 3225 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 7875 3375 m gs 1 -1 sc (3) col0 sh gr % Ellipse n 8175 2775 168 168 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 8119 2651 m 8236 2627 l 8180 2345 l 8169 2593 l 8063 2369 l cp eoclip n 8025 1875 m 8175 2625 l gs col0 s gr gr % arrowhead 0 slj n 8063 2369 m 8169 2593 l 8180 2345 l col0 s % Polyline 2 slj gs clippath 8038 3683 m 8158 3695 l 8186 3409 l 8103 3642 l 8067 3397 l cp eoclip n 8175 2925 m 8100 3675 l gs col0 s gr gr % arrowhead 0 slj n 8067 3397 m 8103 3642 l 8186 3409 l col0 s % Polyline 2 slj gs clippath 8189 3661 m 8296 3715 l 8425 3457 l 8265 3645 l 8318 3403 l cp eoclip n 8250 1875 m 8250 1876 l 8252 1878 l 8254 1882 l 8257 1889 l 8261 1898 l 8267 1910 l 8274 1925 l 8282 1943 l 8291 1963 l 8301 1986 l 8312 2012 l 8324 2039 l 8336 2069 l 8348 2100 l 8361 2133 l 8373 2167 l 8385 2202 l 8397 2238 l 8408 2277 l 8418 2316 l 8429 2358 l 8438 2401 l 8447 2447 l 8455 2496 l 8461 2547 l 8467 2600 l 8471 2657 l 8474 2715 l 8475 2775 l 8474 2835 l 8471 2893 l 8467 2950 l 8461 3003 l 8455 3054 l 8447 3103 l 8438 3149 l 8429 3192 l 8418 3234 l 8408 3273 l 8397 3312 l 8385 3348 l 8373 3383 l 8361 3417 l 8348 3450 l 8336 3481 l 8324 3511 l 8312 3538 l 8301 3564 l 8291 3587 l 8282 3607 l 8274 3625 l 8267 3640 l 8261 3652 l 8257 3661 l 8250 3675 l gs col0 s gr gr % arrowhead 0 slj n 8318 3403 m 8265 3645 l 8425 3457 l col0 s /Symbol ff 255.00 scf sf 11025 2325 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 11100 2475 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 255.00 scf sf 11700 2325 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 11775 2475 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 255.00 scf sf 11025 3225 m gs 1 -1 sc (g) col0 sh gr /Symbol ff 255.00 scf sf 11100 3375 m gs 1 -1 sc (3) col0 sh gr % Ellipse n 11400 2775 168 168 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 11344 2651 m 11461 2627 l 11405 2345 l 11394 2593 l 11288 2369 l cp eoclip n 11250 1875 m 11400 2625 l gs col0 s gr gr % arrowhead 0 slj n 11288 2369 m 11394 2593 l 11405 2345 l col0 s % Polyline 2 slj gs clippath 11263 3683 m 11383 3695 l 11411 3409 l 11328 3642 l 11292 3397 l cp eoclip n 11400 2925 m 11325 3675 l gs col0 s gr gr % arrowhead 0 slj n 11292 3397 m 11328 3642 l 11411 3409 l col0 s % Polyline 2 slj gs clippath 11414 3661 m 11521 3715 l 11650 3457 l 11490 3645 l 11543 3403 l cp eoclip n 11475 1875 m 11475 1876 l 11477 1878 l 11479 1882 l 11482 1889 l 11486 1898 l 11492 1910 l 11499 1925 l 11507 1943 l 11516 1963 l 11526 1986 l 11537 2012 l 11549 2039 l 11561 2069 l 11573 2100 l 11586 2133 l 11598 2167 l 11610 2202 l 11622 2238 l 11633 2277 l 11643 2316 l 11654 2358 l 11663 2401 l 11672 2447 l 11680 2496 l 11686 2547 l 11692 2600 l 11696 2657 l 11699 2715 l 11700 2775 l 11699 2835 l 11696 2893 l 11692 2950 l 11686 3003 l 11680 3054 l 11672 3103 l 11663 3149 l 11654 3192 l 11643 3234 l 11633 3273 l 11622 3312 l 11610 3348 l 11598 3383 l 11586 3417 l 11573 3450 l 11561 3481 l 11549 3511 l 11537 3538 l 11526 3564 l 11516 3587 l 11507 3607 l 11499 3625 l 11492 3640 l 11486 3652 l 11482 3661 l 11475 3675 l gs col0 s gr gr % arrowhead 0 slj n 11543 3403 m 11490 3645 l 11650 3457 l col0 s /Symbol ff 240.00 scf sf 2700 3076 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 2851 3225 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 2700 1005 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 2820 1125 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 2700 1801 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 2851 1950 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 2700 2280 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 2820 2400 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 9450 3001 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 9601 3150 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 9450 5401 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 9601 5550 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 6000 5401 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 6151 5550 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 2625 5401 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 2776 5550 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 2700 4276 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 2851 4425 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 6075 4185 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 6225 4335 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 240.00 scf sf 5925 4185 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 240.00 scf sf 9525 4110 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 9675 4260 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 240.00 scf sf 9375 4110 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 240.00 scf sf 9375 1801 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 9526 1950 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 6075 1801 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 6226 1950 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 9375 2280 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 9495 2400 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 9375 4755 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 9495 4875 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 5925 4755 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 6045 4875 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 2625 4755 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 2745 4875 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 6075 3405 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 6195 3525 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 240.00 scf sf 6000 3001 m gs 1 -1 sc (m) col0 sh gr /Times-Roman ff 240.00 scf sf 6151 3150 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 195.00 scf sf 6000 2280 m gs 1 -1 sc (l) col0 sh gr /Times-Roman ff 195.00 scf sf 6120 2400 m gs 1 -1 sc (S) col0 sh gr /Symbol ff 255.00 scf sf 750 5775 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 360.00 scf sf 600 5700 m gs 1 -1 sc (z) col0 sh gr /Symbol ff 255.00 scf sf 1500 4875 m gs 1 -1 sc (3) col0 sh gr /Symbol ff 360.00 scf sf 1350 4800 m gs 1 -1 sc (z) col0 sh gr /Symbol ff 255.00 scf sf 1500 5850 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 360.00 scf sf 1350 5775 m gs 1 -1 sc (z) col0 sh gr /Symbol ff 255.00 scf sf 4950 4875 m gs 1 -1 sc (3) col0 sh gr /Symbol ff 360.00 scf sf 4800 4800 m gs 1 -1 sc (z) col0 sh gr /Symbol ff 255.00 scf sf 4950 5850 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 360.00 scf sf 4800 5775 m gs 1 -1 sc (z) col0 sh gr /Symbol ff 255.00 scf sf 4200 5775 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 360.00 scf sf 4050 5700 m gs 1 -1 sc (z) col0 sh gr /Symbol ff 255.00 scf sf 7575 5775 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 360.00 scf sf 7425 5700 m gs 1 -1 sc (z) col0 sh gr /Symbol ff 255.00 scf sf 8325 4875 m gs 1 -1 sc (3) col0 sh gr /Symbol ff 360.00 scf sf 8175 4800 m gs 1 -1 sc (z) col0 sh gr /Symbol ff 255.00 scf sf 8325 5850 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 360.00 scf sf 8175 5775 m gs 1 -1 sc (z) col0 sh gr /Symbol ff 255.00 scf sf 11700 4800 m gs 1 -1 sc (3) col0 sh gr /Symbol ff 360.00 scf sf 11550 4725 m gs 1 -1 sc (z) col0 sh gr /Symbol ff 255.00 scf sf 11700 5775 m gs 1 -1 sc (1) col0 sh gr /Symbol ff 360.00 scf sf 11550 5700 m gs 1 -1 sc (z) col0 sh gr /Symbol ff 255.00 scf sf 10950 5700 m gs 1 -1 sc (2) col0 sh gr /Symbol ff 360.00 scf sf 10800 5625 m gs 1 -1 sc (z) col0 sh gr % Ellipse n 4725 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 11325 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 8025 3975 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 4725 3975 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 4725 6375 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 11325 6375 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 8025 8775 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 11325 8775 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 8025 6375 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 1350 6375 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 1425 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 1425 3975 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 1425 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 8025 1575 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 11391 3940 750 300 0 360 DrawEllipse gs col0 s gr % Ellipse n 1200 5175 168 168 0 360 DrawEllipse gs col0 s gr % Ellipse n 4650 5175 168 168 0 360 DrawEllipse gs col0 s gr % Ellipse n 8025 5175 168 168 0 360 DrawEllipse gs col0 s gr % Ellipse n 11400 5100 168 168 0 360 DrawEllipse gs col0 s gr % Polyline 2 slj gs clippath 3958 1559 m 4017 1455 l 3767 1312 l 3946 1484 l 3707 1417 l cp eoclip n 2175 1425 m 2176 1424 l 2178 1423 l 2182 1421 l 2189 1418 l 2198 1413 l 2210 1407 l 2225 1399 l 2243 1391 l 2263 1381 l 2286 1370 l 2312 1358 l 2339 1345 l 2369 1333 l 2400 1320 l 2433 1307 l 2467 1294 l 2502 1281 l 2538 1269 l 2577 1258 l 2616 1247 l 2658 1237 l 2701 1228 l 2747 1219 l 2796 1212 l 2847 1206 l 2900 1202 l 2957 1199 l 3015 1199 l 3075 1200 l 3135 1204 l 3193 1209 l 3250 1217 l 3303 1225 l 3354 1236 l 3403 1247 l 3449 1259 l 3492 1272 l 3534 1285 l 3573 1299 l 3612 1314 l 3648 1329 l 3683 1344 l 3717 1360 l 3750 1376 l 3781 1391 l 3811 1407 l 3838 1421 l 3864 1435 l 3887 1448 l 3907 1460 l 3925 1470 l 3940 1479 l 3952 1486 l 3961 1492 l 3975 1500 l gs col0 s gr gr % arrowhead 0 slj n 3707 1417 m 3946 1484 l 3767 1312 l col0 s % Polyline 2 slj gs clippath 2200 1593 m 2126 1687 l 2352 1865 l 2201 1670 l 2426 1771 l cp eoclip n 3975 1650 m 3974 1651 l 3971 1652 l 3966 1655 l 3959 1659 l 3948 1665 l 3935 1672 l 3917 1682 l 3897 1692 l 3873 1705 l 3847 1719 l 3817 1733 l 3786 1749 l 3752 1765 l 3717 1781 l 3680 1798 l 3642 1814 l 3603 1830 l 3563 1845 l 3521 1860 l 3478 1875 l 3433 1888 l 3386 1901 l 3337 1912 l 3286 1923 l 3233 1932 l 3177 1939 l 3119 1945 l 3060 1949 l 3000 1950 l 2936 1949 l 2875 1944 l 2817 1938 l 2762 1929 l 2711 1919 l 2663 1907 l 2618 1895 l 2576 1881 l 2537 1866 l 2499 1850 l 2464 1833 l 2430 1816 l 2398 1799 l 2367 1781 l 2338 1764 l 2311 1747 l 2286 1730 l 2263 1715 l 2243 1700 l 2225 1688 l 2210 1677 l 2198 1668 l 2189 1661 l 2175 1650 l gs col0 s gr gr % arrowhead 0 slj n 2426 1771 m 2201 1670 l 2352 1865 l col0 s % Polyline 2 slj gs clippath 7183 1559 m 7242 1455 l 6992 1312 l 7171 1484 l 6932 1417 l cp eoclip n 5400 1425 m 5401 1424 l 5403 1423 l 5407 1421 l 5414 1418 l 5423 1413 l 5435 1407 l 5450 1399 l 5468 1391 l 5488 1381 l 5511 1370 l 5537 1358 l 5564 1345 l 5594 1333 l 5625 1320 l 5658 1307 l 5692 1294 l 5727 1281 l 5763 1269 l 5802 1258 l 5841 1247 l 5883 1237 l 5926 1228 l 5972 1219 l 6021 1212 l 6072 1206 l 6125 1202 l 6182 1199 l 6240 1199 l 6300 1200 l 6360 1204 l 6418 1209 l 6475 1217 l 6528 1225 l 6579 1236 l 6628 1247 l 6674 1259 l 6717 1272 l 6759 1285 l 6798 1299 l 6837 1314 l 6873 1329 l 6908 1344 l 6942 1360 l 6975 1376 l 7006 1391 l 7036 1407 l 7063 1421 l 7089 1435 l 7112 1448 l 7132 1460 l 7150 1470 l 7165 1479 l 7177 1486 l 7186 1492 l 7200 1500 l gs col0 s gr gr % arrowhead 0 slj n 6932 1417 m 7171 1484 l 6992 1312 l col0 s % Polyline 2 slj gs clippath 10558 1484 m 10617 1380 l 10367 1237 l 10546 1409 l 10307 1342 l cp eoclip n 8775 1350 m 8776 1349 l 8778 1348 l 8782 1346 l 8789 1343 l 8798 1338 l 8810 1332 l 8825 1324 l 8843 1316 l 8863 1306 l 8886 1295 l 8912 1283 l 8939 1270 l 8969 1258 l 9000 1245 l 9033 1232 l 9067 1219 l 9102 1206 l 9138 1194 l 9177 1183 l 9216 1172 l 9258 1162 l 9301 1153 l 9347 1144 l 9396 1137 l 9447 1131 l 9500 1127 l 9557 1124 l 9615 1124 l 9675 1125 l 9735 1129 l 9793 1134 l 9850 1142 l 9903 1150 l 9954 1161 l 10003 1172 l 10049 1184 l 10092 1197 l 10134 1210 l 10173 1224 l 10212 1239 l 10248 1254 l 10283 1269 l 10317 1285 l 10350 1301 l 10381 1316 l 10411 1332 l 10438 1346 l 10464 1360 l 10487 1373 l 10507 1385 l 10525 1395 l 10540 1404 l 10552 1411 l 10561 1417 l 10575 1425 l gs col0 s gr gr % arrowhead 0 slj n 10307 1342 m 10546 1409 l 10367 1237 l col0 s % Polyline 2 slj gs clippath 3958 3959 m 4017 3855 l 3767 3712 l 3946 3884 l 3707 3817 l cp eoclip n 2175 3825 m 2176 3824 l 2178 3823 l 2182 3821 l 2189 3818 l 2198 3813 l 2210 3807 l 2225 3799 l 2243 3791 l 2263 3781 l 2286 3770 l 2312 3758 l 2339 3745 l 2369 3733 l 2400 3720 l 2433 3707 l 2467 3694 l 2502 3681 l 2538 3669 l 2577 3658 l 2616 3647 l 2658 3637 l 2701 3628 l 2747 3619 l 2796 3612 l 2847 3606 l 2900 3602 l 2957 3599 l 3015 3599 l 3075 3600 l 3135 3604 l 3193 3609 l 3250 3617 l 3303 3625 l 3354 3636 l 3403 3647 l 3449 3659 l 3492 3672 l 3534 3685 l 3573 3699 l 3612 3714 l 3648 3729 l 3683 3744 l 3717 3760 l 3750 3776 l 3781 3791 l 3811 3807 l 3838 3821 l 3864 3835 l 3887 3848 l 3907 3860 l 3925 3870 l 3940 3879 l 3952 3886 l 3961 3892 l 3975 3900 l gs col0 s gr gr % arrowhead 0 slj n 3707 3817 m 3946 3884 l 3767 3712 l col0 s % Polyline 2 slj gs clippath 7183 3959 m 7242 3855 l 6992 3712 l 7171 3884 l 6932 3817 l cp eoclip n 5400 3825 m 5401 3824 l 5403 3823 l 5407 3821 l 5414 3818 l 5423 3813 l 5435 3807 l 5450 3799 l 5468 3791 l 5488 3781 l 5511 3770 l 5537 3758 l 5564 3745 l 5594 3733 l 5625 3720 l 5658 3707 l 5692 3694 l 5727 3681 l 5763 3669 l 5802 3658 l 5841 3647 l 5883 3637 l 5926 3628 l 5972 3619 l 6021 3612 l 6072 3606 l 6125 3602 l 6182 3599 l 6240 3599 l 6300 3600 l 6360 3604 l 6418 3609 l 6475 3617 l 6528 3625 l 6579 3636 l 6628 3647 l 6674 3659 l 6717 3672 l 6759 3685 l 6798 3699 l 6837 3714 l 6873 3729 l 6908 3744 l 6942 3760 l 6975 3776 l 7006 3791 l 7036 3807 l 7063 3821 l 7089 3835 l 7112 3848 l 7132 3860 l 7150 3870 l 7165 3879 l 7177 3886 l 7186 3892 l 7200 3900 l gs col0 s gr gr % arrowhead 0 slj n 6932 3817 m 7171 3884 l 6992 3712 l col0 s % Polyline 2 slj gs clippath 10490 3861 m 10549 3757 l 10299 3614 l 10478 3786 l 10239 3719 l cp eoclip n 8707 3727 m 8708 3726 l 8710 3725 l 8714 3723 l 8721 3720 l 8730 3715 l 8742 3709 l 8757 3701 l 8775 3693 l 8795 3683 l 8818 3672 l 8844 3660 l 8871 3647 l 8901 3635 l 8932 3622 l 8965 3609 l 8999 3596 l 9034 3583 l 9070 3571 l 9109 3560 l 9148 3549 l 9190 3539 l 9233 3530 l 9279 3521 l 9328 3514 l 9379 3508 l 9432 3504 l 9489 3501 l 9547 3501 l 9607 3502 l 9667 3506 l 9725 3511 l 9782 3519 l 9835 3527 l 9886 3538 l 9935 3549 l 9981 3561 l 10024 3574 l 10066 3587 l 10105 3601 l 10144 3616 l 10180 3631 l 10215 3646 l 10249 3662 l 10282 3678 l 10313 3693 l 10343 3709 l 10370 3723 l 10396 3737 l 10419 3750 l 10439 3762 l 10457 3772 l 10472 3781 l 10484 3788 l 10493 3794 l 10507 3802 l gs col0 s gr gr % arrowhead 0 slj n 10239 3719 m 10478 3786 l 10299 3614 l col0 s % Polyline 2 slj gs clippath 10565 8736 m 10624 8632 l 10374 8489 l 10553 8661 l 10314 8594 l cp eoclip n 8782 8602 m 8783 8601 l 8785 8600 l 8789 8598 l 8796 8595 l 8805 8590 l 8817 8584 l 8832 8576 l 8850 8568 l 8870 8558 l 8893 8547 l 8919 8535 l 8946 8522 l 8976 8510 l 9007 8497 l 9040 8484 l 9074 8471 l 9109 8458 l 9145 8446 l 9184 8435 l 9223 8424 l 9265 8414 l 9308 8405 l 9354 8396 l 9403 8389 l 9454 8383 l 9507 8379 l 9564 8376 l 9622 8376 l 9682 8377 l 9742 8381 l 9800 8386 l 9857 8394 l 9910 8402 l 9961 8413 l 10010 8424 l 10056 8436 l 10099 8449 l 10141 8462 l 10180 8476 l 10219 8491 l 10255 8506 l 10290 8521 l 10324 8537 l 10357 8553 l 10388 8568 l 10418 8584 l 10445 8598 l 10471 8612 l 10494 8625 l 10514 8637 l 10532 8647 l 10547 8656 l 10559 8663 l 10568 8669 l 10582 8677 l gs col0 s gr gr % arrowhead 0 slj n 10314 8594 m 10553 8661 l 10374 8489 l col0 s % Polyline 2 slj gs clippath 2206 4089 m 2132 4183 l 2358 4361 l 2207 4166 l 2432 4267 l cp eoclip n 3981 4146 m 3980 4147 l 3977 4148 l 3972 4151 l 3965 4155 l 3954 4161 l 3941 4168 l 3923 4178 l 3903 4188 l 3879 4201 l 3853 4215 l 3823 4229 l 3792 4245 l 3758 4261 l 3723 4277 l 3686 4294 l 3648 4310 l 3609 4326 l 3569 4341 l 3527 4356 l 3484 4371 l 3439 4384 l 3392 4397 l 3343 4408 l 3292 4419 l 3239 4428 l 3183 4435 l 3125 4441 l 3066 4445 l 3006 4446 l 2942 4445 l 2881 4440 l 2823 4434 l 2768 4425 l 2717 4415 l 2669 4403 l 2624 4391 l 2582 4377 l 2543 4362 l 2505 4346 l 2470 4329 l 2436 4312 l 2404 4295 l 2373 4277 l 2344 4260 l 2317 4243 l 2292 4226 l 2269 4211 l 2249 4196 l 2231 4184 l 2216 4173 l 2204 4164 l 2195 4157 l 2181 4146 l gs col0 s gr gr % arrowhead 0 slj n 2432 4267 m 2207 4166 l 2358 4361 l col0 s % Polyline 2 slj gs clippath 5506 4014 m 5432 4108 l 5658 4286 l 5507 4091 l 5732 4192 l cp eoclip n 7281 4071 m 7280 4072 l 7277 4073 l 7272 4076 l 7265 4080 l 7254 4086 l 7241 4093 l 7223 4103 l 7203 4113 l 7179 4126 l 7153 4140 l 7123 4154 l 7092 4170 l 7058 4186 l 7023 4202 l 6986 4219 l 6948 4235 l 6909 4251 l 6869 4266 l 6827 4281 l 6784 4296 l 6739 4309 l 6692 4322 l 6643 4333 l 6592 4344 l 6539 4353 l 6483 4360 l 6425 4366 l 6366 4370 l 6306 4371 l 6242 4370 l 6181 4365 l 6123 4359 l 6068 4350 l 6017 4340 l 5969 4328 l 5924 4316 l 5882 4302 l 5843 4287 l 5805 4271 l 5770 4254 l 5736 4237 l 5704 4220 l 5673 4202 l 5644 4185 l 5617 4168 l 5592 4151 l 5569 4136 l 5549 4121 l 5531 4109 l 5516 4098 l 5504 4089 l 5495 4082 l 5481 4071 l gs col0 s gr gr % arrowhead 0 slj n 5732 4192 m 5507 4091 l 5658 4286 l col0 s % Polyline 2 slj gs clippath 5500 1593 m 5426 1687 l 5652 1865 l 5501 1670 l 5726 1771 l cp eoclip n 7275 1650 m 7274 1651 l 7271 1652 l 7266 1655 l 7259 1659 l 7248 1665 l 7235 1672 l 7217 1682 l 7197 1692 l 7173 1705 l 7147 1719 l 7117 1733 l 7086 1749 l 7052 1765 l 7017 1781 l 6980 1798 l 6942 1814 l 6903 1830 l 6863 1845 l 6821 1860 l 6778 1875 l 6733 1888 l 6686 1901 l 6637 1912 l 6586 1923 l 6533 1932 l 6477 1939 l 6419 1945 l 6360 1949 l 6300 1950 l 6236 1949 l 6175 1944 l 6117 1938 l 6062 1929 l 6011 1919 l 5963 1907 l 5918 1895 l 5876 1881 l 5837 1866 l 5799 1850 l 5764 1833 l 5730 1816 l 5698 1799 l 5667 1781 l 5638 1764 l 5611 1747 l 5586 1730 l 5563 1715 l 5543 1700 l 5525 1688 l 5510 1677 l 5498 1668 l 5489 1661 l 5475 1650 l gs col0 s gr gr % arrowhead 0 slj n 5726 1771 m 5501 1670 l 5652 1865 l col0 s % Polyline 2 slj gs clippath 8800 1593 m 8726 1687 l 8952 1865 l 8801 1670 l 9026 1771 l cp eoclip n 10575 1650 m 10574 1651 l 10571 1652 l 10566 1655 l 10559 1659 l 10548 1665 l 10535 1672 l 10517 1682 l 10497 1692 l 10473 1705 l 10447 1719 l 10417 1733 l 10386 1749 l 10352 1765 l 10317 1781 l 10280 1798 l 10242 1814 l 10203 1830 l 10163 1845 l 10121 1860 l 10078 1875 l 10033 1888 l 9986 1901 l 9937 1912 l 9886 1923 l 9833 1932 l 9777 1939 l 9719 1945 l 9660 1949 l 9600 1950 l 9536 1949 l 9475 1944 l 9417 1938 l 9362 1929 l 9311 1919 l 9263 1907 l 9218 1895 l 9176 1881 l 9137 1866 l 9099 1850 l 9064 1833 l 9030 1816 l 8998 1799 l 8967 1781 l 8938 1764 l 8911 1747 l 8886 1730 l 8863 1715 l 8843 1700 l 8825 1688 l 8810 1677 l 8798 1668 l 8789 1661 l 8775 1650 l gs col0 s gr gr % arrowhead 0 slj n 9026 1771 m 8801 1670 l 8952 1865 l col0 s % Polyline 2 slj gs clippath 8800 3918 m 8726 4012 l 8952 4190 l 8801 3995 l 9026 4096 l cp eoclip n 10575 3975 m 10574 3976 l 10571 3977 l 10566 3980 l 10559 3984 l 10548 3990 l 10535 3997 l 10517 4007 l 10497 4017 l 10473 4030 l 10447 4044 l 10417 4058 l 10386 4074 l 10352 4090 l 10317 4106 l 10280 4123 l 10242 4139 l 10203 4155 l 10163 4170 l 10121 4185 l 10078 4200 l 10033 4213 l 9986 4226 l 9937 4237 l 9886 4248 l 9833 4257 l 9777 4264 l 9719 4270 l 9660 4274 l 9600 4275 l 9536 4274 l 9475 4269 l 9417 4263 l 9362 4254 l 9311 4244 l 9263 4232 l 9218 4220 l 9176 4206 l 9137 4191 l 9099 4175 l 9064 4158 l 9030 4141 l 8998 4124 l 8967 4106 l 8938 4089 l 8911 4072 l 8886 4055 l 8863 4040 l 8843 4025 l 8825 4013 l 8810 4002 l 8798 3993 l 8789 3986 l 8775 3975 l gs col0 s gr gr % arrowhead 0 slj n 9026 4096 m 8801 3995 l 8952 4190 l col0 s % Polyline 2 slj gs clippath 5050 6618 m 4976 6713 l 5203 6890 l 5051 6695 l 5277 6795 l cp eoclip n 7425 8550 m 5025 6675 l gs col0 s gr gr % arrowhead 0 slj n 5277 6795 m 5051 6695 l 5203 6890 l col0 s % Polyline 2 slj gs clippath 8366 6598 m 8292 6693 l 8519 6870 l 8367 6675 l 8593 6775 l cp eoclip n 10741 8530 m 8341 6655 l gs col0 s gr gr % arrowhead 0 slj n 8593 6775 m 8367 6675 l 8519 6870 l col0 s % Polyline 2 slj gs clippath 3890 6336 m 3949 6232 l 3699 6089 l 3878 6261 l 3639 6194 l cp eoclip n 2107 6202 m 2108 6201 l 2110 6200 l 2114 6198 l 2121 6195 l 2130 6190 l 2142 6184 l 2157 6176 l 2175 6168 l 2195 6158 l 2218 6147 l 2244 6135 l 2271 6122 l 2301 6110 l 2332 6097 l 2365 6084 l 2399 6071 l 2434 6058 l 2470 6046 l 2509 6035 l 2548 6024 l 2590 6014 l 2633 6005 l 2679 5996 l 2728 5989 l 2779 5983 l 2832 5979 l 2889 5976 l 2947 5976 l 3007 5977 l 3067 5981 l 3125 5986 l 3182 5994 l 3235 6002 l 3286 6013 l 3335 6024 l 3381 6036 l 3424 6049 l 3466 6062 l 3505 6076 l 3544 6091 l 3580 6106 l 3615 6121 l 3649 6137 l 3682 6153 l 3713 6168 l 3743 6184 l 3770 6198 l 3796 6212 l 3819 6225 l 3839 6237 l 3857 6247 l 3872 6256 l 3884 6263 l 3893 6269 l 3907 6277 l gs col0 s gr gr % arrowhead 0 slj n 3639 6194 m 3878 6261 l 3699 6089 l col0 s % Polyline 2 slj gs clippath 7265 6336 m 7324 6232 l 7074 6089 l 7253 6261 l 7014 6194 l cp eoclip n 5482 6202 m 5483 6201 l 5485 6200 l 5489 6198 l 5496 6195 l 5505 6190 l 5517 6184 l 5532 6176 l 5550 6168 l 5570 6158 l 5593 6147 l 5619 6135 l 5646 6122 l 5676 6110 l 5707 6097 l 5740 6084 l 5774 6071 l 5809 6058 l 5845 6046 l 5884 6035 l 5923 6024 l 5965 6014 l 6008 6005 l 6054 5996 l 6103 5989 l 6154 5983 l 6207 5979 l 6264 5976 l 6322 5976 l 6382 5977 l 6442 5981 l 6500 5986 l 6557 5994 l 6610 6002 l 6661 6013 l 6710 6024 l 6756 6036 l 6799 6049 l 6841 6062 l 6880 6076 l 6919 6091 l 6955 6106 l 6990 6121 l 7024 6137 l 7057 6153 l 7088 6168 l 7118 6184 l 7145 6198 l 7171 6212 l 7194 6225 l 7214 6237 l 7232 6247 l 7247 6256 l 7259 6263 l 7268 6269 l 7282 6277 l gs col0 s gr gr % arrowhead 0 slj n 7014 6194 m 7253 6261 l 7074 6089 l col0 s % Polyline 2 slj gs clippath 10565 6336 m 10624 6232 l 10374 6089 l 10553 6261 l 10314 6194 l cp eoclip n 8782 6202 m 8783 6201 l 8785 6200 l 8789 6198 l 8796 6195 l 8805 6190 l 8817 6184 l 8832 6176 l 8850 6168 l 8870 6158 l 8893 6147 l 8919 6135 l 8946 6122 l 8976 6110 l 9007 6097 l 9040 6084 l 9074 6071 l 9109 6058 l 9145 6046 l 9184 6035 l 9223 6024 l 9265 6014 l 9308 6005 l 9354 5996 l 9403 5989 l 9454 5983 l 9507 5979 l 9564 5976 l 9622 5976 l 9682 5977 l 9742 5981 l 9800 5986 l 9857 5994 l 9910 6002 l 9961 6013 l 10010 6024 l 10056 6036 l 10099 6049 l 10141 6062 l 10180 6076 l 10219 6091 l 10255 6106 l 10290 6121 l 10324 6137 l 10357 6153 l 10388 6168 l 10418 6184 l 10445 6198 l 10471 6212 l 10494 6225 l 10514 6237 l 10532 6247 l 10547 6256 l 10559 6263 l 10568 6269 l 10582 6277 l gs col0 s gr gr % arrowhead 0 slj n 10314 6194 m 10553 6261 l 10374 6089 l col0 s % Polyline 2 slj gs clippath 2200 6393 m 2126 6487 l 2352 6665 l 2201 6470 l 2426 6571 l cp eoclip n 3975 6450 m 3974 6451 l 3971 6452 l 3966 6455 l 3959 6459 l 3948 6465 l 3935 6472 l 3917 6482 l 3897 6492 l 3873 6505 l 3847 6519 l 3817 6533 l 3786 6549 l 3752 6565 l 3717 6581 l 3680 6598 l 3642 6614 l 3603 6630 l 3563 6645 l 3521 6660 l 3478 6675 l 3433 6688 l 3386 6701 l 3337 6712 l 3286 6723 l 3233 6732 l 3177 6739 l 3119 6745 l 3060 6749 l 3000 6750 l 2936 6749 l 2875 6744 l 2817 6738 l 2762 6729 l 2711 6719 l 2663 6707 l 2618 6695 l 2576 6681 l 2537 6666 l 2499 6650 l 2464 6633 l 2430 6616 l 2398 6599 l 2367 6581 l 2338 6564 l 2311 6547 l 2286 6530 l 2263 6515 l 2243 6500 l 2225 6488 l 2210 6477 l 2198 6468 l 2189 6461 l 2175 6450 l gs col0 s gr gr % arrowhead 0 slj n 2426 6571 m 2201 6470 l 2352 6665 l col0 s % Polyline 2 slj gs clippath 5491 6492 m 5417 6586 l 5643 6764 l 5492 6569 l 5717 6670 l cp eoclip n 7266 6549 m 7265 6550 l 7262 6551 l 7257 6554 l 7250 6558 l 7239 6564 l 7226 6571 l 7208 6581 l 7188 6591 l 7164 6604 l 7138 6618 l 7108 6632 l 7077 6648 l 7043 6664 l 7008 6680 l 6971 6697 l 6933 6713 l 6894 6729 l 6854 6744 l 6812 6759 l 6769 6774 l 6724 6787 l 6677 6800 l 6628 6811 l 6577 6822 l 6524 6831 l 6468 6838 l 6410 6844 l 6351 6848 l 6291 6849 l 6227 6848 l 6166 6843 l 6108 6837 l 6053 6828 l 6002 6818 l 5954 6806 l 5909 6794 l 5867 6780 l 5828 6765 l 5790 6749 l 5755 6732 l 5721 6715 l 5689 6698 l 5658 6680 l 5629 6663 l 5602 6646 l 5577 6629 l 5554 6614 l 5534 6599 l 5516 6587 l 5501 6576 l 5489 6567 l 5480 6560 l 5466 6549 l gs col0 s gr gr % arrowhead 0 slj n 5717 6670 m 5492 6569 l 5643 6764 l col0 s % Polyline 2 slj gs clippath 8791 6417 m 8717 6511 l 8943 6689 l 8792 6494 l 9017 6595 l cp eoclip n 10566 6474 m 10565 6475 l 10562 6476 l 10557 6479 l 10550 6483 l 10539 6489 l 10526 6496 l 10508 6506 l 10488 6516 l 10464 6529 l 10438 6543 l 10408 6557 l 10377 6573 l 10343 6589 l 10308 6605 l 10271 6622 l 10233 6638 l 10194 6654 l 10154 6669 l 10112 6684 l 10069 6699 l 10024 6712 l 9977 6725 l 9928 6736 l 9877 6747 l 9824 6756 l 9768 6763 l 9710 6769 l 9651 6773 l 9591 6774 l 9527 6773 l 9466 6768 l 9408 6762 l 9353 6753 l 9302 6743 l 9254 6731 l 9209 6719 l 9167 6705 l 9128 6690 l 9090 6674 l 9055 6657 l 9021 6640 l 8989 6623 l 8958 6605 l 8929 6588 l 8902 6571 l 8877 6554 l 8854 6539 l 8834 6524 l 8816 6512 l 8801 6501 l 8789 6492 l 8780 6485 l 8766 6474 l gs col0 s gr gr % arrowhead 0 slj n 9017 6595 m 8792 6494 l 8943 6689 l col0 s % Polyline 2 slj gs clippath 1179 1904 m 1090 1823 l 896 2035 l 1103 1899 l 985 2116 l cp eoclip n 1050 3675 m 1049 3674 l 1048 3671 l 1045 3666 l 1041 3659 l 1034 3648 l 1026 3635 l 1017 3617 l 1005 3597 l 992 3573 l 977 3547 l 962 3517 l 946 3486 l 929 3452 l 912 3417 l 895 3380 l 878 3342 l 861 3303 l 845 3263 l 830 3221 l 816 3178 l 802 3133 l 790 3086 l 779 3037 l 769 2986 l 761 2933 l 755 2877 l 751 2819 l 749 2760 l 750 2700 l 754 2641 l 760 2583 l 769 2528 l 780 2476 l 792 2427 l 806 2382 l 821 2339 l 837 2298 l 854 2260 l 872 2224 l 890 2190 l 909 2157 l 928 2126 l 948 2096 l 968 2067 l 988 2040 l 1007 2015 l 1026 1991 l 1043 1969 l 1060 1949 l 1074 1932 l 1087 1917 l 1098 1904 l 1107 1894 l 1114 1887 l 1125 1875 l gs col0 s gr gr % arrowhead 0 slj n 985 2116 m 1103 1899 l 896 2035 l col0 s % Polyline 2 slj gs clippath 4485 1907 m 4396 1826 l 4202 2038 l 4409 1902 l 4291 2119 l cp eoclip n 4356 3678 m 4355 3677 l 4354 3674 l 4351 3669 l 4347 3662 l 4340 3651 l 4332 3638 l 4323 3620 l 4311 3600 l 4298 3576 l 4283 3550 l 4268 3520 l 4252 3489 l 4235 3455 l 4218 3420 l 4201 3383 l 4184 3345 l 4167 3306 l 4151 3266 l 4136 3224 l 4122 3181 l 4108 3136 l 4096 3089 l 4085 3040 l 4075 2989 l 4067 2936 l 4061 2880 l 4057 2822 l 4055 2763 l 4056 2703 l 4060 2644 l 4066 2586 l 4075 2531 l 4086 2479 l 4098 2430 l 4112 2385 l 4127 2342 l 4143 2301 l 4160 2263 l 4178 2227 l 4196 2193 l 4215 2160 l 4234 2129 l 4254 2099 l 4274 2070 l 4294 2043 l 4313 2018 l 4332 1994 l 4349 1972 l 4366 1952 l 4380 1935 l 4393 1920 l 4404 1907 l 4413 1897 l 4420 1890 l 4431 1878 l gs col0 s gr gr % arrowhead 0 slj n 4291 2119 m 4409 1902 l 4202 2038 l col0 s % Polyline 2 slj gs clippath 8414 8536 m 8521 8590 l 8650 8332 l 8490 8520 l 8543 8278 l cp eoclip n 8475 4200 m 8475 4201 l 8476 4202 l 8478 4205 l 8480 4210 l 8484 4217 l 8489 4226 l 8495 4238 l 8503 4252 l 8512 4269 l 8523 4290 l 8535 4313 l 8548 4340 l 8563 4369 l 8579 4402 l 8596 4436 l 8615 4474 l 8634 4514 l 8654 4556 l 8674 4600 l 8695 4646 l 8716 4694 l 8738 4744 l 8759 4795 l 8780 4847 l 8801 4901 l 8822 4956 l 8843 5013 l 8863 5071 l 8883 5130 l 8902 5191 l 8921 5254 l 8939 5318 l 8956 5385 l 8972 5453 l 8988 5524 l 9002 5598 l 9016 5674 l 9029 5753 l 9040 5834 l 9050 5919 l 9059 6006 l 9066 6095 l 9071 6187 l 9074 6281 l 9075 6375 l 9074 6469 l 9071 6563 l 9066 6655 l 9059 6744 l 9050 6831 l 9040 6916 l 9029 6997 l 9016 7076 l 9002 7152 l 8988 7226 l 8972 7297 l 8956 7365 l 8939 7432 l 8921 7496 l 8902 7559 l 8883 7620 l 8863 7679 l 8843 7737 l 8822 7794 l 8801 7849 l 8780 7903 l 8759 7955 l 8737 8006 l 8716 8056 l 8695 8104 l 8674 8150 l 8654 8194 l 8634 8236 l 8615 8276 l 8596 8314 l 8579 8348 l 8563 8381 l 8548 8410 l 8535 8437 l 8523 8460 l 8512 8481 l 8503 8498 l 8495 8512 l 8489 8524 l 8484 8533 l 8480 8540 l 8475 8550 l gs col0 s gr gr % arrowhead 0 slj n 8543 8278 m 8490 8520 l 8650 8332 l col0 s % Polyline 2 slj gs clippath 11714 8536 m 11821 8590 l 11950 8332 l 11790 8520 l 11843 8278 l cp eoclip n 11775 4200 m 11775 4201 l 11776 4202 l 11778 4205 l 11780 4210 l 11784 4217 l 11789 4226 l 11795 4238 l 11803 4252 l 11812 4269 l 11823 4290 l 11835 4313 l 11848 4340 l 11863 4369 l 11879 4402 l 11896 4436 l 11915 4474 l 11934 4514 l 11954 4556 l 11974 4600 l 11995 4646 l 12016 4694 l 12038 4744 l 12059 4795 l 12080 4847 l 12101 4901 l 12122 4956 l 12143 5013 l 12163 5071 l 12183 5130 l 12202 5191 l 12221 5254 l 12239 5318 l 12256 5385 l 12272 5453 l 12288 5524 l 12302 5598 l 12316 5674 l 12329 5753 l 12340 5834 l 12350 5919 l 12359 6006 l 12366 6095 l 12371 6187 l 12374 6281 l 12375 6375 l 12374 6469 l 12371 6563 l 12366 6655 l 12359 6744 l 12350 6831 l 12340 6916 l 12329 6997 l 12316 7076 l 12302 7152 l 12288 7226 l 12272 7297 l 12256 7365 l 12239 7432 l 12221 7496 l 12202 7559 l 12183 7620 l 12163 7679 l 12143 7737 l 12122 7794 l 12101 7849 l 12080 7903 l 12059 7955 l 12037 8006 l 12016 8056 l 11995 8104 l 11974 8150 l 11954 8194 l 11934 8236 l 11915 8276 l 11896 8314 l 11879 8348 l 11863 8381 l 11848 8410 l 11835 8437 l 11823 8460 l 11812 8481 l 11803 8498 l 11795 8512 l 11789 8524 l 11784 8533 l 11780 8540 l 11775 8550 l gs col0 s gr gr % arrowhead 0 slj n 11843 8278 m 11790 8520 l 11950 8332 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 4796 2836 m 4831 2722 l 4556 2637 l 4768 2765 l 4520 2751 l cp eoclip n 1725 2700 m 1726 2700 l 1727 2699 l 1731 2698 l 1736 2696 l 1743 2693 l 1753 2689 l 1765 2684 l 1780 2678 l 1798 2672 l 1818 2664 l 1841 2656 l 1867 2647 l 1895 2637 l 1925 2627 l 1957 2616 l 1991 2605 l 2027 2595 l 2065 2584 l 2104 2573 l 2145 2562 l 2188 2552 l 2233 2542 l 2280 2533 l 2328 2524 l 2380 2515 l 2434 2507 l 2491 2500 l 2551 2493 l 2615 2487 l 2682 2482 l 2754 2478 l 2829 2476 l 2908 2474 l 2990 2474 l 3075 2475 l 3152 2478 l 3229 2481 l 3305 2486 l 3380 2492 l 3453 2498 l 3523 2505 l 3592 2513 l 3658 2522 l 3723 2531 l 3786 2540 l 3846 2550 l 3906 2560 l 3964 2571 l 4020 2581 l 4075 2593 l 4129 2604 l 4182 2616 l 4234 2627 l 4284 2639 l 4334 2651 l 4381 2662 l 4428 2674 l 4472 2685 l 4514 2696 l 4554 2707 l 4592 2717 l 4626 2726 l 4658 2735 l 4687 2743 l 4712 2750 l 4733 2756 l 4752 2761 l 4767 2765 l 4778 2769 l 4787 2771 l 4800 2775 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 4520 2751 m 4768 2765 l 4556 2637 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 1710 2790 m 1710 2910 l 1998 2910 l 1758 2850 l 1998 2790 l cp eoclip n 4800 2850 m 4799 2850 l 4797 2850 l 4793 2850 l 4787 2850 l 4778 2850 l 4766 2850 l 4751 2850 l 4733 2850 l 4711 2850 l 4685 2850 l 4656 2850 l 4623 2850 l 4588 2850 l 4549 2850 l 4508 2850 l 4464 2850 l 4417 2850 l 4369 2850 l 4319 2850 l 4268 2850 l 4215 2850 l 4161 2850 l 4106 2850 l 4051 2850 l 3994 2850 l 3936 2850 l 3877 2850 l 3818 2850 l 3757 2850 l 3695 2850 l 3632 2850 l 3567 2850 l 3501 2850 l 3433 2850 l 3364 2850 l 3293 2850 l 3221 2850 l 3147 2850 l 3073 2850 l 2999 2850 l 2925 2850 l 2836 2850 l 2751 2850 l 2670 2850 l 2594 2850 l 2523 2850 l 2457 2850 l 2396 2850 l 2339 2850 l 2285 2850 l 2236 2850 l 2189 2850 l 2146 2850 l 2105 2850 l 2066 2850 l 2029 2850 l 1994 2850 l 1962 2850 l 1931 2850 l 1902 2850 l 1875 2850 l 1850 2850 l 1828 2850 l 1807 2850 l 1789 2850 l 1773 2850 l 1760 2850 l 1749 2850 l 1741 2850 l 1734 2850 l 1725 2850 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 1998 2790 m 1758 2850 l 1998 2910 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 8105 2782 m 8140 2668 l 7865 2583 l 8077 2711 l 7829 2697 l cp eoclip n 5034 2646 m 5035 2646 l 5036 2645 l 5040 2644 l 5045 2642 l 5052 2639 l 5062 2635 l 5074 2630 l 5089 2624 l 5107 2618 l 5127 2610 l 5150 2602 l 5176 2593 l 5204 2583 l 5234 2573 l 5266 2562 l 5300 2551 l 5336 2541 l 5374 2530 l 5413 2519 l 5454 2508 l 5497 2498 l 5542 2488 l 5589 2479 l 5637 2470 l 5689 2461 l 5743 2453 l 5800 2446 l 5860 2439 l 5924 2433 l 5991 2428 l 6063 2424 l 6138 2422 l 6217 2420 l 6299 2420 l 6384 2421 l 6461 2424 l 6538 2427 l 6614 2432 l 6689 2438 l 6762 2444 l 6832 2451 l 6901 2459 l 6967 2468 l 7032 2477 l 7095 2486 l 7155 2496 l 7215 2506 l 7273 2517 l 7329 2527 l 7384 2539 l 7438 2550 l 7491 2562 l 7543 2573 l 7593 2585 l 7643 2597 l 7690 2608 l 7737 2620 l 7781 2631 l 7823 2642 l 7863 2653 l 7901 2663 l 7935 2672 l 7967 2681 l 7996 2689 l 8021 2696 l 8042 2702 l 8061 2707 l 8076 2711 l 8087 2715 l 8096 2717 l 8109 2721 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 7829 2697 m 8077 2711 l 7865 2583 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 11330 2782 m 11365 2668 l 11090 2583 l 11302 2711 l 11054 2697 l cp eoclip n 8259 2646 m 8260 2646 l 8261 2645 l 8265 2644 l 8270 2642 l 8277 2639 l 8287 2635 l 8299 2630 l 8314 2624 l 8332 2618 l 8352 2610 l 8375 2602 l 8401 2593 l 8429 2583 l 8459 2573 l 8491 2562 l 8525 2551 l 8561 2541 l 8599 2530 l 8638 2519 l 8679 2508 l 8722 2498 l 8767 2488 l 8814 2479 l 8862 2470 l 8914 2461 l 8968 2453 l 9025 2446 l 9085 2439 l 9149 2433 l 9216 2428 l 9288 2424 l 9363 2422 l 9442 2420 l 9524 2420 l 9609 2421 l 9686 2424 l 9763 2427 l 9839 2432 l 9914 2438 l 9987 2444 l 10057 2451 l 10126 2459 l 10192 2468 l 10257 2477 l 10320 2486 l 10380 2496 l 10440 2506 l 10498 2517 l 10554 2527 l 10609 2539 l 10663 2550 l 10716 2562 l 10768 2573 l 10818 2585 l 10868 2597 l 10915 2608 l 10962 2620 l 11006 2631 l 11048 2642 l 11088 2653 l 11126 2663 l 11160 2672 l 11192 2681 l 11221 2689 l 11246 2696 l 11267 2702 l 11286 2707 l 11301 2711 l 11312 2715 l 11321 2717 l 11334 2721 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 11054 2697 m 11302 2711 l 11090 2583 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 4430 5257 m 4465 5143 l 4190 5058 l 4402 5186 l 4154 5172 l cp eoclip n 1359 5121 m 1360 5121 l 1361 5120 l 1365 5119 l 1370 5117 l 1377 5114 l 1387 5110 l 1399 5105 l 1414 5099 l 1432 5093 l 1452 5085 l 1475 5077 l 1501 5068 l 1529 5058 l 1559 5048 l 1591 5037 l 1625 5026 l 1661 5016 l 1699 5005 l 1738 4994 l 1779 4983 l 1822 4973 l 1867 4963 l 1914 4954 l 1962 4945 l 2014 4936 l 2068 4928 l 2125 4921 l 2185 4914 l 2249 4908 l 2316 4903 l 2388 4899 l 2463 4897 l 2542 4895 l 2624 4895 l 2709 4896 l 2786 4899 l 2863 4902 l 2939 4907 l 3014 4913 l 3087 4919 l 3157 4926 l 3226 4934 l 3292 4943 l 3357 4952 l 3420 4961 l 3480 4971 l 3540 4981 l 3598 4992 l 3654 5002 l 3709 5014 l 3763 5025 l 3816 5037 l 3868 5048 l 3918 5060 l 3968 5072 l 4015 5083 l 4062 5095 l 4106 5106 l 4148 5117 l 4188 5128 l 4226 5138 l 4260 5147 l 4292 5156 l 4321 5164 l 4346 5171 l 4367 5177 l 4386 5182 l 4401 5186 l 4412 5190 l 4421 5192 l 4434 5196 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 4154 5172 m 4402 5186 l 4190 5058 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 7880 5257 m 7915 5143 l 7640 5058 l 7852 5186 l 7604 5172 l cp eoclip n 4809 5121 m 4810 5121 l 4811 5120 l 4815 5119 l 4820 5117 l 4827 5114 l 4837 5110 l 4849 5105 l 4864 5099 l 4882 5093 l 4902 5085 l 4925 5077 l 4951 5068 l 4979 5058 l 5009 5048 l 5041 5037 l 5075 5026 l 5111 5016 l 5149 5005 l 5188 4994 l 5229 4983 l 5272 4973 l 5317 4963 l 5364 4954 l 5412 4945 l 5464 4936 l 5518 4928 l 5575 4921 l 5635 4914 l 5699 4908 l 5766 4903 l 5838 4899 l 5913 4897 l 5992 4895 l 6074 4895 l 6159 4896 l 6236 4899 l 6313 4902 l 6389 4907 l 6464 4913 l 6537 4919 l 6607 4926 l 6676 4934 l 6742 4943 l 6807 4952 l 6870 4961 l 6930 4971 l 6990 4981 l 7048 4992 l 7104 5002 l 7159 5014 l 7213 5025 l 7266 5037 l 7318 5048 l 7368 5060 l 7418 5072 l 7465 5083 l 7512 5095 l 7556 5106 l 7598 5117 l 7638 5128 l 7676 5138 l 7710 5147 l 7742 5156 l 7771 5164 l 7796 5171 l 7817 5177 l 7836 5182 l 7851 5186 l 7862 5190 l 7871 5192 l 7884 5196 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 7604 5172 m 7852 5186 l 7640 5058 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 11255 5257 m 11290 5143 l 11015 5058 l 11227 5186 l 10979 5172 l cp eoclip n 8184 5121 m 8185 5121 l 8186 5120 l 8190 5119 l 8195 5117 l 8202 5114 l 8212 5110 l 8224 5105 l 8239 5099 l 8257 5093 l 8277 5085 l 8300 5077 l 8326 5068 l 8354 5058 l 8384 5048 l 8416 5037 l 8450 5026 l 8486 5016 l 8524 5005 l 8563 4994 l 8604 4983 l 8647 4973 l 8692 4963 l 8739 4954 l 8787 4945 l 8839 4936 l 8893 4928 l 8950 4921 l 9010 4914 l 9074 4908 l 9141 4903 l 9213 4899 l 9288 4897 l 9367 4895 l 9449 4895 l 9534 4896 l 9611 4899 l 9688 4902 l 9764 4907 l 9839 4913 l 9912 4919 l 9982 4926 l 10051 4934 l 10117 4943 l 10182 4952 l 10245 4961 l 10305 4971 l 10365 4981 l 10423 4992 l 10479 5002 l 10534 5014 l 10588 5025 l 10641 5037 l 10693 5048 l 10743 5060 l 10793 5072 l 10840 5083 l 10887 5095 l 10931 5106 l 10973 5117 l 11013 5128 l 11051 5138 l 11085 5147 l 11117 5156 l 11146 5164 l 11171 5171 l 11192 5177 l 11211 5182 l 11226 5186 l 11237 5190 l 11246 5192 l 11259 5196 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 10979 5172 m 11227 5186 l 11015 5058 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 1410 5190 m 1410 5310 l 1698 5310 l 1458 5250 l 1698 5190 l cp eoclip n 4500 5250 m 4499 5250 l 4497 5250 l 4493 5250 l 4487 5250 l 4478 5250 l 4466 5250 l 4451 5250 l 4433 5250 l 4411 5250 l 4385 5250 l 4356 5250 l 4323 5250 l 4288 5250 l 4249 5250 l 4208 5250 l 4164 5250 l 4117 5250 l 4069 5250 l 4019 5250 l 3968 5250 l 3915 5250 l 3861 5250 l 3806 5250 l 3751 5250 l 3694 5250 l 3636 5250 l 3577 5250 l 3518 5250 l 3457 5250 l 3395 5250 l 3332 5250 l 3267 5250 l 3201 5250 l 3133 5250 l 3064 5250 l 2993 5250 l 2921 5250 l 2847 5250 l 2773 5250 l 2699 5250 l 2625 5250 l 2536 5250 l 2451 5250 l 2370 5250 l 2294 5250 l 2223 5250 l 2157 5250 l 2096 5250 l 2039 5250 l 1985 5250 l 1936 5250 l 1889 5250 l 1846 5250 l 1805 5250 l 1766 5250 l 1729 5250 l 1694 5250 l 1662 5250 l 1631 5250 l 1602 5250 l 1575 5250 l 1550 5250 l 1528 5250 l 1507 5250 l 1489 5250 l 1473 5250 l 1460 5250 l 1449 5250 l 1441 5250 l 1434 5250 l 1425 5250 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 1698 5190 m 1458 5250 l 1698 5310 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 4785 5190 m 4785 5310 l 5073 5310 l 4833 5250 l 5073 5190 l cp eoclip n 7875 5250 m 7874 5250 l 7872 5250 l 7868 5250 l 7862 5250 l 7853 5250 l 7841 5250 l 7826 5250 l 7808 5250 l 7786 5250 l 7760 5250 l 7731 5250 l 7698 5250 l 7663 5250 l 7624 5250 l 7583 5250 l 7539 5250 l 7492 5250 l 7444 5250 l 7394 5250 l 7343 5250 l 7290 5250 l 7236 5250 l 7181 5250 l 7126 5250 l 7069 5250 l 7011 5250 l 6952 5250 l 6893 5250 l 6832 5250 l 6770 5250 l 6707 5250 l 6642 5250 l 6576 5250 l 6508 5250 l 6439 5250 l 6368 5250 l 6296 5250 l 6222 5250 l 6148 5250 l 6074 5250 l 6000 5250 l 5911 5250 l 5826 5250 l 5745 5250 l 5669 5250 l 5598 5250 l 5532 5250 l 5471 5250 l 5414 5250 l 5360 5250 l 5311 5250 l 5264 5250 l 5221 5250 l 5180 5250 l 5141 5250 l 5104 5250 l 5069 5250 l 5037 5250 l 5006 5250 l 4977 5250 l 4950 5250 l 4925 5250 l 4903 5250 l 4882 5250 l 4864 5250 l 4848 5250 l 4835 5250 l 4824 5250 l 4816 5250 l 4809 5250 l 4800 5250 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 5073 5190 m 4833 5250 l 5073 5310 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 8160 5190 m 8160 5310 l 8448 5310 l 8208 5250 l 8448 5190 l cp eoclip n 11250 5250 m 11249 5250 l 11247 5250 l 11243 5250 l 11237 5250 l 11228 5250 l 11216 5250 l 11201 5250 l 11183 5250 l 11161 5250 l 11135 5250 l 11106 5250 l 11073 5250 l 11038 5250 l 10999 5250 l 10958 5250 l 10914 5250 l 10867 5250 l 10819 5250 l 10769 5250 l 10718 5250 l 10665 5250 l 10611 5250 l 10556 5250 l 10501 5250 l 10444 5250 l 10386 5250 l 10327 5250 l 10268 5250 l 10207 5250 l 10145 5250 l 10082 5250 l 10017 5250 l 9951 5250 l 9883 5250 l 9814 5250 l 9743 5250 l 9671 5250 l 9597 5250 l 9523 5250 l 9449 5250 l 9375 5250 l 9286 5250 l 9201 5250 l 9120 5250 l 9044 5250 l 8973 5250 l 8907 5250 l 8846 5250 l 8789 5250 l 8735 5250 l 8686 5250 l 8639 5250 l 8596 5250 l 8555 5250 l 8516 5250 l 8479 5250 l 8444 5250 l 8412 5250 l 8381 5250 l 8352 5250 l 8325 5250 l 8300 5250 l 8278 5250 l 8257 5250 l 8239 5250 l 8223 5250 l 8210 5250 l 8199 5250 l 8191 5250 l 8184 5250 l 8175 5250 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 8448 5190 m 8208 5250 l 8448 5310 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 8310 2790 m 8310 2910 l 8598 2910 l 8358 2850 l 8598 2790 l cp eoclip n 11400 2850 m 11399 2850 l 11397 2850 l 11393 2850 l 11387 2850 l 11378 2850 l 11366 2850 l 11351 2850 l 11333 2850 l 11311 2850 l 11285 2850 l 11256 2850 l 11223 2850 l 11188 2850 l 11149 2850 l 11108 2850 l 11064 2850 l 11017 2850 l 10969 2850 l 10919 2850 l 10868 2850 l 10815 2850 l 10761 2850 l 10706 2850 l 10651 2850 l 10594 2850 l 10536 2850 l 10477 2850 l 10418 2850 l 10357 2850 l 10295 2850 l 10232 2850 l 10167 2850 l 10101 2850 l 10033 2850 l 9964 2850 l 9893 2850 l 9821 2850 l 9747 2850 l 9673 2850 l 9599 2850 l 9525 2850 l 9436 2850 l 9351 2850 l 9270 2850 l 9194 2850 l 9123 2850 l 9057 2850 l 8996 2850 l 8939 2850 l 8885 2850 l 8836 2850 l 8789 2850 l 8746 2850 l 8705 2850 l 8666 2850 l 8629 2850 l 8594 2850 l 8562 2850 l 8531 2850 l 8502 2850 l 8475 2850 l 8450 2850 l 8428 2850 l 8407 2850 l 8389 2850 l 8373 2850 l 8360 2850 l 8349 2850 l 8341 2850 l 8334 2850 l 8325 2850 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 8598 2790 m 8358 2850 l 8598 2910 l col0 s % Polyline 2 slj [90] 0 sd gs clippath 5085 2790 m 5085 2910 l 5373 2910 l 5133 2850 l 5373 2790 l cp eoclip n 8175 2850 m 8174 2850 l 8172 2850 l 8168 2850 l 8162 2850 l 8153 2850 l 8141 2850 l 8126 2850 l 8108 2850 l 8086 2850 l 8060 2850 l 8031 2850 l 7998 2850 l 7963 2850 l 7924 2850 l 7883 2850 l 7839 2850 l 7792 2850 l 7744 2850 l 7694 2850 l 7643 2850 l 7590 2850 l 7536 2850 l 7481 2850 l 7426 2850 l 7369 2850 l 7311 2850 l 7252 2850 l 7193 2850 l 7132 2850 l 7070 2850 l 7007 2850 l 6942 2850 l 6876 2850 l 6808 2850 l 6739 2850 l 6668 2850 l 6596 2850 l 6522 2850 l 6448 2850 l 6374 2850 l 6300 2850 l 6211 2850 l 6126 2850 l 6045 2850 l 5969 2850 l 5898 2850 l 5832 2850 l 5771 2850 l 5714 2850 l 5660 2850 l 5611 2850 l 5564 2850 l 5521 2850 l 5480 2850 l 5441 2850 l 5404 2850 l 5369 2850 l 5337 2850 l 5306 2850 l 5277 2850 l 5250 2850 l 5225 2850 l 5203 2850 l 5182 2850 l 5164 2850 l 5148 2850 l 5135 2850 l 5124 2850 l 5116 2850 l 5109 2850 l 5100 2850 l gs col0 s gr gr [] 0 sd % arrowhead 0 slj n 5373 2790 m 5133 2850 l 5373 2910 l col0 s % Polyline 2 slj gs clippath 1255 5298 m 1138 5322 l 1194 5604 l 1206 5357 l 1311 5580 l cp eoclip n 1350 6075 m 1200 5325 l gs col0 s gr gr % arrowhead 0 slj n 1311 5580 m 1206 5357 l 1194 5604 l col0 s % Polyline 2 slj gs clippath 1336 4266 m 1216 4254 l 1188 4540 l 1272 4308 l 1307 4552 l cp eoclip n 1200 5025 m 1275 4275 l gs col0 s gr gr % arrowhead 0 slj n 1307 4552 m 1272 4308 l 1188 4540 l col0 s % Polyline 2 slj gs clippath 1185 4288 m 1078 4234 l 949 4492 l 1110 4305 l 1056 4546 l cp eoclip n 1125 6075 m 1125 6074 l 1123 6072 l 1121 6068 l 1118 6061 l 1114 6052 l 1108 6040 l 1101 6025 l 1093 6007 l 1084 5987 l 1074 5964 l 1063 5938 l 1051 5911 l 1039 5881 l 1027 5850 l 1014 5817 l 1002 5783 l 990 5748 l 978 5712 l 967 5673 l 957 5634 l 946 5592 l 937 5549 l 928 5503 l 920 5454 l 914 5403 l 908 5350 l 904 5293 l 901 5235 l 900 5175 l 901 5115 l 904 5057 l 908 5000 l 914 4947 l 920 4896 l 928 4847 l 937 4801 l 946 4758 l 957 4716 l 967 4677 l 978 4638 l 990 4602 l 1002 4567 l 1014 4533 l 1027 4500 l 1039 4469 l 1051 4439 l 1063 4412 l 1074 4386 l 1084 4363 l 1093 4343 l 1101 4325 l 1108 4310 l 1114 4298 l 1118 4289 l 1125 4275 l gs col0 s gr gr % arrowhead 0 slj n 1056 4546 m 1110 4305 l 949 4492 l col0 s % Polyline 2 slj gs clippath 4705 5298 m 4588 5322 l 4644 5604 l 4656 5357 l 4761 5580 l cp eoclip n 4800 6075 m 4650 5325 l gs col0 s gr gr % arrowhead 0 slj n 4761 5580 m 4656 5357 l 4644 5604 l col0 s % Polyline 2 slj gs clippath 4786 4266 m 4666 4254 l 4638 4540 l 4722 4308 l 4757 4552 l cp eoclip n 4650 5025 m 4725 4275 l gs col0 s gr gr % arrowhead 0 slj n 4757 4552 m 4722 4308 l 4638 4540 l col0 s % Polyline 2 slj gs clippath 4635 4288 m 4528 4234 l 4399 4492 l 4560 4305 l 4506 4546 l cp eoclip n 4575 6075 m 4575 6074 l 4573 6072 l 4571 6068 l 4568 6061 l 4564 6052 l 4558 6040 l 4551 6025 l 4543 6007 l 4534 5987 l 4524 5964 l 4513 5938 l 4501 5911 l 4489 5881 l 4477 5850 l 4464 5817 l 4452 5783 l 4440 5748 l 4428 5712 l 4417 5673 l 4407 5634 l 4396 5592 l 4387 5549 l 4378 5503 l 4370 5454 l 4364 5403 l 4358 5350 l 4354 5293 l 4351 5235 l 4350 5175 l 4351 5115 l 4354 5057 l 4358 5000 l 4364 4947 l 4370 4896 l 4378 4847 l 4387 4801 l 4396 4758 l 4407 4716 l 4417 4677 l 4428 4638 l 4440 4602 l 4452 4567 l 4464 4533 l 4477 4500 l 4489 4469 l 4501 4439 l 4513 4412 l 4524 4386 l 4534 4363 l 4543 4343 l 4551 4325 l 4558 4310 l 4564 4298 l 4568 4289 l 4575 4275 l gs col0 s gr gr % arrowhead 0 slj n 4506 4546 m 4560 4305 l 4399 4492 l col0 s % Polyline 2 slj gs clippath 8080 5298 m 7963 5322 l 8019 5604 l 8031 5357 l 8136 5580 l cp eoclip n 8175 6075 m 8025 5325 l gs col0 s gr gr % arrowhead 0 slj n 8136 5580 m 8031 5357 l 8019 5604 l col0 s % Polyline 2 slj gs clippath 8161 4266 m 8041 4254 l 8013 4540 l 8097 4308 l 8132 4552 l cp eoclip n 8025 5025 m 8100 4275 l gs col0 s gr gr % arrowhead 0 slj n 8132 4552 m 8097 4308 l 8013 4540 l col0 s % Polyline 2 slj gs clippath 8010 4288 m 7903 4234 l 7774 4492 l 7935 4305 l 7881 4546 l cp eoclip n 7950 6075 m 7950 6074 l 7948 6072 l 7946 6068 l 7943 6061 l 7939 6052 l 7933 6040 l 7926 6025 l 7918 6007 l 7909 5987 l 7899 5964 l 7888 5938 l 7876 5911 l 7864 5881 l 7852 5850 l 7839 5817 l 7827 5783 l 7815 5748 l 7803 5712 l 7792 5673 l 7782 5634 l 7771 5592 l 7762 5549 l 7753 5503 l 7745 5454 l 7739 5403 l 7733 5350 l 7729 5293 l 7726 5235 l 7725 5175 l 7726 5115 l 7729 5057 l 7733 5000 l 7739 4947 l 7745 4896 l 7753 4847 l 7762 4801 l 7771 4758 l 7782 4716 l 7792 4677 l 7803 4638 l 7815 4602 l 7827 4567 l 7839 4533 l 7852 4500 l 7864 4469 l 7876 4439 l 7888 4412 l 7899 4386 l 7909 4363 l 7918 4343 l 7926 4325 l 7933 4310 l 7939 4298 l 7943 4289 l 7950 4275 l gs col0 s gr gr % arrowhead 0 slj n 7881 4546 m 7935 4305 l 7774 4492 l col0 s % Polyline 2 slj gs clippath 11455 5223 m 11338 5247 l 11394 5529 l 11406 5282 l 11511 5505 l cp eoclip n 11550 6000 m 11400 5250 l gs col0 s gr gr % arrowhead 0 slj n 11511 5505 m 11406 5282 l 11394 5529 l col0 s % Polyline 2 slj gs clippath 11536 4191 m 11416 4179 l 11388 4465 l 11472 4233 l 11507 4477 l cp eoclip n 11400 4950 m 11475 4200 l gs col0 s gr gr % arrowhead 0 slj n 11507 4477 m 11472 4233 l 11388 4465 l col0 s % Polyline 2 slj gs clippath 11385 4213 m 11278 4159 l 11149 4417 l 11310 4230 l 11256 4471 l cp eoclip n 11325 6000 m 11325 5999 l 11323 5997 l 11321 5993 l 11318 5986 l 11314 5977 l 11308 5965 l 11301 5950 l 11293 5932 l 11284 5912 l 11274 5889 l 11263 5863 l 11251 5836 l 11239 5806 l 11227 5775 l 11214 5742 l 11202 5708 l 11190 5673 l 11178 5637 l 11167 5598 l 11157 5559 l 11146 5517 l 11137 5474 l 11128 5428 l 11120 5379 l 11114 5328 l 11108 5275 l 11104 5218 l 11101 5160 l 11100 5100 l 11101 5040 l 11104 4982 l 11108 4925 l 11114 4872 l 11120 4821 l 11128 4772 l 11137 4726 l 11146 4683 l 11157 4641 l 11167 4602 l 11178 4563 l 11190 4527 l 11202 4492 l 11214 4458 l 11227 4425 l 11239 4394 l 11251 4364 l 11263 4337 l 11274 4311 l 11284 4288 l 11293 4268 l 11301 4250 l 11308 4235 l 11314 4223 l 11318 4214 l 11325 4200 l gs col0 s gr gr % arrowhead 0 slj n 11256 4471 m 11310 4230 l 11149 4417 l col0 s /Times-Roman ff 315.00 scf sf 7500 8925 m gs 1 -1 sc (2S,1L,S) col0 sh gr /Times-Roman ff 315.00 scf sf 10800 8925 m gs 1 -1 sc (3S,1L,S) col0 sh gr /Times-Roman ff 315.00 scf sf 900 4125 m gs 1 -1 sc (0S,0L) col0 sh gr /Times-Roman ff 315.00 scf sf 4200 4125 m gs 1 -1 sc (1S,0L) col0 sh gr /Times-Roman ff 315.00 scf sf 4200 1725 m gs 1 -1 sc (1S,lL) col0 sh gr /Times-Roman ff 315.00 scf sf 7500 4125 m gs 1 -1 sc (2S,0L,S) col0 sh gr /Times-Roman ff 315.00 scf sf 10875 4125 m gs 1 -1 sc (3S,0L,S) col0 sh gr /Times-Roman ff 285.00 scf sf 10725 6450 m gs 1 -1 sc (3S,\(N+1\)L) col0 sh gr /Times-Roman ff 285.00 scf sf 7425 6450 m gs 1 -1 sc (2S,\(N+1\)L) col0 sh gr /Times-Roman ff 285.00 scf sf 4125 6450 m gs 1 -1 sc (1S,\(N+1\)L) col0 sh gr /Times-Roman ff 285.00 scf sf 675 6450 m gs 1 -1 sc (0S,\(N+1\)L) col0 sh gr /Times-Roman ff 315.00 scf sf 7500 1725 m gs 1 -1 sc (2S,1L,L) col0 sh gr /Times-Roman ff 315.00 scf sf 10800 1725 m gs 1 -1 sc (3S,1L,L) col0 sh gr F2psBegin10setmiterlimit0.060000.06000scF2psEnd rs %%EndDocument endTexFig 1836 4293 a Ff(\(b\))120 4489 y FC(Figure)23 b(6:)28 b Fy(\(a\))23 b(Mark)o(o)o(v)h(c)o(hain)f(corr)m(esponding)j(to)d Fx(CS-central-que)o(ue)o Fy(.)f(This)g(is)g(identical)j(to)e(the)f(c)o (hain)120 4602 y(in)31 b(F)l(igur)m(e)g(5\(a\),)j(e)n(xcept)f(that)e (the)h(tr)o(ansition)h Fu(B)1723 4616 y Ft(N)7 b FE(+1)1911 4602 y Fy(has)32 b(been)g(r)m(eplaced)h(by)e Fu(U)40 b Fy(wher)m(e)31 b Fu(U)41 b Fy(is)31 b(independent)120 4715 y(of)d Fu(E)40 b Fr(\030)34 b Fu(E)5 b(xp)p Fs(\(2)p Fu(\026)735 4729 y Ft(S)786 4715 y Fs(\))p Fy(.)43 b(\(b\))29 b(Same)g(Mark)o(o)o(v)g(c)o(hain)g(as)g(in)f(\(a\),)i(b)n(ut)f(bold)g (tr)o(ansitions)i(have)f(been)f(r)m(eplaced)h(by)120 4828 y(two-phase)25 b(Coxians)g(matc)o(hing)g(the)f(\002r)o(st)g(thr)m (ee)g(moments.)1875 5349 y FC(13)p eop %%Page: 14 16 14 15 bop 120 91 a Fo(4.2)99 b(Deri)o(ving)25 b(the)h(necessary)f(b)n (usy)g(periods)h(f)n(or)e(the)i(chain)120 266 y FC(In)j(order)i(to)e (specify)i(the)e(Mark)o(o)o(v)i(chain,)g(we)e(need)h(to)f(compute)i (the)e(\002rst)g(three)h(moments)g(of)g Fu(B)3369 280 y Ft(L)3449 266 y FC(and)g(the)120 379 y(\002rst)21 b(three)h(moments)g (of)f Fu(B)1003 393 y Ft(E)t FE(+)p Ft(L)1165 379 y FC(.)27 b(These)22 b(will)f(in)g(turn)h(gi)n(v)o(e)f(us)g(the)h(\002rst)e (three)j(moments)e(of)g Fu(U)10 b FC(.)28 b(In)21 b(this)g(section)120 491 y(we)i(complete)i(these)f(deri)n(v)n(ations:)261 604 y Fu(B)330 618 y Ft(L)406 604 y FC(simply)h(represents)j(a)c(b)n (usy)h(period)h(made)f(up)g(of)f(only)i(long)f(jobs.)33 b(Its)24 b(moments)i(were)e(computed)i(in)120 717 y(Section)e(3)g(and)g (are)f(repeated)j(belo)n(w)e(for)f(reference:)1153 1059 y Fu(E)5 b Fs([)p Fu(B)1319 1073 y Ft(L)1372 1059 y Fs(])83 b(=)1646 998 y Fu(E)5 b Fs([)p Fu(X)1818 1012 y Ft(L)1871 998 y Fs(])p 1644 1038 256 4 v 1644 1122 a(1)20 b Fr(\000)g Fu(\032)1847 1136 y Ft(L)1909 1059 y Fu(;)1153 1310 y(E)5 b Fs([)p Fu(B)1324 1272 y FE(2)1319 1332 y Ft(L)1372 1310 y Fs(])83 b(=)1702 1248 y Fu(E)5 b Fs([)p Fu(X)1881 1216 y FE(2)1874 1274 y Ft(L)1927 1248 y Fs(])p 1644 1289 366 4 v 1644 1372 a(\(1)21 b Fr(\000)f Fu(\032)1883 1386 y Ft(L)1935 1372 y Fs(\))1970 1346 y FE(3)2020 1310 y Fu(;)1153 1566 y(E)5 b Fs([)p Fu(B)1324 1528 y FE(3)1319 1588 y Ft(L)1372 1566 y Fs(])83 b(=)1702 1504 y Fu(E)5 b Fs([)p Fu(X)1881 1471 y FE(3)1874 1530 y Ft(L)1927 1504 y Fs(])p 1644 1545 V 1644 1628 a(\(1)21 b Fr(\000)f Fu(\032)1883 1642 y Ft(L)1935 1628 y Fs(\))1970 1602 y FE(4)2040 1566 y Fs(+)2141 1504 y(3)p Fu(\025)2239 1518 y Ft(L)2291 1504 y Fs(\()p Fu(E)5 b Fs([)p Fu(X)2505 1471 y FE(2)2498 1530 y Ft(L)2552 1504 y Fs(]\))2612 1471 y FE(2)p 2141 1545 512 4 v 2213 1628 a Fs(\(1)21 b Fr(\000)f Fu(\032)2452 1642 y Ft(L)2504 1628 y Fs(\))2539 1602 y FE(5)2662 1566 y Fu(:)261 1908 y FC(Ne)o(xt)k(we)f(deri)n(v)o(e) i(the)f(moments)h(of)f Fu(B)1495 1922 y Ft(E)1578 1908 y FC(where)g Fu(B)1892 1922 y Ft(E)1975 1908 y FC(represents)j(the)d (length)i(of)e(a)g(b)n(usy)h(period)g(started)h(by)120 2021 y(a)d(job)h(of)f(size)i Fu(E)30 b Fr(\030)25 b Fu(E)5 b(xp)p Fs(\(2)p Fu(\026)1083 2035 y Ft(S)1135 2021 y Fs(\))p FC(,)22 b(and)i(consisting)j(of)c(only)i(long)f(jobs.)1246 2311 y Fq(g)1242 2338 y Fu(B)1311 2352 y Ft(E)1370 2338 y Fs(\()p Fu(s)p Fs(\))84 b(=)1741 2311 y Fq(e)1720 2338 y Fu(E)6 b Fs(\()p Fu(s)20 b Fs(+)g Fu(\025)2035 2352 y Ft(L)2107 2338 y Fr(\000)g Fu(\025)2251 2352 y Ft(L)2304 2311 y Fq(g)2303 2338 y Fu(B)2372 2352 y Ft(L)2424 2338 y Fs(\()p Fu(s)p Fs(\)\))p Fu(:)261 2542 y FC(Therefore)316 2859 y Fu(E)5 b Fs([)p Fu(B)482 2873 y Ft(E)542 2859 y Fs(])83 b(=)g Fu(E)5 b Fs([)p Fu(E)g Fs(])22 b(+)d Fu(\025)1163 2873 y Ft(L)1216 2859 y Fu(E)5 b Fs([)p Fu(B)1382 2873 y Ft(L)1434 2859 y Fs(])p Fu(E)g Fs([)p Fu(E)g Fs(])p Fu(;)316 2997 y(E)g Fs([)p Fu(B)487 2959 y FE(2)482 3019 y Ft(E)542 2997 y Fs(])83 b(=)g Fu(E)5 b Fs([)p Fu(E)973 2959 y FE(2)1014 2997 y Fs(])20 b(+)g Fu(\025)1203 3011 y Ft(L)1255 2997 y Fu(E)5 b Fs([)p Fu(E)g Fs(])p Fu(E)g Fs([)p Fu(B)1620 2959 y FE(2)1615 3019 y Ft(L)1669 2997 y Fs(])20 b(+)g(\()p Fu(\025)1893 3011 y Ft(L)1946 2997 y Fu(E)5 b Fs([)p Fu(B)2112 3011 y Ft(L)2165 2997 y Fs(]\))2225 2959 y FE(2)2265 2997 y Fu(E)g Fs([)p Fu(E)2434 2959 y FE(2)2474 2997 y Fs(])20 b(+)g(2)p Fu(\025)2708 3011 y Ft(L)2761 2997 y Fu(E)5 b Fs([)p Fu(B)2927 3011 y Ft(L)2980 2997 y Fs(])p Fu(E)g Fs([)p Fu(E)3174 2959 y FE(2)3214 2997 y Fs(])p Fu(;)316 3135 y(E)g Fs([)p Fu(B)487 3097 y FE(3)482 3157 y Ft(E)542 3135 y Fs(])83 b(=)g Fu(E)5 b Fs([)p Fu(E)973 3097 y FE(3)1014 3135 y Fs(])20 b(+)g Fu(\025)1203 3149 y Ft(L)1255 3135 y Fu(E)5 b Fs([)p Fu(E)g Fs(])p Fu(E)g Fs([)p Fu(B)1620 3097 y FE(3)1615 3157 y Ft(L)1669 3135 y Fs(])20 b(+)g(3)p Fu(\025)1903 3097 y FE(2)1903 3157 y Ft(L)1956 3135 y Fu(E)5 b Fs([)p Fu(E)2125 3097 y FE(2)2165 3135 y Fs(])p Fu(E)g Fs([)p Fu(B)2361 3097 y FE(2)2356 3157 y Ft(L)2409 3135 y Fs(])p Fu(E)g Fs([)p Fu(B)2600 3149 y Ft(L)2653 3135 y Fs(])21 b(+)f(\()p Fu(\025)2878 3149 y Ft(L)2930 3135 y Fu(E)5 b Fs([)p Fu(B)3096 3149 y Ft(L)3149 3135 y Fs(]\))3209 3097 y FE(3)3249 3135 y Fu(E)g Fs([)p Fu(E)3418 3097 y FE(3)3458 3135 y Fs(])p Fu(;)804 3273 y Fs(+3)p Fu(\025)973 3287 y Ft(L)1026 3273 y Fu(E)g Fs([)p Fu(E)1195 3235 y FE(2)1235 3273 y Fs(])p Fu(E)g Fs([)p Fu(B)1431 3235 y FE(2)1426 3295 y Ft(L)1479 3273 y Fs(])20 b(+)g(3\()p Fu(\025)1748 3287 y Ft(L)1801 3273 y Fu(E)5 b Fs([)p Fu(B)1967 3287 y Ft(L)2020 3273 y Fs(]\))2080 3235 y FE(2)2120 3273 y Fu(E)g Fs([)p Fu(E)2289 3235 y FE(3)2329 3273 y Fs(])21 b(+)f(3)p Fu(\025)2564 3287 y Ft(L)2616 3273 y Fu(E)5 b Fs([)p Fu(B)2782 3287 y Ft(L)2835 3273 y Fs(])p Fu(E)g Fs([)p Fu(E)3029 3235 y FE(3)3070 3273 y Fs(])p Fu(:)261 3615 y FC(Finally)-6 b(,)24 b(we)f(compute)i(the)f (moments)g(of)f Fu(B)1680 3629 y Ft(E)t FE(+)p Ft(L)1843 3615 y FC(:)835 3932 y Fu(B)904 3946 y Ft(E)t FE(+)p Ft(L)1149 3932 y Fs(=)83 b Fu(B)1372 3946 y Ft(E)1452 3932 y Fs(+)19 b Fu(B)1611 3946 y Ft(L)1664 3932 y Fu(;)712 4070 y(E)5 b Fs([)p Fu(B)878 4084 y Ft(E)t FE(+)p Ft(L)1041 4070 y Fs(])83 b(=)g Fu(E)5 b Fs([)p Fu(B)1469 4084 y Ft(E)1529 4070 y Fs(])20 b(+)g Fu(E)5 b Fs([)p Fu(B)1831 4084 y Ft(L)1884 4070 y Fs(])p Fu(;)602 4207 y(E)g Fs([\()p Fu(B)803 4221 y Ft(E)t FE(+)p Ft(L)966 4207 y Fs(\))1001 4170 y FE(2)1041 4207 y Fs(])83 b(=)g Fu(E)5 b Fs([)p Fu(B)1474 4170 y FE(2)1469 4230 y Ft(E)1529 4207 y Fs(])20 b(+)g(2)p Fu(E)5 b Fs([)p Fu(B)1876 4221 y Ft(E)1937 4207 y Fs(])p Fu(E)g Fs([)p Fu(B)2128 4221 y Ft(L)2181 4207 y Fs(])20 b(+)g Fu(E)5 b Fs([)p Fu(B)2488 4170 y FE(2)2483 4230 y Ft(L)2536 4207 y Fs(])p Fu(;)602 4345 y(E)g Fs([\()p Fu(B)803 4359 y Ft(E)t FE(+)p Ft(L)966 4345 y Fs(\))1001 4308 y FE(3)1041 4345 y Fs(])83 b(=)g Fu(E)5 b Fs([)p Fu(B)1474 4308 y FE(3)1469 4368 y Ft(E)1529 4345 y Fs(])20 b(+)g(3)p Fu(E)5 b Fs([)p Fu(B)1881 4308 y FE(2)1876 4368 y Ft(E)1937 4345 y Fs(])p Fu(E)g Fs([)p Fu(B)2128 4359 y Ft(L)2181 4345 y Fs(])20 b(+)g(3)p Fu(E)5 b Fs([)p Fu(B)2528 4359 y Ft(E)2589 4345 y Fs(])p Fu(E)g Fs([)p Fu(B)2785 4308 y FE(2)2780 4368 y Ft(L)2833 4345 y Fs(])20 b(+)g Fu(E)5 b Fs([)p Fu(B)3140 4308 y FE(3)3135 4368 y Ft(L)3188 4345 y Fs(])p Fu(:)120 4594 y Fo(4.3)99 b(Deri)o(ving)25 b(the)h(perf)n(ormance)g(of)f(short)g(and)g(long)g (jobs)120 4769 y FB(Response)e(time)h(f)n(or)f(short)h(jobs)120 4943 y FC(The)f(e)o(xpected)i(response)h(time)d(for)g(short)h(jobs)g (is)g(easy)g(to)f(compute:)30 b(Simply)23 b(deri)n(v)o(e)h(the)g (limiting)g(probabili-)120 5056 y(ties)h(for)g(the)g(chain)h(sho)n(wn)f (in)g(Figure)g(6.)32 b(The)24 b(chain)i(is)e(analyzable)k(via)d (Matrix-Analytic)j(methods,)e(since)f(it)1875 5349 y(14)p eop %%Page: 15 17 15 16 bop 120 91 a FC(is)26 b(in\002nite)g(in)g(only)h(one)f(dimension) i(and)e(repeats)i(in)e(structure)i(starting)g(at)d(the)h(third)h (column.)37 b(Its)26 b(generator)120 204 y(matrix)e(has)g(the)g(form:) 1264 543 y Fu(Q)h Fs(=)1457 299 y Fq(0)1457 445 y(B)1457 495 y(B)1457 545 y(B)1457 598 y(@)1571 373 y Fu(B)5 b Fs(00)83 b Fu(B)5 b Fs(01)128 b Fr(\000)148 b(\000)1571 486 y Fu(B)5 b Fs(10)83 b Fu(B)5 b Fs(11)84 b Fu(A)p Fs(12)105 b Fr(\000)1618 599 y(\000)132 b Fu(A)p Fs(21)110 b Fu(A)p Fs(1)c Fu(A)p Fs(0)1618 712 y Fr(\000)176 b(\000)153 b Fu(A)p Fs(2)106 b Fu(A)p Fs(1)2463 299 y Fq(1)2463 445 y(C)2463 495 y(C)2463 545 y(C)2463 598 y(A)2551 543 y Fu(:)261 897 y FC(From)34 b(the)g(limiting)i(probabilities)h(we)d (deduce)i(the)e(e)o(xpected)i(number)g(of)e(short)h(jobs)g(in)f(the)h (system.)120 1010 y(Finally)24 b(we)f(di)n(vide)i(by)e Fu(\025)943 1024 y Ft(s)1003 1010 y FC(to)g(get)h(the)g(mean)g (response)i(time)d(for)h(short)g(jobs.)120 1254 y FB(Response)f(time)h (f)n(or)f(long)h(jobs)120 1428 y FC(F)o(or)g(long)i(jobs,)g(computing)h (the)f(e)o(xpected)h(response)g(time)e(is)g(a)g(little)h(more)f(in)l(v) n(olv)o(ed.)36 b(From)24 b(the)h(long)h(jobs')120 1541 y(perspecti)n(v)o(e,)i(the)o(y)d(see)h(an)f(M/G/1)g(queue)h(where,)g (at)f(times,)g(the)g(\002rst)g(job)h(in)f(a)f(b)n(usy)j(period)f(must)f (w)o(ait)g(until)120 1654 y(a)k(short)i(job)f(\002nishes)h(\(as)e (short)i(jobs)f(occup)o(y)i(both)e(serv)o(ers\).)49 b(More)30 b(succinctly)-6 b(,)34 b(assuming)d(that)f(short)h(job)120 1767 y(service)e(requirements)i(are)c(e)o(xponentially-dist)q(rib)o(ut) q(ed)33 b(with)28 b(rate)g Fu(\026)2388 1781 y Ft(S)2438 1767 y FC(,)g(the)g(response)h(time)f(for)g(long)g(jobs)g(is)120 1880 y(the)c(response)i(time)d(under)i(an)e(M/G/1)g(queue)i(with)f (setup)g(time)g Fu(S)j FC(where)603 2241 y Fu(S)k Fs(=)786 1994 y Fq(8)786 2068 y(>)786 2093 y(>)786 2118 y(>)786 2143 y(<)786 2293 y(>)786 2318 y(>)786 2342 y(>)786 2367 y(:)901 2098 y Fs(0)737 b FC(with)23 b(probability)k Fu(a)2337 2112 y FE(1)2402 2098 y Fs(=)2591 2050 y FE(Pr)p Fp(f)p FC(Re)o(gion)d(1)p Fp(g)p 2508 2076 643 4 v 2508 2142 a FE(Pr)o Fp(f)p FC(Re)o(gion)g(1)g(or)f(2)q Fp(g)3160 2098 y Fu(;)901 2384 y(E)31 b Fs(=)25 b Fu(E)5 b(xp)p Fs(\(2)p Fu(\026)1400 2398 y Ft(S)1451 2384 y Fs(\))197 b FC(with)23 b(probability)k Fu(a)2337 2398 y FE(2)2402 2384 y Fs(=)2591 2336 y FE(Pr)p Fp(f)p FC(Re)o(gion)d(2)p Fp(g)p 2508 2363 V 2508 2428 a FE(Pr)o Fp(f)p FC(Re)o(gion)g(1)g(or)f (2)q Fp(g)3160 2384 y Fu(:)261 2599 y FC(Observ)o(e)h(that)g Fu(S)k FC(is)23 b(de\002ned)h(entirely)h(by)e(what)h(the)f(\002rst)g (job)h(to)f(start)h(a)f(b)n(usy)h(period)h(sees.)k(The)23 b(e)o(xpected)120 2712 y(w)o(aiting)i(time)e(for)h(an)f(M/G/1)g(queue)i (with)f(only)g(long)g(jobs)h(and)f(a)f(setup)h(time)g(of)f Fu(S)28 b FC(is)23 b(kno)n(wn)h([26)q(]:)891 2970 y Fu(E)5 b Fs([)p Fu(W)13 b Fs(])1112 2933 y Ft(M)s(=G=)p FE(1)p Ft(=S)t(etupS)1636 2970 y Fs(=)1742 2909 y(2)p Fu(E)5 b Fs([)p Fu(S)g Fs(])22 b(+)e Fu(\025)2136 2923 y Ft(L)2188 2909 y Fu(E)5 b Fs([)p Fu(S)2346 2876 y FE(2)2386 2909 y Fs(])p 1742 2949 669 4 v 1796 3032 a(2\(1)21 b(+)f Fu(\025)2086 3046 y Ft(L)2138 3032 y Fu(E)5 b Fs([)p Fu(S)g Fs(]\))2441 2970 y(+)2550 2909 y Fu(\025)2603 2923 y Ft(L)2656 2909 y Fu(E)g Fs([)p Fu(X)2835 2876 y FE(2)2828 2934 y Ft(L)2881 2909 y Fs(])p 2542 2949 372 4 v 2542 3032 a(2\(1)22 b Fr(\000)e Fu(\032)2827 3046 y Ft(L)2879 3032 y Fs(\))2924 2970 y Fu(:)261 3174 y FC(W)-7 b(e)23 b(thus)h(ha)n(v)o(e:)994 3400 y Fu(E)5 b Fs([)p FC(T)m(ime)23 b(for)g(long)r Fs(])i(=)g Fu(E)5 b Fs([)p Fu(X)1911 3414 y Ft(L)1964 3400 y Fs(])21 b(+)f Fu(E)5 b Fs([)p Fu(W)13 b Fs(])2322 3362 y Ft(M)s(=G=)p FE(1)p Ft(=S)t(etupS)2821 3400 y Fu(:)120 3691 y FG(5)119 b(Stability)31 b(under)g(CS-Immediate-Dispatch)g(and)f (CS-Central-Queue)120 3898 y FC(F)o(or)e Fx(Dedicated)c FC(assignment)31 b(it)e(is)g(required)i(that)e Fu(\032)1939 3912 y Ft(L)2027 3898 y Fu(<)35 b Fs(1)28 b FC(and)i Fu(\032)2413 3912 y Ft(S)2499 3898 y Fu(<)35 b Fs(1)p FC(,)29 b(where)g Fu(\032)2999 3912 y Ft(L)3080 3898 y FC(\(respecti)n(v)o(ely)-6 b(,)33 b Fu(\032)3639 3912 y Ft(S)3690 3898 y FC(\))120 4011 y(denotes)22 b(the)e(load)h(made)f (up)g(of)g(long)h(jobs)f(\(respecti)n(v)o(ely)-6 b(,)24 b(short)d(jobs\).)28 b(F)o(or)20 b Fx(CS-Immediate-D)o(is)o(pa)o(tc)o (h)120 4124 y FC(we)j(will)g(see)h(that)g(the)g(re)o(gion)g(of)g (stability)h(is)f(much)g(wider)l(,)f(and)h(for)g Fx(CS-Central-Queu)o (e)17 b FC(wider)23 b(still.)261 4236 y(Let)e Fu(\032)450 4251 y Ft(hL)563 4236 y FC(\(respecti)n(v)o(ely)-6 b(,)24 b Fu(\032)1113 4251 y Ft(hS)1205 4236 y FC(\))d(denote)h(the)g(load)g (at)f(the)g(long)h(host)g(\(respecti)n(v)o(ely)-6 b(,)25 b(short)d(host\).)29 b(Both)21 b(these)120 4349 y(quantities)26 b(must)e(clearly)h(be)e Fu(<)i Fs(1)p FC(.)261 4462 y(F)o(or)e Fx(CS-Central-Que)o(ue)16 b FC(stability)26 b(conditions)g(are)e(tri)n (vial:)1612 4656 y Fu(\032)1659 4670 y Ft(L)1794 4656 y Fu(<)82 b Fs(1)p Fu(;)1613 4794 y(\032)1660 4808 y Ft(S)1794 4794 y Fu(<)g Fs(2)21 b Fr(\000)f Fu(\032)2151 4808 y Ft(L)2203 4794 y Fu(:)120 4987 y FC(Therefore)39 b(the)e(rest)h(of)f(this)h(section)h(will)e(be)g(de)n(v)n(oted)j(to)d (analyzing)j(the)d(stability)j(conditions)g(for)d Fx(CS-)120 5100 y(Immediate-Dispa)o(tc)o(h)p FC(.)1875 5349 y(15)p eop %%Page: 16 18 16 17 bop 261 91 a FC(W)-7 b(e)23 b(can)h(deduce)h Fu(\032)879 106 y Ft(hL)994 91 y FC(from)f(the)g(follo)n(wing)h(equation:)1432 278 y Fu(\032)1479 293 y Ft(hL)1655 278 y Fs(=)83 b Fu(\032)1856 292 y Ft(S)1906 278 y Fs(\(1)21 b Fr(\000)f Fu(\032)2145 293 y Ft(hL)2238 278 y Fs(\))h(+)f Fu(\032)2432 292 y Ft(L)2484 278 y Fu(;)1316 449 y Fr(\))25 b Fu(\032)1479 464 y Ft(hL)1655 449 y Fs(=)1819 387 y Fu(\032)1866 401 y Ft(S)1937 387 y Fs(+)19 b Fu(\032)2074 401 y Ft(L)p 1819 427 309 4 v 1845 511 a Fs(1)i(+)f Fu(\032)2049 525 y Ft(S)2137 449 y Fu(:)120 673 y FC(W)-7 b(e)23 b(therefore)i(ha)n(v)o (e)g(the)e(constraint)k(that)1403 809 y Fu(\032)1450 823 y Ft(S)1521 809 y Fs(+)20 b Fu(\032)1659 823 y Ft(L)p 1403 850 V 1430 933 a Fs(1)h(+)f Fu(\032)1634 947 y Ft(S)1747 871 y Fu(<)k Fs(1)51 b Fr(\()-15 b(\))51 b Fu(\032)2203 885 y Ft(L)2280 871 y Fu(<)25 b Fs(1)p Fu(;)120 1095 y FC(just)f(as)g(in)f Fx(Dedicated)c FC(and)24 b Fx(CS-Immediate-D)o (is)o(pa)o(tch)o FC(.)e(Ne)o(xt)h(we)g(deduce)i Fu(\032)2984 1110 y Ft(hS)3075 1095 y FC(:)1485 1282 y Fu(\032)1532 1297 y Ft(hS)1706 1282 y Fs(=)83 b Fu(\032)1907 1296 y Ft(S)1978 1282 y Fr(\001)20 b Fu(\032)2070 1297 y Ft(hL)2189 1282 y Fu(<)k Fs(1)p Fu(;)120 1468 y FC(or)l(,)g(equi)n(v)n(alently)-6 b(,)1578 1611 y Fu(\032)1625 1625 y Ft(S)1696 1611 y Fr(\001)1752 1549 y Fu(\032)1799 1563 y Ft(S)1870 1549 y Fs(+)20 b Fu(\032)2008 1563 y Ft(L)p 1752 1590 V 1779 1673 a Fs(1)g(+)g Fu(\032)1982 1687 y Ft(S)2095 1611 y Fu(<)25 b Fs(1)p Fu(:)120 1806 y FC(This)e(is)h(in)f(turn)h(equi)n(v) n(alent)i(to:)1556 1954 y Fu(\032)1603 1968 y Ft(L)1680 1954 y Fu(<)1812 1893 y Fs(1)p 1786 1933 98 4 v 1786 2017 a Fu(\032)1833 2031 y Ft(S)1914 1954 y Fs(+)20 b(1)g Fr(\000)g Fu(\032)2208 1968 y Ft(S)2259 1954 y Fu(:)120 2150 y FC(So)j(that)h(ultimately)h(it)f(it)f(is)g(required)j(that)1402 2372 y Fu(\032)1449 2386 y Ft(L)1526 2372 y Fu(<)f Fs(min)n(\(1)p Fu(;)1931 2310 y Fs(1)p 1905 2351 V 1905 2434 a Fu(\032)1952 2448 y Ft(S)2033 2372 y Fs(+)19 b(1)i Fr(\000)f Fu(\032)2327 2386 y Ft(S)2378 2372 y Fs(\))p Fu(:)120 2596 y FC(The)j(abo)o(v)o(e)h (constraint)i(on)e Fu(\032)1063 2610 y Ft(L)1138 2596 y FC(is)f(depicted)j(graphically)h(in)c(Figure)h(7.)1260 2709 y 10419816 8648442 3749560 12959006 35916840 39732183 startTexFig 1260 2709 a %%BeginDocument: ../figures/stability.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: stability.eps %%CreationDate: 05/26/ 2 19:53:47 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 57 197 546 604 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 57 197 546 604 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 470 93 5874 4886 MR c np 93 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4226 5356 0 0 -4226 899 4615 4 MP PP -5356 0 0 4226 5356 0 0 -4226 899 4615 5 MP stroke 4 w DO SO 6 w 0 sg 899 4615 mt 6255 4615 L 899 389 mt 6255 389 L 899 4615 mt 899 389 L 6255 4615 mt 6255 389 L 899 4615 mt 6255 4615 L 899 4615 mt 899 389 L 899 4615 mt 899 4561 L 899 389 mt 899 443 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 144 FMSR 859 4784 mt (0) s 1435 4615 mt 1435 4561 L 1435 389 mt 1435 443 L 1335 4784 mt (0.2) s 1970 4615 mt 1970 4561 L 1970 389 mt 1970 443 L 1870 4784 mt (0.4) s 2506 4615 mt 2506 4561 L 2506 389 mt 2506 443 L 2406 4784 mt (0.6) s 3041 4615 mt 3041 4561 L 3041 389 mt 3041 443 L 2941 4784 mt (0.8) s 3577 4615 mt 3577 4561 L 3577 389 mt 3577 443 L 3537 4784 mt (1) s 4113 4615 mt 4113 4561 L 4113 389 mt 4113 443 L 4013 4784 mt (1.2) s 4648 4615 mt 4648 4561 L 4648 389 mt 4648 443 L 4548 4784 mt (1.4) s 5184 4615 mt 5184 4561 L 5184 389 mt 5184 443 L 5084 4784 mt (1.6) s 5719 4615 mt 5719 4561 L 5719 389 mt 5719 443 L 5619 4784 mt (1.8) s 6255 4615 mt 6255 4561 L 6255 389 mt 6255 443 L 6215 4784 mt (2) s 899 4615 mt 953 4615 L 6255 4615 mt 6201 4615 L 784 4668 mt (0) s 899 4192 mt 953 4192 L 6255 4192 mt 6201 4192 L 664 4245 mt (0.1) s 899 3770 mt 953 3770 L 6255 3770 mt 6201 3770 L 664 3823 mt (0.2) s 899 3347 mt 953 3347 L 6255 3347 mt 6201 3347 L 664 3400 mt (0.3) s 899 2925 mt 953 2925 L 6255 2925 mt 6201 2925 L 664 2978 mt (0.4) s 899 2502 mt 953 2502 L 6255 2502 mt 6201 2502 L 664 2555 mt (0.5) s 899 2079 mt 953 2079 L 6255 2079 mt 6201 2079 L 664 2132 mt (0.6) s 899 1657 mt 953 1657 L 6255 1657 mt 6201 1657 L 664 1710 mt (0.7) s 899 1234 mt 953 1234 L 6255 1234 mt 6201 1234 L 664 1287 mt (0.8) s 899 812 mt 953 812 L 6255 812 mt 6201 812 L 664 865 mt (0.9) s 899 389 mt 953 389 L 6255 389 mt 6201 389 L 784 442 mt (1) s 899 4615 mt 6255 4615 L 899 389 mt 6255 389 L 899 4615 mt 899 389 L 6255 4615 mt 6255 389 L gs 899 389 5357 4227 MR c np 24 w 268 423 268 422 267 423 268 422 268 423 268 423 268 422 267 423 268 422 268 423 268 0 268 0 267 0 268 0 268 0 268 0 268 0 267 0 268 0 268 0 899 389 21 MP stroke DA 268 598 268 624 268 655 267 693 268 743 268 807 268 0 268 0 267 0 268 0 268 0 268 0 268 0 267 0 268 0 268 0 899 389 17 MP stroke DO 0 4226 268 0 268 0 267 0 268 0 268 0 268 0 268 0 267 0 268 0 268 0 899 389 12 MP stroke gr 24 w DO 3436 4945 mt (rhos) s 609 2622 mt -90 rotate (rhol) s 90 rotate 2779 275 mt (Stability condition on rhol) s SO 6 w 1 sg 0 524 1481 0 0 -524 4714 973 4 MP PP -1481 0 0 524 1481 0 0 -524 4714 973 5 MP stroke 4 w DO SO 6 w 0 sg 4714 973 mt 6195 973 L 4714 449 mt 6195 449 L 4714 973 mt 4714 449 L 6195 973 mt 6195 449 L 4714 973 mt 6195 973 L 4714 973 mt 4714 449 L 4714 973 mt 6195 973 L 4714 449 mt 6195 449 L 4714 973 mt 4714 449 L 6195 973 mt 6195 449 L 5117 596 mt (CentralQueue ) s 5117 762 mt (ImmedDispatch) s 5117 928 mt (Dedicated ) s gs 4714 449 1482 525 MR c np 24 w 241 0 4795 547 2 MP stroke DA 241 0 4795 713 2 MP stroke DO 241 0 4795 880 2 MP stroke gr 24 w DO SO 6 w end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 120 4001 a FC(Figure)34 b(7:)50 b(Stability)36 b(constraint)g(on)e Fu(\032)1414 4015 y Ft(L)1500 4001 y FC(for)g Fx(Dedicated)p FC(,)d Fx(CS-Immediate-Di)o(sp)o(at)o(ch)o FC(,)f(and)k Fx(CS-)120 4114 y(Central-Queue)261 4313 y FC(W)-7 b(e)23 b(can)h(also)g(turn)g(the)g(abo)o(v)o(e)g(constraint)i(into)e(a)f (constraint)k(on)c Fu(\032)2411 4327 y Ft(S)2485 4313 y FC(as)g(follo)n(ws:)1302 4555 y Fu(\032)1349 4569 y Ft(S)1425 4555 y Fu(<)1531 4493 y Fs(1)d Fr(\000)g Fu(\032)1734 4507 y Ft(L)1807 4493 y Fs(+)1898 4420 y Fq(p)p 1981 4420 523 4 v 73 x Fs(\(1)h Fr(\000)f Fu(\032)2220 4507 y Ft(L)2272 4493 y Fs(\))2307 4467 y FE(2)2367 4493 y Fs(+)g(4)p 1531 4534 973 4 v 1994 4617 a(2)2513 4555 y Fu(:)261 4761 y FC(The)e(restriction)j(on)e Fu(\032)962 4775 y Ft(S)1030 4761 y FC(for)g(each)g(of)f(the)h(three)g(task)g (assignment)h(policies)h(is)d(sho)n(wn)h(in)f(Figure)h(8.)26 b(Observ)o(e)120 4874 y(the)i(adv)n(antage)h(of)f(c)o(ycle)g(stealing)h (in)e(e)o(xtending)j(the)e(stability)h(re)o(gion.)42 b(When)27 b Fu(\032)2801 4888 y Ft(L)2880 4874 y FC(is)g(near)h(zero,)h Fu(\032)3404 4888 y Ft(S)3481 4874 y FC(can)f(be)120 4987 y(as)d(high)i(as)e(about)h Fs(1)p Fu(:)p Fs(6)g FC(under)h Fx(CS-Immediate-D)o(is)o(pat)o(ch)18 b FC(and)26 b(as)f(high)h(as)f Fs(2)g FC(under)i Fx(CS-Central-)120 5100 y(Queue)p FC(.)1875 5349 y(16)p eop %%Page: 17 19 17 18 bop 1260 0 a 10419816 8752640 2499706 11972280 36114186 40521564 startTexFig 1260 0 a %%BeginDocument: ../figures/stabilityrhos.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: stabilityrhos.eps %%CreationDate: 06/07/2002 00:11:53 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 38 182 549 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 38 182 549 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 248 -48 6124 5208 MR c np 92 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5357 0 0 -4227 899 4616 4 MP PP -5357 0 0 4227 5357 0 0 -4227 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L 899 4616 mt 6256 4616 L 899 4616 mt 899 389 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1970 4616 mt 1970 4562 L 1970 389 mt 1970 442 L 1804 4873 mt (0.2) s 3041 4616 mt 3041 4562 L 3041 389 mt 3041 442 L 2875 4873 mt (0.4) s 4113 4616 mt 4113 4562 L 4113 389 mt 4113 442 L 3947 4873 mt (0.6) s 5184 4616 mt 5184 4562 L 5184 389 mt 5184 442 L 5018 4873 mt (0.8) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6190 4873 mt (1) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3559 mt 952 3559 L 6256 3559 mt 6202 3559 L 531 3648 mt (0.5) s 899 2502 mt 952 2502 L 6256 2502 mt 6202 2502 L 731 2591 mt (1) s 899 1445 mt 952 1445 L 6256 1445 mt 6202 1445 L 531 1534 mt (1.5) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 731 478 mt (2) s 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L gs 899 389 5358 4228 MR c np DO 24 w 536 0 536 0 536 0 535 0 536 0 536 0 535 0 536 0 536 0 535 0 899 2502 11 MP stroke SO 536 108 536 114 536 119 535 124 536 128 536 134 535 138 536 143 536 147 535 151 899 1196 11 MP stroke DA 536 211 536 212 536 211 535 211 536 212 536 211 535 211 536 212 536 211 535 211 899 389 11 MP stroke gr 24 w DA 3377 5104 mt (rhol) s 476 2736 mt -90 rotate (rhos) s 90 rotate 2215 198 mt (Stability condition on rhos) s SO 6 w 1 sg 0 875 2153 0 0 -875 4043 1324 4 MP PP -2153 0 0 875 2153 0 0 -875 4043 1324 5 MP stroke 4 w DO SO 6 w 0 sg 4043 1324 mt 6196 1324 L 4043 449 mt 6196 449 L 4043 1324 mt 4043 449 L 6196 1324 mt 6196 449 L 4043 1324 mt 6196 1324 L 4043 1324 mt 4043 449 L 4043 1324 mt 6196 1324 L 4043 449 mt 6196 449 L 4043 1324 mt 4043 449 L 6196 1324 mt 6196 449 L 4711 694 mt (Dedicated) s 4711 971 mt (Immed-Disp) s 4711 1248 mt (Central-Q) s gs 4043 449 2154 876 MR c np DO 24 w 401 0 4176 613 2 MP stroke SO 401 0 4176 890 2 MP stroke DA 401 0 4176 1168 2 MP stroke SO 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 120 1305 a FC(Figure)35 b(8:)50 b(Stability)35 b(constraint)i(on)d Fu(\032)1415 1319 y Ft(S)1499 1305 y FC(for)g Fx(Dedicated)p FC(,)e Fx(CS-Immediate-D)o(is)o(pat)o(ch)o FC(,)e(and)k Fx(CS-)120 1418 y(Central-Queue)p FC(.)120 1688 y FG(6)119 b(V)-11 b(alidation)31 b(of)f(Analysis)120 1895 y FC(As)21 b(we)f(are)i(proposing)i(a)d(ne)n(w)g(analytical)j(scheme)e(to)g(arri)n (v)o(e)g(at)f(near)n(-e)o(xact)j(calculations)h(of)c(w)o(aiting)i (times,)e(it)120 2007 y(is)e(of)g(paramount)j(importance)f(that)f(we)e (demonstrate)k(the)e(correctness)i(of)d(our)h(proposed)h(method.)29 b(In)19 b(both)h(the)120 2120 y(analysis)j(of)e Fx(CS-Immediate-D)o(is) o(pa)o(tc)o(h)14 b FC(and)21 b Fx(CS-Central-Queu)o(e)p FC(,)14 b(we)20 b(approximate)k(the)d(length)120 2233 y(of)27 b(a)g(b)n(usy)h(period,)h(consisting)h(of)d(long)h(jobs)g(or)f (primarily)i(long)f(jobs,)g(by)f(its)h(\002rst)e(three)j(moments.)40 b(In)27 b(this)120 2346 y(section,)e(we)e(v)n(alidate)i(the)f(accurac)o (y)h(of)f(our)g(methods)g(in)g(tw)o(o)f(w)o(ays:)234 2559 y(1.)45 b FB(V)-8 b(alidation)34 b(against)h(kno)o(wn)d(limiting)j (cases:)51 b FC(W)-7 b(e)33 b(compare)i(the)g(output)g(of)f(our)h (algorithm)g(with)347 2672 y(e)o(xact)28 b(results)h(from)e(the)g (literature)i(when)f(these)g(e)o(xist.)40 b(Due)26 b(to)h(the)h(comple) o(xity)h(of)e(our)g(system,)i(this)347 2785 y(is)h(possible)i(only)f (in)f(a)f(limited)i(number)g(of)f(special)h(cases;)k(speci\002cally)d (when)e(the)g(traf)n(\002c)g(intensity)347 2897 y(of)h(one)g(of)g(the)g (customer)h(classes)g(approaches)i(either)e(zero)g(or)e(the)h (saturation)j(point)e(of)e(the)h(system)347 3010 y(\(this)25 b(saturation)i(point)e(may)f(be)g(strictly)i(greater)g(than)f(one)f (for)h(the)f(small)h(jobs)f(who)g(ha)n(v)o(e)h(access)h(to)e(a)347 3123 y(second)h(serv)o(er\).)k(Depending)c(on)e(the)g(model,)g(and)g (whether)h(the)f(traf)n(\002c)g(intensity)i(approaches)h(zero)d(or)347 3236 y(saturation,)30 b(the)c(system)h(approaches)j(either)d(an)g (M/G/1)f(queue,)i(an)e(M/G/1/queue)i(with)e(initial)i(setup)347 3349 y(time,)21 b(or)f(an)h(M/G/2)f(queue.)29 b(The)20 b(performance)j(of)e(the)g(\002rst)f(tw)o(o)g(of)h(these)g(models)h (for)e(general)j(service)347 3462 y(times)f(are)f(kno)n(wn,)h(while)g (the)f(third)h(is)f(only)i(a)n(v)n(ailable)g(in)e(the)h(literature)i (only)e(for)f(e)o(xponential)k(service)347 3575 y(times.)k(Gi)n(v)o(en) 23 b(these)i(kno)n(wn)f(results,)g(these)h(comparisons)h(may)d(be)h (carried)h(out)e(for)h(an)o(y)f(stable)i(traf)n(\002c)347 3688 y(intensity)-6 b(.)234 3875 y(2.)45 b FB(V)-8 b(alidation)32 b(against)h(simulation:)46 b FC(Ha)n(ving)32 b(e)n(v)n(aluated)i(our)e (approximation)j(methods)e(for)f(limiting)347 3988 y(cases)c (approaching)h(saturation)g(and)e(approaching)j(zero,)d(we)f(ne)o(xt)h (use)f(computer)i(simulation)h(to)d(test)347 4101 y(our)21 b(analytical)i(results)g(o)o(v)o(er)d(a)g(broad)i(range)g(of)e(loads.) 29 b(Simulations)22 b(are)f(limited)h(only)f(by)g(the)f(f)o(act)i(that) 347 4214 y(simulation)k(accurac)o(y)f(decreases)h(as)e(the)g(relati)n (v)o(e)g(traf)n(\002c)g(intensities)i(approach)g(saturation)g([3)q(,)d (27)q(].)261 4427 y(F)o(or)g(both)h(types)h(of)e(v)n(alidation)j(we)d (consider)j(three)e(de\002nitions)i(of)d(\223short\224)j(and)e (\223long.)-6 b(\224)256 4614 y Fr(\017)46 b FC(Shorts)24 b(ha)n(v)o(e)h(mean)e(size)h(1;)g(Longs)g(ha)n(v)o(e)g(mean)g(size)g(1) 256 4802 y Fr(\017)46 b FC(Shorts)24 b(ha)n(v)o(e)h(mean)e(size)h(1;)g (Longs)g(ha)n(v)o(e)g(mean)g(size)g(10)256 4990 y Fr(\017)46 b FC(Shorts)24 b(ha)n(v)o(e)h(mean)e(size)h(10;)g(Longs)g(ha)n(v)o(e)g (mean)g(size)g(1)1875 5349 y(17)p eop %%Page: 18 20 18 19 bop 261 91 a FC(Although)21 b(our)e(c)o(ycle-stealing)k (algorithms)e(were)e(designed)i(with)e(the)g(second)i(case)e(abo)o(v)o (e)h(in)f(mind)g(\(short)120 204 y(jobs)25 b(shorter)h(than)f(long)g (jobs\),)h(there)f(is)f(no)h(reason)g(why)f(the)h(analysis)h(shouldn')n (t)i(w)o(ork)c(as)g(well)g(for)h(the)g(\002rst)120 317 y(and)f(third)g(cases)h(abo)o(v)o(e,)f(and)g(thus)g(for)g(completeness) i(we)d(v)n(alidate)i(under)g(all)f(cases.)120 566 y Fo(6.1)99 b(V)-9 b(alidation)24 b(against)h(kno)o(wn)h(limiting)e(cases)120 741 y FC(W)-7 b(e)28 b(ha)n(v)o(e)h(four)g(limiting)g(cases,)i (described)g(belo)n(w)-6 b(,)29 b(which)g(we)f(use)h(to)f(e)n(v)n (aluate)i(our)f(analysis.)45 b(In)29 b(all)f(cases)120 854 y(illustrated)39 b(belo)n(w)d(we)g(assume)h(that)f(short)h(jobs)g (are)g(e)o(xponentially-distrib)o(ut)q(ed)42 b(and)36 b(that)h(long)g(jobs)g(are)120 966 y(dra)o(wn)23 b(from)h(a)e(Coxian)j (distrib)n(ution)i(with)c Fu(C)1612 933 y FE(2)1676 966 y Fs(=)i(8)p Fu(:)e FC(Other)h(distrib)n(utions)j(of)c(job)h(sizes)g (and)g(loads)g(were)g(also)120 1079 y(e)n(v)n(aluated,)h(all)f(sho)n (wing)g(similar)h(limiting)f(beha)n(vior)-5 b(.)120 1292 y FB(Limiting)23 b(Case)h(1:)29 b(Fix)23 b Fu(\032)991 1306 y Ft(S)1041 1292 y FB(,)g(tak)o(e)g Fu(\032)1322 1306 y Ft(L)1400 1292 y Fr(!)i Fs(1)p FB(.)p 120 1324 1465 4 v 46 w FC(Under)j(this)h(case,)i(for)d(both)i Fx(CS-Immediate-D)o(is)o(pa)o(tc)o(h)347 1405 y FC(and)23 b Fx(CS-Central-Queu)o(e)16 b FC(it)22 b(becomes)i(increasingly)i(dif)n (\002cult)d(for)g(the)g(short)g(jobs)h(to)e(gain)h(access)347 1518 y(to)d(the)g(long)h(serv)o(er)-5 b(.)28 b(Thus,)21 b(the)f(mean)g(response)i(time)e(for)g Fy(short)h(jobs)g FC(under)g(both)g(c)o(ycle-stealing)i(algo-)347 1631 y(rithms)d(should)h(approach)g(that)f(of)f(an)g(M/G/1)g(queue)h(with)f (load)h Fu(\032)2461 1645 y Ft(S)2512 1631 y FC(.)26 b(This)19 b(is)g(in)g(f)o(act)h(the)f(case,)i(as)e(sho)n(wn)347 1744 y(in)27 b(Figure)g(9\(ro)n(w)g(1\),)g(where)h(we)e(\002x)g Fu(\032)1623 1758 y Ft(S)1705 1744 y Fs(=)31 b(0)p Fu(:)p Fs(9)c FC(and)g(e)n(v)n(aluate)i(both)e(c)o(ycle)h(stealing)g (algorithms)h(with)347 1856 y(respect)h(to)e(mean)g(response)i(time)e (for)g(short)h(jobs)f(as)g Fu(\032)2158 1870 y Ft(L)2238 1856 y FC(is)f(set)i(progressi)n(v)o(ely)i(closer)e(to)f Fs(1)p FC(.)41 b(Observ)o(e)347 1969 y(that)21 b Fx(CS-Immediate-D)o (isp)o(at)o(ch)13 b FC(is)19 b(a)h(little)h(f)o(aster)g(to)f(con)l(v)o (er)n(ge)j(than)e Fx(CS-Central-Que)o(ue)o FC(.)347 2082 y(This)j(is)f(because)i(more)f(short)h(jobs)f(sneak)h(into)f(the)g (long)g(serv)o(er)g(under)h Fx(CS-Central-Queu)o(e)p FC(.)120 2270 y FB(Limiting)e(Case)h(2:)29 b(Fix)23 b Fu(\032)991 2284 y Ft(L)1043 2270 y FB(,)f(tak)o(e)i Fu(\032)1324 2284 y Ft(S)1400 2270 y Fr(!)h Fs(0)p FB(.)p 120 2302 V 46 w FC(Under)j(this)h(case,)i(for)d(both)i Fx(CS-Immediate-D)o(is)o(pa)o(tc)o(h)347 2383 y FC(and)40 b Fx(CS-Central-Que)o(ue)31 b FC(it)39 b(becomes)h(increasingly)i (unlik)o(ely)f(that)f(a)e(long)h(job)h(will)e(be)h(ob-)347 2496 y(structed)28 b(by)d(a)g(short)h(job)l(.)35 b(Thus)25 b(the)g(mean)h(response)h(time)e(for)h Fy(long)g(jobs)g FC(under)g(both)g(c)o(ycle-stealing)347 2609 y(algorithms)33 b(should)f(approach)g(that)f(of)g(an)f(M/G/1)g(queue)i(with)e(load)h Fu(\032)2730 2623 y Ft(L)2782 2609 y FC(.)49 b(This)30 b(is)g(in)g(f)o(act)h(the)g(case,)347 2722 y(as)i(sho)n(wn)g(in)g (Figure)h(9\(ro)n(w)f(2\),)i(where)e(we)f(\002x)g Fu(\032)2042 2736 y Ft(L)2137 2722 y Fs(=)42 b(0)p Fu(:)p Fs(9)34 b FC(and)f(e)n(v)n(aluate)i(both)f(c)o(ycle)f(stealing)i(al-)347 2834 y(gorithms)c(with)e(respect)i(to)e(mean)g(response)j(time)d(for)g (long)h(jobs)g(as)f Fu(\032)2691 2848 y Ft(S)2770 2834 y FC(is)g(set)g(progressi)n(v)o(ely)k(closer)347 2947 y(to)e Fs(0)p FC(.)51 b(Observ)o(e)32 b(that)g(this)f(time)g Fx(CS-Central-Queu)o(e)24 b FC(is)31 b(a)g(little)h(f)o(aster)g(to)f (con)l(v)o(er)n(ge)j(than)d Fx(CS-)347 3060 y(Immediate-Dispa)o(tch)o FC(.)21 b(T)-7 b(o)21 b(understand)k(why)-6 b(,)21 b(we)g(need)h(to)g (consider)h(ho)n(w)f(man)o(y)f(short)i(jobs)f(in-)347 3173 y(terfere)h(with)e(long)h(jobs.)28 b(Consider)23 b(times)e(when)g(the)h(long)g(host)g(is)f(idle.)28 b(Observ)o(e)22 b(that)g(as)f Fu(\032)3328 3187 y Ft(S)3404 3173 y Fr(!)k Fs(0)p FC(,)c(the)347 3286 y(short)i(host)g(is)f(usually)h(idle.)29 b(A)21 b(ne)n(w)g(arri)n(v)n(al)i(under)g Fx(CS-Central-Queue)14 b FC(will)22 b(go)g(to)g(either)h(queue)347 3399 y(and)33 b(that)h(will)e(be)g(named)i(the)e(short)i(queue.)57 b(Ho)n(we)n(v)o(er)32 b(a)h(ne)n(w)f(arri)n(v)n(al)h(under)h Fx(CS-Immediate-)347 3512 y(Dispatch)d FC(will)j(al)o(w)o(ays)i(try)f (to)g(go)f(to)h(the)g(long)h(host)f(\002rst)g(\(and)g(there)h(is)f(no)g (renaming\).)64 b(Thus)347 3625 y(fe)n(wer)28 b(short)g(arri)n(v)n(als) h(will)f(interfere)h(with)f(a)f(long)h(job)g(under)h Fx(CS-Central-Queu)o(e)p FC(,)22 b(than)28 b(under)347 3738 y Fx(CS-Immediate-Di)o(spa)o(tc)o(h)p FC(.)120 3925 y FB(Limiting)23 b(Case)h(3:)29 b(Fix)23 b Fu(\032)991 3939 y Ft(L)1065 3925 y FB(and)g(let)g Fu(\032)1400 3939 y Ft(S)1476 3925 y Fr(!)48 b FB(stability-condition)26 b(under)c(CS-Central-Queue.)p 120 3957 3231 4 v 46 w FC(The)17 b(mean)347 4038 y(response)25 b(time)d(for)g Fy(long)h(jobs)h FC(should)f(approach)i(an)d(M/G/1)g(queue)i(where)e (the)h(\002rst)f(job)h(in)f(a)g(b)n(usy)h(pe-)347 4151 y(riod)g(e)o(xperiences)h(a)e(setup)h(cost)f Fu(S)5 b FC(,)21 b(where)h Fu(S)31 b Fs(=)25 b Fu(min)p Fs(\()p Fu(E)5 b(xcess)p Fs(\()p Fu(X)2538 4165 y Ft(S)2589 4151 y Fs(\))p Fu(;)15 b(E)5 b(xcess)p Fs(\()p Fu(X)3065 4165 y Ft(S)3118 4151 y Fs(\)\))p FC(.)28 b(The)21 b(reason)i(is)347 4264 y(that)j(an)f(arri)n(ving)i(long)f(job)g(which)f(sees)h(no)f (other)h(long)g(jobs,)h(will)d(lik)o(ely)j(see)e(both)h(serv)o(ers)h (occupied)347 4377 y(by)k(short)g(jobs.)50 b(If)30 b(the)h(short)h(job) e(at)h(the)f(long)h(host)h(\002nishes)f(\002rst,)h(the)e(long)h(host)h (will)e(go)g(there.)50 b(If)347 4490 y(the)27 b(short)h(job)f(at)f(the) h(short)h(host)f(\002nishes)h(\002rst,)f(the)g(long)g(job)g(will)f(go)h (there)h(and)f(the)g(short)g(host)h(will)347 4603 y(be)h(renamed)g(to)g (be)f(the)h(long)g(host.)45 b(In)28 b(the)h(case)g(where)g Fu(X)2310 4617 y Ft(S)2388 4603 y FC(is)g(e)o(xponential,)j(as)c(we)g (ha)n(v)o(e)h(assumed,)347 4716 y Fu(E)5 b(xcess)p Fs(\()p Fu(X)748 4730 y Ft(S)800 4716 y Fs(\))26 b(=)g Fu(X)1033 4730 y Ft(S)1107 4716 y FC(and)e(thus)h(we)e(should)j(ha)n(v)o(e)e (simply:)31 b Fu(S)g Fs(=)25 b Fu(min)p Fs(\()p Fu(X)2783 4730 y Ft(S)2834 4716 y Fu(;)15 b(X)2949 4730 y Ft(S)3001 4716 y Fs(\))p FC(.)29 b(This)24 b(is)g(in)f(f)o(act)i(the)347 4829 y(case,)i(as)g(sho)n(wn)f(in)g(Figure)h(9\(ro)n(w)f(3\),)g(where)h (we)e(hold)i Fu(\032)2250 4843 y Ft(L)2328 4829 y FC(\002x)o(ed)e (arbitrarily)k(at)d Fu(\032)3060 4843 y Ft(L)3142 4829 y Fs(=)k Fu(:)p Fs(6)c FC(and)h(set)f Fu(\032)3669 4843 y Ft(S)347 4942 y FC(progressi)n(v)o(ely)h(closer)e(to)e Fs(2)e Fr(\000)f Fu(\032)1393 4956 y Ft(L)1470 4942 y Fs(=)25 b(1)p Fu(:)p Fs(4)p FC(,)f(the)g(stability)i(condition)g(for)d Fx(CS-Central-Queue)o FC(.)1875 5349 y(18)p eop %%Page: 19 21 19 20 bop 120 91 a FB(Limiting)23 b(Case)h(4:)29 b(Let)23 b Fu(\032)996 105 y Ft(L)1073 91 y Fr(!)i Fs(0)e FB(under)f (CS-Central-Queue.)p 120 123 2143 4 v 46 w FC(Under)c Fx(CS-Central-Queu)o(e)p FC(,)12 b(as)18 b Fu(\032)3606 105 y Ft(L)3683 91 y Fr(!)347 204 y Fs(0)p FC(,)k(the)h(mean)g (response)h(time)f(for)f Fy(short)i(jobs)f FC(should)h(approach)h(an)d (M/M/2)g(queue.)30 b(This)22 b(is)h(in)f(f)o(act)h(the)347 317 y(case,)k(as)f(sho)n(wn)g(in)g(Figure)g(9\(ro)n(w)g(4\),)g(where)h (we)e(hold)h Fu(\032)2247 331 y Ft(S)2323 317 y FC(\002x)o(ed)g(at)g (1.89,)g(and)g(set)h Fu(\032)3157 331 y Ft(L)3234 317 y FC(progressi)n(v)o(ely)347 430 y(closer)e(to)f(zero.)261 616 y(Ha)n(ving)31 b(v)n(alidated)h(cases)f(with)e(traf)n(\002c)h (intensity)i(approaching)h(zero)e(or)e(saturation,)34 b(we)29 b(ne)o(xt)h(consider)120 729 y(intermediate)c(v)n(alues)f(of)e (traf)n(\002c)h(intensity)-6 b(.)31 b(These)24 b(are)g(e)n(v)n(aluated) h(via)f(simulation.)120 974 y Fo(6.2)99 b(V)-9 b(alidation)24 b(against)h(simulation)120 1148 y FC(W)-7 b(e)23 b(performed)i(e)n(v)o (ent-dri)n(v)o(en)h(simulations)g(of)d(our)h(c)o(ycle)h(stealing)g (algorithm)g(in)f(C)e(on)i(a)f(700MHz)h(Pentium)120 1261 y(III)i(processor)i(with)e(256)g(MB)f(RAM.)f(W)-7 b(e)25 b(e)o(xperimented)j(with)e(a)f(range)i(of)f(loads)h(\()p Fu(\032)2915 1275 y Ft(S)2966 1261 y FC(,)e Fu(\032)3061 1275 y Ft(L)3114 1261 y FC(\),)g(v)n(arious)j(de\002ni-)120 1374 y(tions)f(of)e(short)i(and)g(long,)f(and)h(dif)n(ferent)g(job)f (size)h(distrib)n(utions)j(\(e)o(xponential)f(and)d(Coxian)h(with)e Fu(C)3453 1341 y FE(2)3521 1374 y Fs(=)30 b(8)p FC(\).)120 1487 y(Each)d(e)o(xperiment)i(consisted)h(of)d(measuring)i(mean)e (response)j(time)d(o)o(v)o(er)g Fs(10)2665 1454 y FE(6)2731 1487 y FC(arri)n(v)n(als)i(with)e(a)g(w)o(armup)g(pe-)120 1600 y(riod)c(of)e(50,000)i(arri)n(v)n(als.)30 b(Each)22 b(e)o(xperiment)h(w)o(as)f(then)h(replicated)h(thirty)f(times)f (\(using)i(dif)n(ferent)f(seeds\))h(and)120 1713 y(the)k(a)n(v)o(erage) h(of)e(the)g(thirty)i(replications)i(w)o(as)c(compared)h(with)g(the)f (analytically-predic)q(ted)33 b(v)n(alue)c(from)e(our)120 1826 y(algorithm.)261 1939 y(In)c(Figure)g(10)g(we)f(sho)n(w)h(just)h (a)e Fy(small)h(subset)h FC(of)f(our)g(e)o(xperiments,)i(restricted)h (to)c(e)o(xponential)k(job)e(sizes,)120 2051 y(where)36 b Fu(\032)424 2065 y Ft(S)511 2051 y FC(is)g(held)g(\002x)o(ed)g(at)g Fs(0)p Fu(:)p Fs(9)h FC(and)f Fu(\032)1480 2065 y Ft(L)1568 2051 y FC(is)g(allo)n(wed)h(to)f(range)h(o)o(v)o(er)f(all)h(stable)g(v) n(alues.)68 b(Almost)36 b(all)g(of)120 2164 y(our)28 b(simulation)i(results)f(were)f(within)g(1-2)g(percent)h(of)f (predicted)i(analysis;)i(in)c(some)f(cases)i(the)f(simulation)120 2277 y(numbers)f(were)e(a)h(little)g(higher)h(than)g(analysis)h(and)e (in)f(some)h(cases)h(a)e(little)i(lo)n(wer)-5 b(.)35 b(Simulation)27 b(replications)120 2390 y(were)34 b(quite)h(consistent) i(at)d(lo)n(w)g(loads,)j(b)n(ut)e(e)o(xhibited)h(high)f(v)n(ariability) i(at)d(higher)i(loads,)h(e)n(v)o(en)e(under)g(an)120 2503 y(e)o(xponential)f(job)d(size)g(distrib)n(ution.)55 b(When)31 b(the)g(job)g(size)h(distrib)n(ution)i(w)o(as)d(Coxian)g (\(with)g Fu(C)3291 2470 y FE(2)3369 2503 y Fs(=)39 b(8)p FC(\),)32 b(the)120 2616 y(v)n(ariation)d(within)e(the)f(simulation)j (results)f(increased)h(further)-5 b(.)39 b(W)-7 b(e)25 b(do)i(not)g(sho)n(w)f(the)h(Coxian)g(plots,)h(b)n(ut)f(we)120 2729 y(do)d(include)h(those)g(results)g(in)e(our)h(discussion)j(belo)n (w)-6 b(.)261 2842 y(Ov)o(er)24 b(all)h(our)g(simulation)i(e)o (xperiments,)g(we)d(found)i(that)f(with)g(respect)h(to)e(mean)h (response)i(time)e(of)f Fy(long)120 2955 y(jobs)p FC(,)36 b(there)d(is)g(no)g(visible)i(discrepanc)o(y)g(between)f(analysis)h (and)f(simulation)h(under)f(either)g(c)o(ycle)f(stealing)120 3068 y(algorithm.)h(T)-7 b(o)24 b(understand)k(why)c(this)h(is)g(the)g (case)g(for)g Fx(CS-Immediate-Di)o(spa)o(tc)o(h)p FC(,)18 b(recall)26 b(that)f(under)120 3181 y Fx(CS-Immediate-Di)o(sp)o(at)o (ch)18 b FC(there)26 b(are)g(tw)o(o)f(Mark)o(o)o(v)h(chains,)h(one)f (for)g(the)f(long)h(host)h(and)e(one)h(for)g(the)120 3293 y(short.)35 b(The)26 b(Mark)o(o)o(v)g(chain)g(representing)j(the)d (state)g(at)g(the)f(long)i(host)f(is)f(e)o(xact)h(\(it)g(in)l(v)n(olv)o (es)i(no)d(b)n(usy)i(period)120 3406 y(approximations\).)k(Thus)19 b(it)g(is)g(understandable)24 b(that)c(there)g(is)f(no)g(discrepanc)o (y)j(for)d(the)h(long)g(jobs.)28 b(Under)19 b Fx(CS-)120 3519 y(Central-Queue)14 b FC(there)22 b(is)e(a)h(single)h(Mark)o(o)o(v) g(chain,)g(which)f(does)h(in)l(v)n(olv)o(e)g(b)n(usy)g(period)h (approximations.)120 3632 y(The)32 b(b)n(usy)i(periods)g(are)f(up-do)n (wn)h(arro)n(ws)f(in)f(this)h(chain.)57 b(Nonetheless,)37 b(recall)d(that)f(the)g(performance)i(of)120 3745 y(the)e(long)h(jobs,) h(as)e(described)j(in)c(Section)i(4.3)f(depends)i(only)e(on)g(the)h (parameters)g Fu(a)2975 3759 y FE(1)3047 3745 y FC(and)f Fu(a)3258 3759 y FE(2)3298 3745 y FC(,)h(which)f(are)120 3858 y(the)25 b(probabilities)j(of)d(being)g(in)g(Re)o(gion)g(1)f(v)o (ersus)i(Re)o(gion)f(2.)31 b(These)25 b(stationary)i(probabilities)i (are)24 b(a)n(v)o(erages,)120 3971 y(which)g(are)g(lik)o(ely)h(less)f (sensiti)n(v)o(e)h(to)e(the)h(v)o(ery)g(high)g(moments)h(in)e(the)h (lengths)h(of)f(the)f(b)n(usy)i(periods.)261 4084 y(W)l(ith)e(respect)h (to)e(mean)g(response)j(time)d(of)g Fy(short)i(jobs)p FC(,)f(there)g(w)o(as)f(more)g(discrepanc)o(y)k(between)d(analysis)120 4197 y(and)f(simulation.)30 b(This)22 b(discrepanc)o(y)j(w)o(as)c (limited)i(to)f(the)g(case)g(of)g(high)g(load)h(and)f(w)o(as)g(more)f (pre)n(v)n(alent)j(in)e(the)120 4310 y(case)j(where)g(long)g(jobs)h (were)e(v)o(ery)h(long.)33 b(It)24 b(is)g(easy)i(to)e(see)h(why)f (short)h(jobs)h(are)e(more)h(greatly)h(impacted)g(by)120 4423 y(the)h(long)h(b)n(usy)h(period)f(approximations)j(under)e(both)f (c)o(ycle)f(stealing)j(algorithms:)38 b(The)27 b(length)i(of)e(the)g(b) n(usy)120 4535 y(period)20 b(of)f(the)g(long)g(jobs)h(af)n(fects)g(the) f(left/right)i(motion)f(of)e(the)h(chain)h(which)f(represents)j(the)d (number)g(of)g(small)120 4648 y(jobs.)29 b(Since)22 b(we)e(only)j (match)e(the)h(length)h(of)f(the)g(b)n(usy)g(period)h(to)f(three)g (moments,)g(we)f(may)g(be)h(creating)h(error)120 4761 y(in)g(the)g(number)h(of)e(short)i(jobs.)29 b(Furthermore,)c(observ)o (e)f(that)f(since)h(these)g(b)n(usy)g(periods)g(consist)h(primarily)f (of)120 4874 y(long)j(jobs,)g(the)f(v)n(ariability)j(in)d(the)h(length) g(of)f(these)h(b)n(usy)g(periods)h(becomes)g(more)e(pronounced)j(when)d (long)120 4987 y(jobs)31 b(are)g(v)o(ery)g(long)h(and)f(loads)h(are)f (v)o(ery)g(high.)51 b(T)-7 b(o)29 b(fully)j(capture)g(the)f(ef)n(fect)h (of)e(these)i(b)n(usy)g(periods,)i(we)120 5100 y(will)28 b(need)h(to)f(match)h(more)f(moments.)44 b(Using)29 b(more)f (sophisticated)k(simulation)f(techniques)g(to)d(ameliorate)1875 5349 y(19)p eop %%Page: 20 22 20 21 bop 1228 68 a FF(V)-11 b(alidation)24 b(against)g(Limiting)e (Case)k(1)p 1228 103 1384 4 v 104 189 a 8241137 7104430 2894397 11972280 36245749 40521564 startTexFig 104 189 a %%BeginDocument: ../figures/validationIDCQrhol1_11ID.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationIDCQrhol1_11ID.eps %%CreationDate: 07/18/2002 21:03:42 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 44 182 551 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 44 182 551 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 315 -48 6082 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 733 4873 mt (0.9) s 1970 4616 mt 1970 4562 L 1970 389 mt 1970 442 L 1737 4873 mt (0.92) s 3041 4616 mt 3041 4562 L 3041 389 mt 3041 442 L 2808 4873 mt (0.94) s 4113 4616 mt 4113 4562 L 4113 389 mt 4113 442 L 3880 4873 mt (0.96) s 5184 4616 mt 5184 4562 L 5184 389 mt 5184 442 L 4951 4873 mt (0.98) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6190 4873 mt (1) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (6) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 731 3859 mt (7) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 731 3014 mt (8) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 731 2168 mt (9) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 598 1323 mt (10) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 598 478 mt (11) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 48 0 482 0 2143 0 2678 0 899 1234 5 MP stroke SO 48 -36 482 -342 2143 -1125 2678 -991 899 3736 5 MP stroke gr 24 w gs 801 1144 5548 2691 MR c np 36 36 899 3736 FO 36 36 3577 2745 FO 36 36 5720 1620 FO 36 36 6202 1278 FO 36 36 6250 1242 FO gr gs 899 389 5358 4228 MR c np DA 48 -71 482 -598 2143 -1540 2678 -1115 899 4574 5 MP stroke gr DA gs 801 1152 5548 3521 MR c np SO 36 36 899 4574 FO 36 36 3577 3459 FO 36 36 5720 1919 FO 36 36 6202 1321 FO 36 36 6250 1250 FO DA gr gs 899 389 5358 4228 MR c np DO 1 sg 48 0 482 0 2143 0 2678 0 899 473 5 MP stroke gr 1 sg DO 0 sg 3377 5104 mt (rhol) s 543 4269 mt -90 rotate (mean response time of short jobs) s 90 rotate 1711 198 mt (Convergence to M/M/1 as rhol -> 1) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (M/M/1) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DA 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 1373 189 a 8241137 7104430 2894397 11972280 36245749 40521564 startTexFig 1373 189 a %%BeginDocument: ../figures/validationIDCQrhol1_110ID.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationIDCQrhol1_110ID.eps %%CreationDate: 07/18/2002 15:39:22 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 44 182 551 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 44 182 551 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 315 -48 6082 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 733 4873 mt (0.9) s 1970 4616 mt 1970 4562 L 1970 389 mt 1970 442 L 1737 4873 mt (0.92) s 3041 4616 mt 3041 4562 L 3041 389 mt 3041 442 L 2808 4873 mt (0.94) s 4113 4616 mt 4113 4562 L 4113 389 mt 4113 442 L 3880 4873 mt (0.96) s 5184 4616 mt 5184 4562 L 5184 389 mt 5184 442 L 4951 4873 mt (0.98) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6190 4873 mt (1) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (6) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 731 3859 mt (7) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 731 3014 mt (8) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 731 2168 mt (9) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 598 1323 mt (10) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 598 478 mt (11) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 48 0 482 0 2143 0 2678 0 899 1234 5 MP stroke SO 48 -35 482 -328 2143 -1079 2678 -926 899 3610 5 MP stroke gr 24 w gs 801 1144 5548 2565 MR c np 36 36 899 3610 FO 36 36 3577 2684 FO 36 36 5720 1605 FO 36 36 6202 1277 FO 36 36 6250 1242 FO gr gs 899 389 5358 4228 MR c np DA 48 -70 482 -603 2143 -1539 2678 -1116 899 4574 5 MP stroke gr DA gs 801 1148 5548 3525 MR c np SO 36 36 899 4574 FO 36 36 3577 3458 FO 36 36 5720 1919 FO 36 36 6202 1316 FO 36 36 6250 1246 FO DA gr gs 899 389 5358 4228 MR c np DO 1 sg 48 0 482 0 2143 0 2678 0 899 473 5 MP stroke gr 1 sg DO 0 sg 3377 5104 mt (rhol) s 543 4269 mt -90 rotate (mean response time of short jobs) s 90 rotate 1711 198 mt (Convergence to M/M/1 as rhol -> 1) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (M/M/1) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DA 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 2643 189 a 8454269 7104430 2170798 11972280 36245749 40521564 startTexFig 2643 189 a %%BeginDocument: ../figures/validationIDCQrhol1_101ID.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationIDCQrhol1_101ID.eps %%CreationDate: 07/18/2002 21:19:37 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 33 182 551 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 33 182 551 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 181 -48 6216 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 733 4873 mt (0.9) s 1970 4616 mt 1970 4562 L 1970 389 mt 1970 442 L 1737 4873 mt (0.92) s 3041 4616 mt 3041 4562 L 3041 389 mt 3041 442 L 2808 4873 mt (0.94) s 4113 4616 mt 4113 4562 L 4113 389 mt 4113 442 L 3880 4873 mt (0.96) s 5184 4616 mt 5184 4562 L 5184 389 mt 5184 442 L 4951 4873 mt (0.98) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6190 4873 mt (1) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 598 4705 mt (50) s 899 3911 mt 952 3911 L 6256 3911 mt 6202 3911 L 598 4000 mt (60) s 899 3207 mt 952 3207 L 6256 3207 mt 6202 3207 L 598 3296 mt (70) s 899 2502 mt 952 2502 L 6256 2502 mt 6202 2502 L 598 2591 mt (80) s 899 1798 mt 952 1798 L 6256 1798 mt 6202 1798 L 598 1887 mt (90) s 899 1093 mt 952 1093 L 6256 1093 mt 6202 1093 L 464 1182 mt (100) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 464 478 mt (110) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 48 0 482 0 2143 0 2678 0 899 1093 5 MP stroke SO 48 -31 482 -298 2143 -1013 2678 -939 899 3379 5 MP stroke gr 24 w gs 801 1000 5548 2478 MR c np 36 36 899 3379 FO 36 36 3577 2440 FO 36 36 5720 1427 FO 36 36 6202 1129 FO 36 36 6250 1098 FO gr gs 899 389 5358 4228 MR c np DA 48 -66 482 -560 2143 -1513 2678 -1152 899 4396 5 MP stroke gr DA gs 801 1007 5548 3488 MR c np SO 36 36 899 4396 FO 36 36 3577 3244 FO 36 36 5720 1731 FO 36 36 6202 1171 FO 36 36 6250 1105 FO DA gr gs 899 389 5358 4228 MR c np DO 1 sg 48 0 482 0 2143 0 2678 0 899 459 5 MP stroke gr 1 sg DO 0 sg 3377 5104 mt (rhol) s 409 4269 mt -90 rotate (mean response time of short jobs) s 90 rotate 1711 198 mt (Convergence to M/M/1 as rhol -> 1) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (M/M/1) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DA 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 248 1202 a FC(\(a\))e(shorts)h(1,)e(longs)i(1)646 b(\(b\))23 b(shorts)i(1,)e(longs)i(10)646 b(\(c\))24 b(shorts)h(10,)e(longs)i(1) 1228 1428 y FF(V)-11 b(alidation)24 b(against)g(Limiting)e(Case)k(2)p 1228 1463 1384 4 v 18 1474 a 8809492 7104430 1184071 11972280 36640440 40521564 startTexFig 18 1474 a %%BeginDocument: ../figures/validationIDCQrhos0_11ID.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationIDCQrhos0_11ID.eps %%CreationDate: 07/18/2002 21:21:16 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 18 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 18 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 0 -48 6472 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5358 0 0 -4227 898 4616 4 MP PP -5358 0 0 4227 5358 0 0 -4227 898 4616 5 MP stroke 4 w DO SO 6 w 0 sg 898 4616 mt 6256 4616 L 898 389 mt 6256 389 L 898 4616 mt 898 389 L 6256 4616 mt 6256 389 L 898 4616 mt 6256 4616 L 898 4616 mt 898 389 L 898 4616 mt 898 4562 L 898 389 mt 898 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 832 4873 mt (0) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3344 4873 mt (0.05) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (0.1) s 898 4334 mt 952 4334 L 6256 4334 mt 6202 4334 L 264 4423 mt (41.46) s 898 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 264 3859 mt (41.48) s 898 3207 mt 952 3207 L 6256 3207 mt 6202 3207 L 397 3296 mt (41.5) s 898 2643 mt 952 2643 L 6256 2643 mt 6202 2643 L 264 2732 mt (41.52) s 898 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 264 2168 mt (41.54) s 898 1516 mt 952 1516 L 6256 1516 mt 6202 1516 L 264 1605 mt (41.56) s 898 952 mt 952 952 L 6256 952 mt 6202 952 L 264 1041 mt (41.58) s 898 389 mt 952 389 L 6256 389 mt 6202 389 L 397 478 mt (41.6) s 898 4616 mt 6256 4616 L 898 389 mt 6256 389 L 898 4616 mt 898 389 L 6256 4616 mt 6256 389 L gs 898 389 5359 4228 MR c np DA 24 w -48 0 -482 0 -2143 0 -2679 0 6256 3206 5 MP stroke SO -48 26 -482 251 -2143 1063 -2679 1219 6256 648 5 MP stroke gr 24 w gs 806 550 5549 2756 MR c np 36 36 6256 648 FO 36 36 3577 1867 FO 36 36 1434 2930 FO 36 36 952 3181 FO 36 36 904 3207 FO gr gs 898 389 5359 4228 MR c np DA -48 0 -482 1 -2143 30 -2679 92 6256 3083 5 MP stroke gr DA gs 806 2985 5549 320 MR c np SO 36 36 6256 3083 FO 36 36 3577 3175 FO 36 36 1434 3205 FO 36 36 952 3206 FO 36 36 904 3206 FO DA gr gs 898 389 5359 4228 MR c np DO 1 sg -48 0 -482 0 -2143 0 -2679 0 6256 4376 5 MP stroke gr 1 sg DO 0 sg 3343 5104 mt (rhos) s 209 4230 mt -90 rotate (mean response time of long jobs) s 90 rotate 1676 198 mt (Convergence to M/G/1 as rhos -> 0) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (M/G/1) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DA 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 1360 1474 a 8809492 7104430 1184071 11972280 36640440 40521564 startTexFig 1360 1474 a %%BeginDocument: ../figures/validationIDCQrhos0_110ID.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationIDCQrhos0_110ID.eps %%CreationDate: 07/18/2002 21:21:38 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 18 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 18 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 0 -48 6472 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5358 0 0 -4227 898 4615 4 MP PP -5358 0 0 4227 5358 0 0 -4227 898 4615 5 MP stroke 4 w DO SO 6 w 0 sg 898 4615 mt 6256 4615 L 898 388 mt 6256 388 L 898 4615 mt 898 388 L 6256 4615 mt 6256 388 L 898 4615 mt 6256 4615 L 898 4615 mt 898 388 L 898 4615 mt 898 4562 L 898 388 mt 898 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 832 4873 mt (0) s 3577 4615 mt 3577 4562 L 3577 388 mt 3577 442 L 3344 4873 mt (0.05) s 6256 4615 mt 6256 4562 L 6256 388 mt 6256 442 L 6090 4873 mt (0.1) s 898 4615 mt 952 4615 L 6256 4615 mt 6202 4615 L 131 4704 mt (414.94) s 898 4087 mt 952 4087 L 6256 4087 mt 6202 4087 L 131 4176 mt (414.96) s 898 3559 mt 952 3559 L 6256 3559 mt 6202 3559 L 131 3648 mt (414.98) s 898 3030 mt 952 3030 L 6256 3030 mt 6202 3030 L 464 3119 mt (415) s 898 2502 mt 952 2502 L 6256 2502 mt 6202 2502 L 131 2591 mt (415.02) s 898 1974 mt 952 1974 L 6256 1974 mt 6202 1974 L 131 2063 mt (415.04) s 898 1445 mt 952 1445 L 6256 1445 mt 6202 1445 L 131 1534 mt (415.06) s 898 917 mt 952 917 L 6256 917 mt 6202 917 L 131 1006 mt (415.08) s 898 388 mt 952 388 L 6256 388 mt 6202 388 L 264 477 mt (415.1) s 898 4615 mt 6256 4615 L 898 388 mt 6256 388 L 898 4615 mt 898 388 L 6256 4615 mt 6256 388 L gs 898 388 5359 4228 MR c np DA 24 w -48 0 -482 0 -2143 0 -2679 0 6256 3030 5 MP stroke SO -48 24 -482 235 -2143 997 -2679 1143 6256 656 5 MP stroke gr 24 w gs 806 558 5549 2596 MR c np 36 36 6256 656 FO 36 36 3577 1799 FO 36 36 1434 2796 FO 36 36 952 3031 FO 36 36 904 3055 FO gr gs 898 388 5359 4228 MR c np DA -48 0 -482 0 -2143 17 -2679 52 6256 2961 5 MP stroke gr DA gs 806 2863 5549 266 MR c np SO 36 36 6256 2961 FO 36 36 3577 3013 FO 36 36 1434 3030 FO 36 36 952 3030 FO 36 36 904 3030 FO DA gr gs 898 388 5359 4228 MR c np DO 1 sg -48 0 -482 0 -2143 0 -2679 0 6256 4127 5 MP stroke gr 1 sg DO 0 sg 3343 5104 mt (rhos) s 76 4230 mt -90 rotate (mean response time of long jobs) s 90 rotate 1676 197 mt (Convergence to M/G/1 as rhos -> 0) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (M/G/1) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DA 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 2701 1474 a 8667404 7104430 1776107 11972280 36640440 40521564 startTexFig 2701 1474 a %%BeginDocument: ../figures/validationIDCQrhos0_101ID.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationIDCQrhos0_101ID.eps %%CreationDate: 07/18/2002 21:22:01 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 27 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 27 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 114 -48 6358 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5357 0 0 -4227 899 4616 4 MP PP -5357 0 0 4227 5357 0 0 -4227 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L 899 4616 mt 6256 4616 L 899 4616 mt 899 389 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3344 4873 mt (0.05) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (0.1) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 598 4705 mt (41) s 899 3559 mt 952 3559 L 6256 3559 mt 6202 3559 L 397 3648 mt (41.5) s 899 2502 mt 952 2502 L 6256 2502 mt 6202 2502 L 598 2591 mt (42) s 899 1445 mt 952 1445 L 6256 1445 mt 6202 1445 L 397 1534 mt (42.5) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 598 478 mt (43) s 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L gs 899 389 5358 4228 MR c np DA 24 w -48 0 -482 0 -2143 0 -2679 0 6256 3559 5 MP stroke SO -48 19 -482 188 -2143 797 -2679 915 6256 1638 5 MP stroke gr 24 w gs 806 1540 5549 2116 MR c np 36 36 6256 1638 FO 36 36 3577 2553 FO 36 36 1434 3350 FO 36 36 952 3538 FO 36 36 904 3557 FO gr gs 899 389 5358 4228 MR c np DA -48 0 -482 3 -2143 54 -2679 158 6256 3344 5 MP stroke gr DA gs 806 3246 5549 412 MR c np SO 36 36 6256 3344 FO 36 36 3577 3502 FO 36 36 1434 3556 FO 36 36 952 3559 FO 36 36 904 3559 FO DA gr gs 899 389 5358 4228 MR c np DO 1 sg -48 0 -482 0 -2143 0 -2679 0 6256 3646 5 MP stroke gr 1 sg DO 0 sg 3343 5104 mt (rhos) s 342 4230 mt -90 rotate (mean response time of long jobs) s 90 rotate 1677 198 mt (Convergence to M/G/1 as rhos -> 0) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (M/G/1) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DA 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 248 2487 a FC(\(a\))e(shorts)h(1,)e(longs)i(1)646 b(\(b\))23 b(shorts)i(1,)e(longs)i(10)646 b(\(c\))24 b(shorts)h(10,)e(longs)i(1) 1228 2713 y FF(V)-11 b(alidation)24 b(against)g(Limiting)e(Case)k(3)p 1228 2748 1384 4 v 21 2760 a 8809492 7104430 1184071 11972280 36640440 40521564 startTexFig 21 2760 a %%BeginDocument: ../figures/validationCQrhol6_11.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationCQrhol6_11.eps %%CreationDate: 07/19/2002 00:19:25 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 18 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 18 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 0 -48 6472 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5357 0 0 -4227 898 4615 4 MP PP -5357 0 0 4227 5357 0 0 -4227 898 4615 5 MP stroke 4 w DO SO 6 w 0 sg 898 4615 mt 6255 4615 L 898 388 mt 6255 388 L 898 4615 mt 898 388 L 6255 4615 mt 6255 388 L 898 4615 mt 6255 4615 L 898 4615 mt 898 388 L 1791 4615 mt 1791 4562 L 1791 388 mt 1791 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 1625 4873 mt (1.3) s 4023 4615 mt 4023 4562 L 4023 388 mt 4023 442 L 3790 4873 mt (1.35) s 6256 4615 mt 6256 4562 L 6256 388 mt 6256 442 L 6090 4873 mt (1.4) s 898 4615 mt 952 4615 L 6256 4615 mt 6202 4615 L 397 4704 mt (8.15) s 898 2502 mt 952 2502 L 6256 2502 mt 6202 2502 L 531 2591 mt (8.2) s 898 388 mt 952 388 L 6256 388 mt 6202 388 L 397 477 mt (8.25) s 898 4615 mt 6255 4615 L 898 388 mt 6255 388 L 898 4615 mt 898 388 L 6255 4615 mt 6255 388 L gs 898 388 5359 4228 MR c np DA 24 w 4 0 40 0 402 0 1786 0 2232 0 1791 388 6 MP stroke 4 -1 40 -22 402 -252 1786 -1112 2232 -1355 1791 3137 6 MP stroke gr 24 w DA gs 1693 297 4661 2939 MR c np SO 36 36 1791 3137 FO 36 36 4023 1782 FO 36 36 5809 670 FO 36 36 6211 418 FO 36 36 6251 396 FO 36 36 6255 395 FO DA gr gs 898 388 5359 4228 MR c np gr 3343 5104 mt (rhos) s 342 4230 mt -90 rotate (mean response time of long jobs) s 90 rotate 1803 197 mt (Convergence to M/G/1 with setup) s SO 6 w 1 sg 0 598 2905 0 0 -598 959 1047 4 MP PP -2905 0 0 598 2905 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 3864 1047 L 959 449 mt 3864 449 L 959 1047 mt 959 449 L 3864 1047 mt 3864 449 L 959 1047 mt 3864 1047 L 959 1047 mt 959 449 L 959 1047 mt 3864 1047 L 959 449 mt 3864 449 L 959 1047 mt 959 449 L 3864 1047 mt 3864 449 L 1627 694 mt (M/G/1 with setup) s 1627 971 mt (CS-Central-Queue) s gs 959 449 2906 599 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO DA 401 0 1092 891 2 MP stroke SO gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 1339 2760 a 8809492 7104430 1184071 11972280 36640440 40521564 startTexFig 1339 2760 a %%BeginDocument: ../figures/validationCQrhol6_110.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationCQrhol6_110.eps %%CreationDate: 07/19/2002 01:08:47 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 18 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 18 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 0 -48 6472 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5356 0 0 -4227 899 4616 4 MP PP -5356 0 0 4227 5356 0 0 -4227 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6255 4616 L 899 389 mt 6255 389 L 899 4616 mt 899 389 L 6255 4616 mt 6255 389 L 899 4616 mt 6255 4616 L 899 4616 mt 899 389 L 1791 4616 mt 1791 4562 L 1791 389 mt 1791 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 1625 4873 mt (1.3) s 4023 4616 mt 4023 4562 L 4023 389 mt 4023 442 L 3790 4873 mt (1.35) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.4) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 264 4705 mt (77.92) s 899 4087 mt 952 4087 L 6256 4087 mt 6202 4087 L 264 4176 mt (77.93) s 899 3559 mt 952 3559 L 6256 3559 mt 6202 3559 L 264 3648 mt (77.94) s 899 3030 mt 952 3030 L 6256 3030 mt 6202 3030 L 264 3119 mt (77.95) s 899 2502 mt 952 2502 L 6256 2502 mt 6202 2502 L 264 2591 mt (77.96) s 899 1974 mt 952 1974 L 6256 1974 mt 6202 1974 L 264 2063 mt (77.97) s 899 1445 mt 952 1445 L 6256 1445 mt 6202 1445 L 264 1534 mt (77.98) s 899 917 mt 952 917 L 6256 917 mt 6202 917 L 264 1006 mt (77.99) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 598 478 mt (78) s 899 4616 mt 6255 4616 L 899 389 mt 6255 389 L 899 4616 mt 899 389 L 6255 4616 mt 6255 389 L gs 899 389 5358 4228 MR c np DA 24 w 4 0 40 0 402 0 1786 0 2232 0 1791 389 6 MP stroke 4 -2 40 -30 402 -377 1786 -1674 2232 -2034 1791 4522 6 MP stroke gr 24 w DA gs 1693 307 4661 4314 MR c np SO 36 36 1791 4522 FO 36 36 4023 2488 FO 36 36 5809 814 FO 36 36 6211 437 FO 36 36 6251 407 FO 36 36 6255 405 FO DA gr gs 899 389 5358 4228 MR c np gr 3343 5104 mt (rhos) s 209 4230 mt -90 rotate (mean response time of long jobs) s 90 rotate 1804 198 mt (Convergence to M/G/1 with setup) s SO 6 w 1 sg 0 598 2905 0 0 -598 959 1047 4 MP PP -2905 0 0 598 2905 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 3864 1047 L 959 449 mt 3864 449 L 959 1047 mt 959 449 L 3864 1047 mt 3864 449 L 959 1047 mt 3864 1047 L 959 1047 mt 959 449 L 959 1047 mt 3864 1047 L 959 449 mt 3864 449 L 959 1047 mt 959 449 L 3864 1047 mt 3864 449 L 1627 694 mt (M/G/1 with setup) s 1627 971 mt (CS-Central-Queue) s gs 959 449 2906 599 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO DA 401 0 1092 891 2 MP stroke SO gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 2681 2760 a 8809492 7104430 1184071 11972280 36640440 40521564 startTexFig 2681 2760 a %%BeginDocument: ../figures/validationCQrhol6_101.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationCQrhol6_101.eps %%CreationDate: 07/19/2002 01:11:04 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 18 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 18 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 0 -48 6472 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5356 0 0 -4228 899 4616 4 MP PP -5356 0 0 4228 5356 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6255 4616 L 899 388 mt 6255 388 L 899 4616 mt 899 388 L 6255 4616 mt 6255 388 L 899 4616 mt 6255 4616 L 899 4616 mt 899 388 L 1791 4616 mt 1791 4562 L 1791 389 mt 1791 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 1625 4873 mt (1.3) s 4023 4616 mt 4023 4562 L 4023 389 mt 4023 442 L 3790 4873 mt (1.35) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.4) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 598 4705 mt (12) s 899 3559 mt 952 3559 L 6256 3559 mt 6202 3559 L 397 3648 mt (12.2) s 899 2502 mt 952 2502 L 6256 2502 mt 6202 2502 L 397 2591 mt (12.4) s 899 1445 mt 952 1445 L 6256 1445 mt 6202 1445 L 397 1534 mt (12.6) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 397 478 mt (12.8) s 899 4616 mt 6255 4616 L 899 388 mt 6255 388 L 899 4616 mt 899 388 L 6255 4616 mt 6255 388 L gs 899 389 5358 4228 MR c np DA 24 w 4 0 40 0 402 0 1786 0 2232 0 1791 653 6 MP stroke 4 -2 40 -23 402 -266 1786 -1174 2232 -1444 1791 3567 6 MP stroke gr 24 w DA gs 1693 560 4661 3106 MR c np SO 36 36 1791 3567 FO 36 36 4023 2123 FO 36 36 5809 949 FO 36 36 6211 683 FO 36 36 6251 660 FO 36 36 6255 658 FO DA gr gs 899 389 5358 4228 MR c np gr 3343 5104 mt (rhos) s 342 4230 mt -90 rotate (mean response time of long jobs) s 90 rotate 1804 198 mt (Convergence to M/G/1 with setup) s SO 6 w 1 sg 0 598 2905 0 0 -598 959 1047 4 MP PP -2905 0 0 598 2905 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 3864 1047 L 959 449 mt 3864 449 L 959 1047 mt 959 449 L 3864 1047 mt 3864 449 L 959 1047 mt 3864 1047 L 959 1047 mt 959 449 L 959 1047 mt 3864 1047 L 959 449 mt 3864 449 L 959 1047 mt 959 449 L 3864 1047 mt 3864 449 L 1627 694 mt (M/G/1 with setup) s 1627 971 mt (CS-Central-Queue) s gs 959 449 2906 599 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO DA 401 0 1092 891 2 MP stroke SO gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 248 3772 a FC(\(a\))e(shorts)h(1,)e(longs)i(1)646 b(\(b\))23 b(shorts)i(1,)e(longs)i(10)646 b(\(c\))24 b(shorts)h(10,)e(longs)i(1) 1228 3998 y FF(V)-11 b(alidation)24 b(against)g(Limiting)e(Case)k(4)p 1228 4033 1384 4 v 41 4045 a 8525316 7104430 2170798 11972280 36640440 40521564 startTexFig 41 4045 a %%BeginDocument: ../figures/validationCQrhol0_11rhos189.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationCQrhol0_11rhos189.eps %%CreationDate: 07/19/2002 01:24:23 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 33 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 33 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 181 -48 6291 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5357 0 0 -4227 899 4616 4 MP PP -5357 0 0 4227 5357 0 0 -4227 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L 899 4616 mt 6256 4616 L 899 4616 mt 899 389 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3344 4873 mt (0.05) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (0.1) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 4012 mt 952 4012 L 6256 4012 mt 6202 4012 L 598 4101 mt (20) s 899 3408 mt 952 3408 L 6256 3408 mt 6202 3408 L 598 3497 mt (40) s 899 2804 mt 952 2804 L 6256 2804 mt 6202 2804 L 598 2893 mt (60) s 899 2200 mt 952 2200 L 6256 2200 mt 6202 2200 L 598 2289 mt (80) s 899 1596 mt 952 1596 L 6256 1596 mt 6202 1596 L 464 1685 mt (100) s 899 992 mt 952 992 L 6256 992 mt 6202 992 L 464 1081 mt (120) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 464 478 mt (140) s 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L gs 899 389 5358 4228 MR c np DA 24 w -48 0 -482 0 -2143 0 -2679 0 6256 4333 5 MP stroke SO -48 3 -482 31 -2143 250 -2679 3167 6256 882 5 MP stroke gr 24 w gs 806 784 5549 3648 MR c np 36 36 6256 882 FO 36 36 3577 4049 FO 36 36 1434 4299 FO 36 36 952 4330 FO 36 36 904 4333 FO gr gs 899 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 409 4269 mt -90 rotate (mean response time of short jobs) s 90 rotate 1671 198 mt (Convergence to M/M/2 as rhol -> 0) s 6 w 1 sg 0 598 2905 0 0 -598 959 1047 4 MP PP -2905 0 0 598 2905 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 3864 1047 L 959 449 mt 3864 449 L 959 1047 mt 959 449 L 3864 1047 mt 3864 449 L 959 1047 mt 3864 1047 L 959 1047 mt 959 449 L 959 1047 mt 3864 1047 L 959 449 mt 3864 449 L 959 1047 mt 959 449 L 3864 1047 mt 3864 449 L 1627 694 mt (M/M/2) s 1627 971 mt (CS-Central-Queue) s gs 959 449 2906 599 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 891 2 MP stroke gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 1346 4045 a 8667404 7104430 1776107 11972280 36640440 40521564 startTexFig 1346 4045 a %%BeginDocument: ../figures/validationCQrhol0_110rhos189.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationCQrhol0_110rhos189.eps %%CreationDate: 07/19/2002 01:24:50 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 27 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 27 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 114 -48 6358 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5357 0 0 -4227 899 4616 4 MP PP -5357 0 0 4227 5357 0 0 -4227 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L 899 4616 mt 6256 4616 L 899 4616 mt 899 389 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3344 4873 mt (0.05) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (0.1) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (9) s 899 3559 mt 952 3559 L 6256 3559 mt 6202 3559 L 531 3648 mt (9.5) s 899 2502 mt 952 2502 L 6256 2502 mt 6202 2502 L 598 2591 mt (10) s 899 1445 mt 952 1445 L 6256 1445 mt 6202 1445 L 397 1534 mt (10.5) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 598 478 mt (11) s 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L gs 899 389 5358 4228 MR c np DA 24 w -48 0 -482 0 -2143 0 -2679 0 6256 3880 5 MP stroke SO -48 19 -482 196 -2143 911 -2679 1242 6256 1510 5 MP stroke gr 24 w gs 806 1412 5549 2565 MR c np 36 36 6256 1510 FO 36 36 3577 2752 FO 36 36 1434 3663 FO 36 36 952 3859 FO 36 36 904 3878 FO gr gs 899 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 342 4269 mt -90 rotate (mean response time of short jobs) s 90 rotate 1671 198 mt (Convergence to M/M/2 as rhol -> 0) s 6 w 1 sg 0 598 2905 0 0 -598 959 1047 4 MP PP -2905 0 0 598 2905 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 3864 1047 L 959 449 mt 3864 449 L 959 1047 mt 959 449 L 3864 1047 mt 3864 449 L 959 1047 mt 3864 1047 L 959 1047 mt 959 449 L 959 1047 mt 3864 1047 L 959 449 mt 3864 449 L 959 1047 mt 959 449 L 3864 1047 mt 3864 449 L 1627 694 mt (M/M/2) s 1627 971 mt (CS-Central-Queue) s gs 959 449 2906 599 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 891 2 MP stroke gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 2670 4045 a 8738448 7104430 1447198 11972280 36640440 40521564 startTexFig 2670 4045 a %%BeginDocument: ../figures/validationCQrhol0_101rhos189.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationCQrhol0_101rhos189.eps %%CreationDate: 07/19/2002 01:25:15 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 22 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 22 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 48 -48 6424 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3344 4873 mt (0.05) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (0.1) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3911 mt 952 3911 L 6256 3911 mt 6202 3911 L 464 4000 mt (200) s 899 3207 mt 952 3207 L 6256 3207 mt 6202 3207 L 464 3296 mt (400) s 899 2502 mt 952 2502 L 6256 2502 mt 6202 2502 L 464 2591 mt (600) s 899 1798 mt 952 1798 L 6256 1798 mt 6202 1798 L 464 1887 mt (800) s 899 1093 mt 952 1093 L 6256 1093 mt 6202 1093 L 331 1182 mt (1000) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 331 478 mt (1200) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w -48 0 -482 0 -2143 0 -2679 0 6256 4286 5 MP stroke SO -48 3 -482 29 -2143 239 -2679 2984 6256 1031 5 MP stroke gr 24 w gs 806 933 5549 3452 MR c np 36 36 6256 1031 FO 36 36 3577 4015 FO 36 36 1434 4254 FO 36 36 952 4283 FO 36 36 904 4286 FO gr gs 899 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 276 4269 mt -90 rotate (mean response time of short jobs) s 90 rotate 1671 198 mt (Convergence to M/M/2 as rhol -> 0) s 6 w 1 sg 0 598 2905 0 0 -598 959 1047 4 MP PP -2905 0 0 598 2905 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 3864 1047 L 959 449 mt 3864 449 L 959 1047 mt 959 449 L 3864 1047 mt 3864 449 L 959 1047 mt 3864 1047 L 959 1047 mt 959 449 L 959 1047 mt 3864 1047 L 959 449 mt 3864 449 L 959 1047 mt 959 449 L 3864 1047 mt 3864 449 L 1627 694 mt (M/M/2) s 1627 971 mt (CS-Central-Queue) s gs 959 449 2906 599 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 891 2 MP stroke gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 248 5058 a FC(\(a\))e(shorts)h(1,)e(longs)i(1)646 b(\(b\))23 b(shorts)i(1,)e(longs)i(10)646 b(\(c\))24 b(shorts)h(10,)e(longs)i(1) 120 5254 y(Figure)19 b(9:)27 b Fy(V)-10 b(alidation)20 b(of)f(analysis)h(a)o(gainst)h(four)e(limiting)h(cases.)28 b(In)18 b(r)l(ow)g(1)h Fu(\032)2627 5268 y Ft(S)2703 5254 y Fs(=)25 b(0)p Fu(:)p Fs(9)p Fy(.)i(As)18 b Fu(\032)3120 5268 y Ft(L)3197 5254 y Fr(!)25 b Fs(1)p Fy(,)19 b(r)m(esponse)120 5367 y(times)h(for)g(short)i(jobs)e(under)i(both)f(cycle)g(stealing)h (algorithms)g(con)l(ver)m(g)o(e)h(to)d(an)g(M/M/1)f(with)h(load)h Fu(\032)3387 5381 y Ft(S)3438 5367 y Fy(.)27 b(In)20 b(r)l(ow)120 5479 y(2)h Fu(\032)233 5493 y Ft(L)311 5479 y Fs(=)k(0)p Fu(:)p Fs(9)p Fy(.)j(As)21 b Fu(\032)732 5493 y Ft(S)808 5479 y Fr(!)k Fs(0)p Fy(,)c(r)m(esponse)j(times)e(for)g (long)g(jobs)g(under)h(both)g(cycle)f(stealing)i(algorithms)g(con)l (ver)m(g)o(e)120 5592 y(to)33 b(an)g(M/G/1/)g(with)g(load)h Fu(\032)1071 5606 y Ft(L)1123 5592 y Fy(.)56 b(In)33 b(r)l(ow)g(3)g Fu(\032)1605 5606 y Ft(L)1700 5592 y Fs(=)42 b(0)p Fu(:)p Fs(6)p Fy(.)58 b(As)32 b Fu(\032)2179 5606 y Ft(S)2273 5592 y Fr(!)43 b Fs(1)p Fu(:)p Fs(4)p Fy(,)35 b(under)g Fx(CS-Central-Que)o(ue)o Fy(,)120 5705 y(r)m(esponse)27 b(times)d(of)h(long)g(jobs)h(con)l(ver)m(g)o(e)h(to)d(an)h(M/G/1)f (with)h(setup)g Fu(S)33 b Fr(\030)27 b Fu(E)5 b(xp)p Fs(\(2)p Fu(\026)2842 5719 y Ft(S)2893 5705 y Fs(\))p Fy(.)32 b(In)24 b(r)l(ow)g(4)h Fu(\032)3360 5719 y Ft(S)3438 5705 y Fs(=)i(1)p Fu(:)p Fs(89)p Fy(.)120 5818 y(As)c Fu(\032)281 5832 y Ft(L)358 5818 y Fr(!)i Fs(0)p Fy(,)e(under)i Fx(CS-Central-Queu)o(e)p Fy(,)16 b(short)25 b(jobs)f(con)l(ver)m(g)o(e) i(to)d(an)h(M/M/2.)1875 5349 y FC(20)p eop %%Page: 21 23 21 22 bop 120 91 a FC(the)24 b(v)n(ariability)j(in)d(simulation)i (results)f(caused)h(by)e(the)g(high)g(traf)n(\002c)g(intensity)j(will)c (lik)o(ely)i(help)g(as)f(well.)30 b Fy(One)120 204 y(should)21 b(note)f(that)g(o)o(ver)g(all)g(the)f(simulation)j(e)n(xperiments)g (that)e(we)e(r)o(an,)i(the)g(dif)n(fer)m(ence)i(between)e(analysis)i (and)120 317 y(simulation)31 b(was)d(ne)o(ver)i(mor)m(e)e(than)i Fs(10\045)p Fy(,)g(and)f(that)h(dif)n(fer)m(ence)h(occurr)m(ed)g(r)o (ar)m(ely)e(and)h(only)f(at)g(high)h(tr)o(af)n(\002c)120 430 y(intensity)-5 b(.)261 543 y FC(It)27 b(is)h(w)o(orth)f(pointing)j (out)e(that)g(for)g(each)g(graph)g(in)g(Figure)g(10,)g(the)g (simulation)h(portion)h(required)f(close)120 656 y(to)23 b(an)h(hour)g(to)g(generate,)h(whereas)g(the)f(analysis)h(portion)h (required)f(less)f(than)h(a)e(second)i(to)e(compute.)120 941 y FG(7)119 b(Results)30 b(of)g(Analysis)120 1148 y FC(Recall)21 b(that)f(the)h(moti)n(v)n(ation)g(behind)h(c)o (ycle-stealing)i(algorithms)e(is)e(to)g(impro)o(v)o(e)g(the)h (performance)h(of)e(\223short\224)120 1261 y(jobs)25 b(without)f(in\003icting)i(too)e(much)g(penalty)i(on)e(\223long\224)h (jobs.)31 b(Some)23 b(penalty)i(to)f(long)h(jobs)f(is)g(ine)n(vitable,) i(of)120 1374 y(course,)32 b(since)f(our)f(model)g(is)f(non-preempti)n (v)o(e,)34 b(meaning)d(that)f(a)f(long)h(arri)n(v)n(al)h(can')n(t)f (interrupt)i(a)d(short)i(job)120 1487 y(running)26 b(at)d(its)h(serv)o (er)-5 b(.)261 1600 y(In)32 b(this)h(section)i(we)c(will)h(study)i(the) f(results)h(of)e(our)h(analysis)h(of)e(the)h(tw)o(o)f(c)o (ycle-stealing)k(algorithms,)120 1713 y Fx(CS-Immediate-Di)o(sp)o(at)o (ch)15 b FC(and)24 b Fx(CS-Central-Que)o(ue)o FC(.)e(All)g(\002gures)i (will)e(be)h(or)n(ganized)i(into)f(tw)o(o)120 1826 y(parts,)38 b(where)d(the)g(\002rst)f(part)i(will)e(sho)n(w)g(the)h(bene\002t)h(to) e(short)i(jobs)f(and)h(the)f(second)h(part)f(will)f(sho)n(w)h(the)120 1939 y(penalty)23 b(to)e(long)g(jobs.)29 b(In)21 b(order)h(to)e(e)n(v)n (aluate)j(these)f(bene\002ts/penalties)j(we)20 b(compare)i(with)f(the)g Fx(Dedicated)120 2051 y FC(algorithm)k(which)f(in)l(v)n(olv)o(es)i(no)e (c)o(ycle)g(stealing.)261 2164 y(In)h(Figure)h(11)f(and)h(12,)f(we)f (hold)i Fu(\032)1395 2178 y Ft(L)1472 2164 y FC(\(the)f(load)h(at)f (the)h(long)g(serv)o(er\))g(\002x)o(ed)f(at)g(tw)o(o)f(representati)n (v)o(e)29 b(v)n(alues)120 2277 y(and)24 b(consider)h(the)e(full)h (range)g(of)f Fu(\032)1255 2291 y Ft(S)1306 2277 y FC(.)28 b(Recall)c(from)f(Section)h(5,)e(for)i Fx(Dedicated)18 b FC(we)k(can)i(ne)n(v)o(er)f(ha)n(v)o(e)h Fu(\032)3573 2291 y Ft(S)3649 2277 y Fu(>)120 2390 y Fs(1)p FC(.)37 b(Ho)n(we)n(v)o(er)26 b(for)g Fx(CS-Central-Queu)o(e)p FC(,)20 b Fu(\032)1678 2404 y Ft(S)1754 2390 y FC(is)26 b(allo)n(wed)h(as)g(high)g(as)f Fs(2)d Fr(\000)f Fu(\032)2749 2404 y Ft(L)2801 2390 y FC(.)36 b(F)o(or)26 b Fx(CS-Immediate-)120 2503 y(Dispatch)p FC(,)e Fu(\032)654 2517 y Ft(S)731 2503 y FC(is)k(allo)n(wed)g(as)g(high)g(as)f(some)h(intermediate)i(v)n (alue)f(sho)n(wn)e(in)h(Figure)g(8,)g(which)g(is)f(not)h(as)120 2616 y(high)c(as)g Fs(2)c Fr(\000)g Fu(\032)606 2630 y Ft(L)681 2616 y FC(and)k(yet)g(is)f(higher)i(than)g Fx(Dedicated)p FC(.)261 2729 y(Figure)g(11)g(sho)n(ws)g(analytical)i (results)g(in)d(the)h(case)h(where)f(both)g(shorts)h(and)f(longs)h (come)f(from)g(an)f(e)o(xpo-)120 2842 y(nential)j(distrib)n(ution.)36 b(In)25 b(ro)n(w)f(1)h(and)g(ro)n(w)f(2)h(we)f(\002x)g Fu(\032)1882 2856 y Ft(L)1962 2842 y Fs(=)k(0)p Fu(:)p Fs(5)d FC(and)g(v)n(ary)h Fu(\032)2587 2856 y Ft(S)2662 2842 y FC(o)o(v)o(er)f(all)g(stable)h(v)n(alues.)34 b(In)25 b(ro)n(w)120 2955 y(3)e(and)h(ro)n(w)f(4)g(we)g(\002x)g Fu(\032)867 2969 y Ft(L)944 2955 y Fs(=)i(0)p Fu(:)p Fs(8)f FC(and)g(v)n(ary)g Fu(\032)1562 2969 y Ft(S)1635 2955 y FC(o)o(v)o(er)g(all)g(stable)g(v)n(alues.)261 3068 y(Looking)30 b(at)d(Figure)i(11)f(ro)n(w)g(1,)g(column)h(\(a\))g (\(where)f(shorts)i(and)e(longs)i(ha)n(v)o(e)e(mean)h(size)f Fs(1)g FC(and)h(we)e(\002x)120 3181 y Fu(\032)167 3196 y Ft(l)237 3181 y Fs(=)45 b(0)p Fu(:)p Fs(5)p FC(\),)36 b(we)e(see)g(that)g(the)g(short)h(jobs)g(bene\002t)f(tremendously)j (from)d(c)o(ycle)h(stealing.)62 b(F)o(or)33 b Fu(\032)3371 3195 y Ft(S)3466 3181 y Fu(>)44 b Fs(0)p Fu(:)p Fs(8)p FC(,)120 3293 y(the)29 b(mean)g(impro)o(v)o(ement)h(of)f(c)o(ycle)h (stealing)h(algorithms)g(o)o(v)o(er)e Fx(Dedicated)24 b FC(serv)o(ers)30 b(is)f(o)o(v)o(er)f(an)h(order)h(of)120 3406 y(magnitude.)52 b(As)29 b Fu(\032)753 3420 y Ft(S)842 3406 y Fr(!)38 b Fs(1)p FC(,)32 b(the)e(mean)h(response)i(time)d(under) i Fx(Dedicated)25 b FC(goes)32 b(to)e(in\002nity)-6 b(,)33 b(whereas)e(it)120 3519 y(is)g(only)g(around)i(4)d(under)i Fx(CS-Immediate-Di)o(sp)o(at)o(ch)23 b FC(and)32 b(only)f(around)i(3)d (under)i Fx(CS-Central-)120 3632 y(Queue)p FC(.)47 b(\(Graphs)31 b(ha)n(v)o(e)h(been)f(truncated)i(so)e(as)f(to)h(\002t)e(on)i(the)g (page\).)51 b(This)30 b(sho)n(ws)h(the)g(huge)g(bene\002t)h(that)120 3745 y(short)25 b(jobs)f(obtain)h(by)e(being)i(able)f(to)g(steal)g (idle)g(c)o(ycles)h(from)e(the)h(long)g(host.)261 3858 y(Again)h(looking)h(at)f(Figure)g(11)g(ro)n(w)e(1,)i(column)g(\(a\))g (we)f(see)h(that)g(the)g(impro)o(v)o(ement)g(of)g Fx(CS-Central-)120 3971 y(Queue)19 b FC(o)o(v)o(er)j Fx(CS-Immediate-Di)o(sp)o(at)o(ch)15 b FC(is)21 b(also)i(v)n(ast.)29 b(As)21 b Fu(\032)2374 3985 y Ft(S)2450 3971 y Fr(!)k Fs(1)p Fu(:)p Fs(3)p FC(,)d(the)h(mean)f (response)i(time)e(un-)120 4084 y(der)c Fx(CS-Immediate-Dis)o(pa)o(tc)o (h)11 b FC(goes)19 b(to)f(in\002nity)h(whereas)g(it)f(is)g(only)h (around)g(7)f(under)h Fx(CS-Central-)120 4197 y(Queue)p FC(.)34 b(This)26 b(mak)o(es)h(sense)h(since)f(under)h Fx(CS-Immediate-D)o(isp)o(at)o(ch)19 b FC(only)27 b Fy(ne)o(w)f FC(short)h(arri)n(v)n(als)h(can)120 4310 y(bene\002t)23 b(from)g(idle)g(c)o(ycles,)h(whereas)f(under)h Fx(CS-Central-Queu)o(e) 16 b FC(the)23 b(long)g(host,)h(when)e(seeing)j(no)d(long)120 4423 y(jobs,)i(can)g(tak)o(e)g(on)g(short)g(jobs)h(already)g(w)o (aiting.)261 4535 y(Looking)j(at)f(Figure)g(11)g(ro)n(w)f(1,)h(columns) h(\(b\))f(and)g(\(c\),)h(we)e(see)h(that)g(trends)h(are)f(similar)h(to) f(column)g(\(a\),)120 4648 y(with)c(only)i(the)f(absolute)h(magnitude)h (of)d(the)h(numbers)h(gro)n(wing.)261 4761 y(Ne)o(xt)f(we)g(look)i(at)e (Figure)h(11)g(ro)n(w)f(2,)h(column)g(\(a\))g(\(where)g(shorts)h(and)f (longs)h(ha)n(v)o(e)g(mean)e(size)i Fs(1)e FC(and)h(we)120 4874 y(\002x)19 b Fu(\032)282 4889 y Ft(l)334 4874 y Fs(=)25 b(0)p Fu(:)p Fs(5)p FC(\))20 b(and)h(\002nd)f(that)h(the)f (penalty)i(imposed)g(on)e(long)h(jobs)g(by)g(c)o(ycle)f(stealing)j(is)d (relati)n(v)o(ely)i(small.)28 b(The)120 4987 y(penalty)f(increases)h (with)e Fu(\032)1004 5001 y Ft(S)1054 4987 y FC(,)f(b)n(ut)h(e)n(v)o (en)g(when)g Fu(\032)1703 5001 y Ft(S)1782 4987 y Fs(=)j(1)p FC(,)c(the)h(penalty)i(to)d(long)h(jobs)h(is)e(only)h(20\045)g(under)g Fx(CS-)120 5100 y(Central-Queue)16 b FC(and)23 b(50\045)g(under)h Fx(CS-Immediate-D)o(is)o(pa)o(tc)o(h)16 b FC(\(compared)24 b(with)f(the)g(unbounded)1875 5349 y(21)p eop %%Page: 22 24 22 23 bop 405 68 a FF(V)-11 b(alidation)24 b(against)f(Simulation)h (\226)g(Immediate)g(Dispatch,)g(Performance)i(of)f(Shorts)p 405 103 3030 4 v 117 114 a 8170093 7104430 3617996 11972280 36640440 40521564 startTexFig 117 114 a %%BeginDocument: ../figures/validationsimIDrhos9_11shorts.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationsimIDrhos9_11shorts.eps %%CreationDate: 06/06/2002 10:45:58 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 55 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 55 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 448 -48 6023 5208 MR c np 92 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 898 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 898 4616 5 MP stroke 4 w DO SO 6 w 0 sg 898 4616 mt 6255 4616 L 898 388 mt 6255 388 L 898 4616 mt 898 388 L 6255 4616 mt 6255 388 L 898 4616 mt 6255 4616 L 898 4616 mt 898 388 L 898 4616 mt 898 4562 L 898 389 mt 898 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 732 4873 mt (0.2) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3344 4873 mt (0.55) s 6255 4616 mt 6255 4562 L 6255 389 mt 6255 442 L 6089 4873 mt (0.9) s 898 4616 mt 952 4616 L 6255 4616 mt 6202 4616 L 731 4705 mt (2) s 898 3770 mt 952 3770 L 6255 3770 mt 6202 3770 L 731 3859 mt (3) s 898 2925 mt 952 2925 L 6255 2925 mt 6202 2925 L 731 3014 mt (4) s 898 2079 mt 952 2079 L 6255 2079 mt 6202 2079 L 731 2168 mt (5) s 898 1234 mt 952 1234 L 6255 1234 mt 6202 1234 L 731 1323 mt (6) s 898 389 mt 952 389 L 6255 389 mt 6202 389 L 731 478 mt (7) s 898 4616 mt 6255 4616 L 898 388 mt 6255 388 L 898 4616 mt 898 388 L 6255 4616 mt 6255 388 L gs 898 389 5358 4228 MR c np 24 w 1530 -2389 1531 -1128 1530 -613 1664 4527 4 MP stroke gr 24 w gs 1566 299 4788 4327 MR c np 36 36 1664 4527 FO 36 36 3194 3914 FO 36 36 4725 2786 FO 36 36 6255 397 FO gr gs 898 389 5358 4228 MR c np DA 1530 -2410 1531 -1115 1530 -609 1664 4529 4 MP stroke gr DA gs 1566 297 4788 4331 MR c np SO 36 36 1664 4529 FO 36 36 3194 3920 FO 36 36 4725 2805 FO 36 36 6255 395 FO DA gr gs 898 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 676 4269 mt -90 rotate (mean response time of short jobs) s 90 rotate 1986 198 mt (Immediate Dispatch. rhos = .9) s SO 6 w 1 sg 0 598 1920 0 0 -598 959 1047 4 MP PP -1920 0 0 598 1920 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 959 1047 mt 2879 1047 L 959 1047 mt 959 449 L 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 1627 694 mt (Simulation) s 1627 971 mt (Analysis) s gs 959 449 1921 599 MR c np 24 w 401 0 1092 613 2 MP stroke gs 1195 515 197 197 MR c np 36 36 1293 613 FO gr DA 401 0 1092 891 2 MP stroke SO gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 1378 114 a 8170093 7104430 3617996 11972280 36640440 40521564 startTexFig 1378 114 a %%BeginDocument: ../figures/validationsimIDrhos9_110shorts.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationsimIDrhos9_110shorts.eps %%CreationDate: 06/06/2002 10:46:00 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 55 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 55 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 448 -48 6023 5208 MR c np 92 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5357 0 0 -4227 898 4616 4 MP PP -5357 0 0 4227 5357 0 0 -4227 898 4616 5 MP stroke 4 w DO SO 6 w 0 sg 898 4616 mt 6255 4616 L 898 389 mt 6255 389 L 898 4616 mt 898 389 L 6255 4616 mt 6255 389 L 898 4616 mt 6255 4616 L 898 4616 mt 898 389 L 898 4616 mt 898 4562 L 898 389 mt 898 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 732 4873 mt (0.2) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3344 4873 mt (0.55) s 6255 4616 mt 6255 4562 L 6255 389 mt 6255 442 L 6089 4873 mt (0.9) s 898 4616 mt 952 4616 L 6255 4616 mt 6202 4616 L 731 4705 mt (2) s 898 4012 mt 952 4012 L 6255 4012 mt 6202 4012 L 731 4101 mt (3) s 898 3408 mt 952 3408 L 6255 3408 mt 6202 3408 L 731 3497 mt (4) s 898 2804 mt 952 2804 L 6255 2804 mt 6202 2804 L 731 2893 mt (5) s 898 2200 mt 952 2200 L 6255 2200 mt 6202 2200 L 731 2289 mt (6) s 898 1596 mt 952 1596 L 6255 1596 mt 6202 1596 L 731 1685 mt (7) s 898 992 mt 952 992 L 6255 992 mt 6202 992 L 731 1081 mt (8) s 898 389 mt 952 389 L 6255 389 mt 6202 389 L 731 478 mt (9) s 898 4616 mt 6255 4616 L 898 389 mt 6255 389 L 898 4616 mt 898 389 L 6255 4616 mt 6255 389 L gs 898 389 5358 4228 MR c np 24 w 1530 -1672 1531 -1026 1530 -661 1664 4301 4 MP stroke gr 24 w gs 1566 844 4788 3556 MR c np 36 36 1664 4301 FO 36 36 3194 3640 FO 36 36 4725 2614 FO 36 36 6255 942 FO gr gs 898 389 5358 4228 MR c np DA 1530 -1434 1531 -905 1530 -606 1664 4319 4 MP stroke gr DA gs 1566 1276 4788 3142 MR c np SO 36 36 1664 4319 FO 36 36 3194 3713 FO 36 36 4725 2808 FO 36 36 6255 1374 FO DA gr gs 898 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 676 4269 mt -90 rotate (mean response time of short jobs) s 90 rotate 1986 198 mt (Immediate Dispatch. rhos = .9) s SO 6 w 1 sg 0 598 1920 0 0 -598 959 1047 4 MP PP -1920 0 0 598 1920 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 959 1047 mt 2879 1047 L 959 1047 mt 959 449 L 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 1627 694 mt (Simulation) s 1627 971 mt (Analysis) s gs 959 449 1921 599 MR c np 24 w 401 0 1092 613 2 MP stroke gs 1195 515 197 197 MR c np 36 36 1293 613 FO gr DA 401 0 1092 891 2 MP stroke SO gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 2638 114 a 8383225 7104430 2894397 11972280 36640440 40521564 startTexFig 2638 114 a %%BeginDocument: ../figures/validationsimIDrhos9_101shorts.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationsimIDrhos9_101shorts.eps %%CreationDate: 06/06/2002 10:46:01 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 44 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 44 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 315 -48 6156 5208 MR c np 92 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 898 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 898 4616 5 MP stroke 4 w DO SO 6 w 0 sg 898 4616 mt 6255 4616 L 898 388 mt 6255 388 L 898 4616 mt 898 388 L 6255 4616 mt 6255 388 L 898 4616 mt 6255 4616 L 898 4616 mt 898 388 L 898 4616 mt 898 4562 L 898 389 mt 898 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 732 4873 mt (0.2) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3344 4873 mt (0.55) s 6255 4616 mt 6255 4562 L 6255 389 mt 6255 442 L 6089 4873 mt (0.9) s 898 4616 mt 952 4616 L 6255 4616 mt 6202 4616 L 598 4705 mt (20) s 898 3770 mt 952 3770 L 6255 3770 mt 6202 3770 L 598 3859 mt (30) s 898 2925 mt 952 2925 L 6255 2925 mt 6202 2925 L 598 3014 mt (40) s 898 2079 mt 952 2079 L 6255 2079 mt 6202 2079 L 598 2168 mt (50) s 898 1234 mt 952 1234 L 6255 1234 mt 6202 1234 L 598 1323 mt (60) s 898 389 mt 952 389 L 6255 389 mt 6202 389 L 598 478 mt (70) s 898 4616 mt 6255 4616 L 898 388 mt 6255 388 L 898 4616 mt 898 388 L 6255 4616 mt 6255 388 L gs 898 389 5358 4228 MR c np 24 w 1530 -2442 1531 -1006 1530 -527 1664 4614 4 MP stroke gr 24 w gs 1566 541 4788 4172 MR c np 36 36 1664 4614 FO 36 36 3194 4087 FO 36 36 4725 3081 FO 36 36 6255 639 FO gr gs 898 389 5358 4228 MR c np DA 1530 -2392 1531 -1005 1530 -527 1664 4614 4 MP stroke gr DA gs 1566 592 4788 4121 MR c np SO 36 36 1664 4614 FO 36 36 3194 4087 FO 36 36 4725 3082 FO 36 36 6255 690 FO DA gr gs 898 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 543 4269 mt -90 rotate (mean response time of short jobs) s 90 rotate 1986 198 mt (Immediate Dispatch. rhos = .9) s SO 6 w 1 sg 0 598 1920 0 0 -598 959 1047 4 MP PP -1920 0 0 598 1920 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 959 1047 mt 2879 1047 L 959 1047 mt 959 449 L 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 1627 694 mt (Simulation) s 1627 971 mt (Analysis) s gs 959 449 1921 599 MR c np 24 w 401 0 1092 613 2 MP stroke gs 1195 515 197 197 MR c np 36 36 1293 613 FO gr DA 401 0 1092 891 2 MP stroke SO gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 260 1127 a FC(\(a\))e(shorts)i(1,)e(longs)i(1)646 b(\(b\))24 b(shorts)h(1,)d(longs)j(10)647 b(\(c\))23 b(shorts)i(10,)e(longs)i(1) 408 1353 y FF(V)-11 b(alidation)23 b(against)h(Simulation)f(\226)i (Immediate)f(Dispatch,)g(Performance)i(of)f(Longs)p 408 1388 3024 4 v 81 1400 a 8383225 7104430 2894397 11972280 36640440 40521564 startTexFig 81 1400 a %%BeginDocument: ../figures/validationsimIDrhos9_11longs.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationsimIDrhos9_11longs.eps %%CreationDate: 06/06/2002 10:46:03 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 44 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 44 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 315 -48 6156 5208 MR c np 92 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5357 0 0 -4227 898 4616 4 MP PP -5357 0 0 4227 5357 0 0 -4227 898 4616 5 MP stroke 4 w DO SO 6 w 0 sg 898 4616 mt 6255 4616 L 898 389 mt 6255 389 L 898 4616 mt 898 389 L 6255 4616 mt 6255 389 L 898 4616 mt 6255 4616 L 898 4616 mt 898 389 L 898 4616 mt 898 4562 L 898 389 mt 898 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 732 4873 mt (0.2) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3344 4873 mt (0.55) s 6255 4616 mt 6255 4562 L 6255 389 mt 6255 442 L 6089 4873 mt (0.9) s 898 4616 mt 952 4616 L 6255 4616 mt 6202 4616 L 731 4705 mt (0) s 898 3911 mt 952 3911 L 6255 3911 mt 6202 3911 L 731 4000 mt (2) s 898 3207 mt 952 3207 L 6255 3207 mt 6202 3207 L 731 3296 mt (4) s 898 2502 mt 952 2502 L 6255 2502 mt 6202 2502 L 731 2591 mt (6) s 898 1798 mt 952 1798 L 6255 1798 mt 6202 1798 L 731 1887 mt (8) s 898 1093 mt 952 1093 L 6255 1093 mt 6202 1093 L 598 1182 mt (10) s 898 389 mt 952 389 L 6255 389 mt 6202 389 L 598 478 mt (12) s 898 4616 mt 6255 4616 L 898 389 mt 6255 389 L 898 4616 mt 898 389 L 6255 4616 mt 6255 389 L gs 898 389 5358 4228 MR c np 24 w 1530 -2335 1531 -469 1530 -203 1664 3945 4 MP stroke gr 24 w gs 1566 840 4788 3204 MR c np 36 36 1664 3945 FO 36 36 3194 3742 FO 36 36 4725 3273 FO 36 36 6255 938 FO gr gs 898 389 5358 4228 MR c np DA 1530 -2348 1531 -470 1530 -201 1664 3945 4 MP stroke gr DA gs 1566 828 4788 3216 MR c np SO 36 36 1664 3945 FO 36 36 3194 3744 FO 36 36 4725 3274 FO 36 36 6255 926 FO DA gr gs 898 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 543 4230 mt -90 rotate (mean response time of long jobs) s 90 rotate 1986 198 mt (Immediate Dispatch. rhos = .9) s SO 6 w 1 sg 0 598 1920 0 0 -598 959 1047 4 MP PP -1920 0 0 598 1920 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 959 1047 mt 2879 1047 L 959 1047 mt 959 449 L 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 1627 694 mt (Simulation) s 1627 971 mt (Analysis) s gs 959 449 1921 599 MR c np 24 w 401 0 1092 613 2 MP stroke gs 1195 515 197 197 MR c np 36 36 1293 613 FO gr DA 401 0 1092 891 2 MP stroke SO gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 1369 1400 a 8525316 7104430 2170798 11972280 36640440 40521564 startTexFig 1369 1400 a %%BeginDocument: ../figures/validationsimIDrhos9_110longs.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationsimIDrhos9_110longs.eps %%CreationDate: 06/06/2002 10:46:05 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 33 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 33 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 181 -48 6290 5208 MR c np 92 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 898 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 898 4616 5 MP stroke 4 w DO SO 6 w 0 sg 898 4616 mt 6255 4616 L 898 388 mt 6255 388 L 898 4616 mt 898 388 L 6255 4616 mt 6255 388 L 898 4616 mt 6255 4616 L 898 4616 mt 898 388 L 898 4616 mt 898 4562 L 898 389 mt 898 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 732 4873 mt (0.2) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3344 4873 mt (0.55) s 6255 4616 mt 6255 4562 L 6255 389 mt 6255 442 L 6089 4873 mt (0.9) s 898 4616 mt 952 4616 L 6255 4616 mt 6202 4616 L 731 4705 mt (0) s 898 3911 mt 952 3911 L 6255 3911 mt 6202 3911 L 598 4000 mt (20) s 898 3207 mt 952 3207 L 6255 3207 mt 6202 3207 L 598 3296 mt (40) s 898 2502 mt 952 2502 L 6255 2502 mt 6202 2502 L 598 2591 mt (60) s 898 1798 mt 952 1798 L 6255 1798 mt 6202 1798 L 598 1887 mt (80) s 898 1093 mt 952 1093 L 6255 1093 mt 6202 1093 L 464 1182 mt (100) s 898 389 mt 952 389 L 6255 389 mt 6202 389 L 464 478 mt (120) s 898 4616 mt 6255 4616 L 898 388 mt 6255 388 L 898 4616 mt 898 388 L 6255 4616 mt 6255 388 L gs 898 389 5358 4228 MR c np 24 w 1530 -2375 1531 -482 1530 -206 1664 4098 4 MP stroke gr 24 w gs 1566 937 4788 3260 MR c np 36 36 1664 4098 FO 36 36 3194 3892 FO 36 36 4725 3410 FO 36 36 6255 1035 FO gr gs 898 389 5358 4228 MR c np DA 1530 -2348 1531 -469 1530 -202 1664 4096 4 MP stroke gr DA gs 1566 979 4788 3216 MR c np SO 36 36 1664 4096 FO 36 36 3194 3894 FO 36 36 4725 3425 FO 36 36 6255 1077 FO DA gr gs 898 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 409 4230 mt -90 rotate (mean response time of long jobs) s 90 rotate 1986 198 mt (Immediate Dispatch. rhos = .9) s SO 6 w 1 sg 0 598 1920 0 0 -598 959 1047 4 MP PP -1920 0 0 598 1920 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 959 1047 mt 2879 1047 L 959 1047 mt 959 449 L 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 1627 694 mt (Simulation) s 1627 971 mt (Analysis) s gs 959 449 1921 599 MR c np 24 w 401 0 1092 613 2 MP stroke gs 1195 515 197 197 MR c np 36 36 1293 613 FO gr DA 401 0 1092 891 2 MP stroke SO gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 2674 1400 a 8383225 7104430 2894397 11972280 36640440 40521564 startTexFig 2674 1400 a %%BeginDocument: ../figures/validationsimIDrhos9_101longs.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationsimIDrhos9_101longs.eps %%CreationDate: 06/06/2002 10:46:06 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 44 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 44 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 315 -48 6156 5208 MR c np 92 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 898 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 898 4616 5 MP stroke 4 w DO SO 6 w 0 sg 898 4616 mt 6255 4616 L 898 388 mt 6255 388 L 898 4616 mt 898 388 L 6255 4616 mt 6255 388 L 898 4616 mt 6255 4616 L 898 4616 mt 898 388 L 898 4616 mt 898 4562 L 898 389 mt 898 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 732 4873 mt (0.2) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3344 4873 mt (0.55) s 6255 4616 mt 6255 4562 L 6255 389 mt 6255 442 L 6089 4873 mt (0.9) s 898 4616 mt 952 4616 L 6255 4616 mt 6202 4616 L 731 4705 mt (6) s 898 3770 mt 952 3770 L 6255 3770 mt 6202 3770 L 731 3859 mt (8) s 898 2925 mt 952 2925 L 6255 2925 mt 6202 2925 L 598 3014 mt (10) s 898 2079 mt 952 2079 L 6255 2079 mt 6202 2079 L 598 2168 mt (12) s 898 1234 mt 952 1234 L 6255 1234 mt 6202 1234 L 598 1323 mt (14) s 898 389 mt 952 389 L 6255 389 mt 6202 389 L 598 478 mt (16) s 898 4616 mt 6255 4616 L 898 388 mt 6255 388 L 898 4616 mt 898 388 L 6255 4616 mt 6255 388 L gs 898 389 5358 4228 MR c np 24 w 1530 -2793 1531 -565 1530 -244 1664 4545 4 MP stroke gr 24 w gs 1566 845 4788 3799 MR c np 36 36 1664 4545 FO 36 36 3194 4301 FO 36 36 4725 3736 FO 36 36 6255 943 FO gr gs 898 389 5358 4228 MR c np DA 1530 -2818 1531 -564 1530 -242 1664 4546 4 MP stroke gr DA gs 1566 824 4788 3821 MR c np SO 36 36 1664 4546 FO 36 36 3194 4304 FO 36 36 4725 3740 FO 36 36 6255 922 FO DA gr gs 898 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 543 4230 mt -90 rotate (mean response time of long jobs) s 90 rotate 1986 198 mt (Immediate Dispatch. rhos = .9) s SO 6 w 1 sg 0 598 1920 0 0 -598 959 1047 4 MP PP -1920 0 0 598 1920 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 959 1047 mt 2879 1047 L 959 1047 mt 959 449 L 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 1627 694 mt (Simulation) s 1627 971 mt (Analysis) s gs 959 449 1921 599 MR c np 24 w 401 0 1092 613 2 MP stroke gs 1195 515 197 197 MR c np 36 36 1293 613 FO gr DA 401 0 1092 891 2 MP stroke SO gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 260 2413 a FC(\(a\))e(shorts)i(1,)e(longs)i(1)646 b(\(b\))24 b(shorts)h(1,)d(longs)j(10)647 b(\(c\))23 b(shorts)i(10,)e(longs)i(1) 515 2638 y FF(V)-11 b(alidation)23 b(against)h(Simulation)f(\226)i (Central-Queue,)g(Performance)h(of)f(Shorts)p 515 2673 2811 4 v 117 2685 a 8170093 7104430 3617996 11972280 36640440 40521564 startTexFig 117 2685 a %%BeginDocument: ../figures/validationsimCQrhos9_11shorts.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationsimCQrhos9_11shorts.eps %%CreationDate: 06/06/2002 10:46:08 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 55 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 55 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 448 -48 6023 5208 MR c np 92 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5357 0 0 -4227 898 4616 4 MP PP -5357 0 0 4227 5357 0 0 -4227 898 4616 5 MP stroke 4 w DO SO 6 w 0 sg 898 4616 mt 6255 4616 L 898 389 mt 6255 389 L 898 4616 mt 898 389 L 6255 4616 mt 6255 389 L 898 4616 mt 6255 4616 L 898 4616 mt 898 389 L 898 4616 mt 898 4562 L 898 389 mt 898 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 732 4873 mt (0.2) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3344 4873 mt (0.55) s 6255 4616 mt 6255 4562 L 6255 389 mt 6255 442 L 6089 4873 mt (0.9) s 898 4616 mt 952 4616 L 6255 4616 mt 6202 4616 L 731 4705 mt (1) s 898 3911 mt 952 3911 L 6255 3911 mt 6202 3911 L 731 4000 mt (2) s 898 3207 mt 952 3207 L 6255 3207 mt 6202 3207 L 731 3296 mt (3) s 898 2502 mt 952 2502 L 6255 2502 mt 6202 2502 L 731 2591 mt (4) s 898 1798 mt 952 1798 L 6255 1798 mt 6202 1798 L 731 1887 mt (5) s 898 1093 mt 952 1093 L 6255 1093 mt 6202 1093 L 731 1182 mt (6) s 898 389 mt 952 389 L 6255 389 mt 6202 389 L 731 478 mt (7) s 898 4616 mt 6255 4616 L 898 389 mt 6255 389 L 898 4616 mt 898 389 L 6255 4616 mt 6255 389 L gs 898 389 5358 4228 MR c np 24 w 1530 -2103 1531 -758 1530 -360 1664 4174 4 MP stroke gr 24 w gs 1566 855 4788 3418 MR c np 36 36 1664 4174 FO 36 36 3194 3814 FO 36 36 4725 3056 FO 36 36 6255 953 FO gr gs 898 389 5358 4228 MR c np DA 1530 -1964 1531 -731 1530 -350 1664 4176 4 MP stroke gr DA gs 1566 1033 4788 3242 MR c np SO 36 36 1664 4176 FO 36 36 3194 3826 FO 36 36 4725 3095 FO 36 36 6255 1131 FO DA gr gs 898 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 676 4269 mt -90 rotate (mean response time of short jobs) s 90 rotate 2228 198 mt (Central-Queue. rhos = .9) s SO 6 w 1 sg 0 598 1920 0 0 -598 959 1047 4 MP PP -1920 0 0 598 1920 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 959 1047 mt 2879 1047 L 959 1047 mt 959 449 L 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 1627 694 mt (Simulation) s 1627 971 mt (Analysis) s gs 959 449 1921 599 MR c np 24 w 401 0 1092 613 2 MP stroke gs 1195 515 197 197 MR c np 36 36 1293 613 FO gr DA 401 0 1092 891 2 MP stroke SO gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 1378 2685 a 8170093 7104430 3617996 11972280 36640440 40521564 startTexFig 1378 2685 a %%BeginDocument: ../figures/validationsimCQrhos9_110shorts.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationsimCQrhos9_110shorts.eps %%CreationDate: 06/06/2002 10:46:10 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 55 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 55 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 448 -48 6023 5208 MR c np 92 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5357 0 0 -4227 898 4616 4 MP PP -5357 0 0 4227 5357 0 0 -4227 898 4616 5 MP stroke 4 w DO SO 6 w 0 sg 898 4616 mt 6255 4616 L 898 389 mt 6255 389 L 898 4616 mt 898 389 L 6255 4616 mt 6255 389 L 898 4616 mt 6255 4616 L 898 4616 mt 898 389 L 898 4616 mt 898 4562 L 898 389 mt 898 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 732 4873 mt (0.2) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3344 4873 mt (0.55) s 6255 4616 mt 6255 4562 L 6255 389 mt 6255 442 L 6089 4873 mt (0.9) s 898 4616 mt 952 4616 L 6255 4616 mt 6202 4616 L 731 4705 mt (2) s 898 3911 mt 952 3911 L 6255 3911 mt 6202 3911 L 731 4000 mt (3) s 898 3207 mt 952 3207 L 6255 3207 mt 6202 3207 L 731 3296 mt (4) s 898 2502 mt 952 2502 L 6255 2502 mt 6202 2502 L 731 2591 mt (5) s 898 1798 mt 952 1798 L 6255 1798 mt 6202 1798 L 731 1887 mt (6) s 898 1093 mt 952 1093 L 6255 1093 mt 6202 1093 L 731 1182 mt (7) s 898 389 mt 952 389 L 6255 389 mt 6202 389 L 731 478 mt (8) s 898 4616 mt 6255 4616 L 898 389 mt 6255 389 L 898 4616 mt 898 389 L 6255 4616 mt 6255 389 L gs 898 389 5358 4228 MR c np 24 w 1530 -2009 1531 -1163 1530 -701 1664 4531 4 MP stroke gr 24 w gs 1566 560 4788 4070 MR c np 36 36 1664 4531 FO 36 36 3194 3830 FO 36 36 4725 2667 FO 36 36 6255 658 FO gr gs 898 389 5358 4228 MR c np DA 1530 -1825 1531 -1100 1530 -685 1664 4528 4 MP stroke gr DA gs 1566 820 4788 3807 MR c np SO 36 36 1664 4528 FO 36 36 3194 3843 FO 36 36 4725 2743 FO 36 36 6255 918 FO DA gr gs 898 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 676 4269 mt -90 rotate (mean response time of short jobs) s 90 rotate 2228 198 mt (Central-Queue. rhos = .9) s SO 6 w 1 sg 0 598 1920 0 0 -598 959 1047 4 MP PP -1920 0 0 598 1920 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 959 1047 mt 2879 1047 L 959 1047 mt 959 449 L 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 1627 694 mt (Simulation) s 1627 971 mt (Analysis) s gs 959 449 1921 599 MR c np 24 w 401 0 1092 613 2 MP stroke gs 1195 515 197 197 MR c np 36 36 1293 613 FO gr DA 401 0 1092 891 2 MP stroke SO gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 2638 2685 a 8383225 7104430 2894397 11972280 36640440 40521564 startTexFig 2638 2685 a %%BeginDocument: ../figures/validationsimCQrhos9_101shorts.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationsimCQrhos9_101shorts.eps %%CreationDate: 06/06/2002 10:46:11 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 44 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 44 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 315 -48 6156 5208 MR c np 92 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 898 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 898 4616 5 MP stroke 4 w DO SO 6 w 0 sg 898 4616 mt 6255 4616 L 898 388 mt 6255 388 L 898 4616 mt 898 388 L 6255 4616 mt 6255 388 L 898 4616 mt 6255 4616 L 898 4616 mt 898 388 L 898 4616 mt 898 4562 L 898 389 mt 898 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 732 4873 mt (0.2) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3344 4873 mt (0.55) s 6255 4616 mt 6255 4562 L 6255 389 mt 6255 442 L 6089 4873 mt (0.9) s 898 4616 mt 952 4616 L 6255 4616 mt 6202 4616 L 598 4705 mt (10) s 898 3770 mt 952 3770 L 6255 3770 mt 6202 3770 L 598 3859 mt (20) s 898 2925 mt 952 2925 L 6255 2925 mt 6202 2925 L 598 3014 mt (30) s 898 2079 mt 952 2079 L 6255 2079 mt 6202 2079 L 598 2168 mt (40) s 898 1234 mt 952 1234 L 6255 1234 mt 6202 1234 L 598 1323 mt (50) s 898 389 mt 952 389 L 6255 389 mt 6202 389 L 598 478 mt (60) s 898 4616 mt 6255 4616 L 898 388 mt 6255 388 L 898 4616 mt 898 388 L 6255 4616 mt 6255 388 L gs 898 389 5358 4228 MR c np 24 w 1530 -2177 1531 -657 1530 -286 1664 4199 4 MP stroke gr 24 w gs 1566 981 4788 3317 MR c np 36 36 1664 4199 FO 36 36 3194 3913 FO 36 36 4725 3256 FO 36 36 6255 1079 FO gr gs 898 389 5358 4228 MR c np DA 1530 -2140 1531 -612 1530 -258 1664 4219 4 MP stroke gr DA gs 1566 1111 4788 3207 MR c np SO 36 36 1664 4219 FO 36 36 3194 3961 FO 36 36 4725 3349 FO 36 36 6255 1209 FO DA gr gs 898 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 543 4230 mt -90 rotate (mean response time of long jobs) s 90 rotate 2228 198 mt (Central-Queue. rhos = .9) s SO 6 w 1 sg 0 598 1920 0 0 -598 959 1047 4 MP PP -1920 0 0 598 1920 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 959 1047 mt 2879 1047 L 959 1047 mt 959 449 L 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 1627 694 mt (Simulation) s 1627 971 mt (Analysis) s gs 959 449 1921 599 MR c np 24 w 401 0 1092 613 2 MP stroke gs 1195 515 197 197 MR c np 36 36 1293 613 FO gr DA 401 0 1092 891 2 MP stroke SO gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 260 3698 a FC(\(a\))e(shorts)i(1,)e(longs)i(1)646 b(\(b\))24 b(shorts)h(1,)d(longs)j(10)647 b(\(c\))23 b(shorts)i(10,)e(longs)i(1) 517 3924 y FF(V)-11 b(alidation)24 b(against)f(Simulation)h(\226)g (Central-Queue,)i(Performance)g(of)f(Longs)p 517 3958 2806 4 v 81 3970 a 8383225 7104430 2894397 11972280 36640440 40521564 startTexFig 81 3970 a %%BeginDocument: ../figures/validationsimCQrhos9_11longs.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationsimCQrhos9_11longs.eps %%CreationDate: 06/06/2002 10:46:13 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 44 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 44 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 315 -48 6156 5208 MR c np 92 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5357 0 0 -4227 898 4616 4 MP PP -5357 0 0 4227 5357 0 0 -4227 898 4616 5 MP stroke 4 w DO SO 6 w 0 sg 898 4616 mt 6255 4616 L 898 389 mt 6255 389 L 898 4616 mt 898 389 L 6255 4616 mt 6255 389 L 898 4616 mt 6255 4616 L 898 4616 mt 898 389 L 898 4616 mt 898 4562 L 898 389 mt 898 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 732 4873 mt (0.2) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3344 4873 mt (0.55) s 6255 4616 mt 6255 4562 L 6255 389 mt 6255 442 L 6089 4873 mt (0.9) s 898 4616 mt 952 4616 L 6255 4616 mt 6202 4616 L 731 4705 mt (0) s 898 3911 mt 952 3911 L 6255 3911 mt 6202 3911 L 731 4000 mt (2) s 898 3207 mt 952 3207 L 6255 3207 mt 6202 3207 L 731 3296 mt (4) s 898 2502 mt 952 2502 L 6255 2502 mt 6202 2502 L 731 2591 mt (6) s 898 1798 mt 952 1798 L 6255 1798 mt 6202 1798 L 731 1887 mt (8) s 898 1093 mt 952 1093 L 6255 1093 mt 6202 1093 L 598 1182 mt (10) s 898 389 mt 952 389 L 6255 389 mt 6202 389 L 598 478 mt (12) s 898 4616 mt 6255 4616 L 898 389 mt 6255 389 L 898 4616 mt 898 389 L 6255 4616 mt 6255 389 L gs 898 389 5358 4228 MR c np 24 w 1530 -2375 1531 -484 1530 -211 1664 4052 4 MP stroke gr 24 w gs 1566 884 4788 3267 MR c np 36 36 1664 4052 FO 36 36 3194 3841 FO 36 36 4725 3357 FO 36 36 6255 982 FO gr gs 898 389 5358 4228 MR c np DA 1530 -2373 1531 -484 1530 -211 1664 4052 4 MP stroke gr DA gs 1566 886 4788 3265 MR c np SO 36 36 1664 4052 FO 36 36 3194 3841 FO 36 36 4725 3357 FO 36 36 6255 984 FO DA gr gs 898 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 543 4230 mt -90 rotate (mean response time of long jobs) s 90 rotate 2228 198 mt (Central-Queue. rhos = .9) s SO 6 w 1 sg 0 598 1920 0 0 -598 959 1047 4 MP PP -1920 0 0 598 1920 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 959 1047 mt 2879 1047 L 959 1047 mt 959 449 L 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 1627 694 mt (Simulation) s 1627 971 mt (Analysis) s gs 959 449 1921 599 MR c np 24 w 401 0 1092 613 2 MP stroke gs 1195 515 197 197 MR c np 36 36 1293 613 FO gr DA 401 0 1092 891 2 MP stroke SO gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 1369 3970 a 8525316 7104430 2170798 11972280 36640440 40521564 startTexFig 1369 3970 a %%BeginDocument: ../figures/validationsimCQrhos9_110longs.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationsimCQrhos9_110longs.eps %%CreationDate: 06/06/2002 10:46:15 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 33 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 33 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 181 -48 6290 5208 MR c np 92 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 898 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 898 4616 5 MP stroke 4 w DO SO 6 w 0 sg 898 4616 mt 6255 4616 L 898 388 mt 6255 388 L 898 4616 mt 898 388 L 6255 4616 mt 6255 388 L 898 4616 mt 6255 4616 L 898 4616 mt 898 388 L 898 4616 mt 898 4562 L 898 389 mt 898 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 732 4873 mt (0.2) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3344 4873 mt (0.55) s 6255 4616 mt 6255 4562 L 6255 389 mt 6255 442 L 6089 4873 mt (0.9) s 898 4616 mt 952 4616 L 6255 4616 mt 6202 4616 L 731 4705 mt (0) s 898 3911 mt 952 3911 L 6255 3911 mt 6202 3911 L 598 4000 mt (20) s 898 3207 mt 952 3207 L 6255 3207 mt 6202 3207 L 598 3296 mt (40) s 898 2502 mt 952 2502 L 6255 2502 mt 6202 2502 L 598 2591 mt (60) s 898 1798 mt 952 1798 L 6255 1798 mt 6202 1798 L 598 1887 mt (80) s 898 1093 mt 952 1093 L 6255 1093 mt 6202 1093 L 464 1182 mt (100) s 898 389 mt 952 389 L 6255 389 mt 6202 389 L 464 478 mt (120) s 898 4616 mt 6255 4616 L 898 388 mt 6255 388 L 898 4616 mt 898 388 L 6255 4616 mt 6255 388 L gs 898 389 5358 4228 MR c np 24 w 1530 -2355 1531 -466 1530 -207 1664 4109 4 MP stroke gr 24 w gs 1566 983 4788 3225 MR c np 36 36 1664 4109 FO 36 36 3194 3902 FO 36 36 4725 3436 FO 36 36 6255 1081 FO gr gs 898 389 5358 4228 MR c np DA 1530 -2350 1531 -470 1530 -202 1664 4107 4 MP stroke gr DA gs 1566 987 4788 3219 MR c np SO 36 36 1664 4107 FO 36 36 3194 3905 FO 36 36 4725 3435 FO 36 36 6255 1085 FO DA gr gs 898 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 409 4230 mt -90 rotate (mean response time of long jobs) s 90 rotate 2228 198 mt (Central-Queue. rhos = .9) s SO 6 w 1 sg 0 598 1920 0 0 -598 959 1047 4 MP PP -1920 0 0 598 1920 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 959 1047 mt 2879 1047 L 959 1047 mt 959 449 L 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 1627 694 mt (Simulation) s 1627 971 mt (Analysis) s gs 959 449 1921 599 MR c np 24 w 401 0 1092 613 2 MP stroke gs 1195 515 197 197 MR c np 36 36 1293 613 FO gr DA 401 0 1092 891 2 MP stroke SO gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 2674 3970 a 8383225 7104430 2894397 11972280 36640440 40521564 startTexFig 2674 3970 a %%BeginDocument: ../figures/validationsimCQrhos9_101longs.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: validationsimCQrhos9_101longs.eps %%CreationDate: 06/06/2002 10:46:17 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 44 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 44 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 315 -48 6156 5208 MR c np 92 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5357 0 0 -4227 898 4616 4 MP PP -5357 0 0 4227 5357 0 0 -4227 898 4616 5 MP stroke 4 w DO SO 6 w 0 sg 898 4616 mt 6255 4616 L 898 389 mt 6255 389 L 898 4616 mt 898 389 L 6255 4616 mt 6255 389 L 898 4616 mt 6255 4616 L 898 4616 mt 898 389 L 898 4616 mt 898 4562 L 898 389 mt 898 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 732 4873 mt (0.2) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3344 4873 mt (0.55) s 6255 4616 mt 6255 4562 L 6255 389 mt 6255 442 L 6089 4873 mt (0.9) s 898 4616 mt 952 4616 L 6255 4616 mt 6202 4616 L 731 4705 mt (2) s 898 3911 mt 952 3911 L 6255 3911 mt 6202 3911 L 731 4000 mt (4) s 898 3207 mt 952 3207 L 6255 3207 mt 6202 3207 L 731 3296 mt (6) s 898 2502 mt 952 2502 L 6255 2502 mt 6202 2502 L 731 2591 mt (8) s 898 1798 mt 952 1798 L 6255 1798 mt 6202 1798 L 598 1887 mt (10) s 898 1093 mt 952 1093 L 6255 1093 mt 6202 1093 L 598 1182 mt (12) s 898 389 mt 952 389 L 6255 389 mt 6202 389 L 598 478 mt (14) s 898 4616 mt 6255 4616 L 898 389 mt 6255 389 L 898 4616 mt 898 389 L 6255 4616 mt 6255 389 L gs 898 389 5358 4228 MR c np 24 w 1530 -2650 1531 -678 1530 -341 1664 4186 4 MP stroke gr 24 w gs 1566 419 4788 3866 MR c np 36 36 1664 4186 FO 36 36 3194 3845 FO 36 36 4725 3167 FO 36 36 6255 517 FO gr gs 898 389 5358 4228 MR c np DA 1530 -2683 1531 -686 1530 -349 1664 4180 4 MP stroke gr DA gs 1566 364 4788 3915 MR c np SO 36 36 1664 4180 FO 36 36 3194 3831 FO 36 36 4725 3145 FO 36 36 6255 462 FO DA gr gs 898 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 543 4230 mt -90 rotate (mean response time of long jobs) s 90 rotate 2228 198 mt (Central-Queue. rhos = .9) s SO 6 w 1 sg 0 598 1920 0 0 -598 959 1047 4 MP PP -1920 0 0 598 1920 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 959 1047 mt 2879 1047 L 959 1047 mt 959 449 L 959 1047 mt 2879 1047 L 959 449 mt 2879 449 L 959 1047 mt 959 449 L 2879 1047 mt 2879 449 L 1627 694 mt (Simulation) s 1627 971 mt (Analysis) s gs 959 449 1921 599 MR c np 24 w 401 0 1092 613 2 MP stroke gs 1195 515 197 197 MR c np 36 36 1293 613 FO gr DA 401 0 1092 891 2 MP stroke SO gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 260 4983 a FC(\(a\))e(shorts)i(1,)e(longs)i(1)646 b(\(b\))24 b(shorts)h(1,)d(longs)j(10)647 b(\(c\))23 b(shorts)i(10,)e(longs)i(1) 120 5179 y(Figure)d(10:)29 b Fy(V)-10 b(alidation)23 b(of)f(Analysis)h(a)o(gainst)h(simulation.)30 b(Row)20 b(1)i(shows)g(performance)i(of)e(short)g(jobs)h(under)120 5292 y Fx(CS-Immediate-Di)o(sp)o(at)o(ch)15 b Fy(wher)m(e)23 b(we)f(\002x)h Fu(\032)1806 5306 y Ft(S)1882 5292 y Fs(=)i(0)p Fu(:)p Fs(9)e Fy(and)g Fu(\032)2321 5306 y Ft(L)2395 5292 y Fy(varies.)30 b(Row)21 b(2)i(shows)g(performance)i(of)120 5405 y(long)e(jobs)f(under)h Fx(CS-Immediate-Di)o(sp)o(at)o(ch)14 b Fy(wher)m(e)22 b(we)f(\002x)h Fu(\032)2390 5419 y Ft(S)2466 5405 y Fs(=)j(0)p Fu(:)p Fs(9)d Fy(and)g Fu(\032)2903 5419 y Ft(L)2976 5405 y Fy(varies.)30 b(Row)20 b(3)i(shows)120 5518 y(performance)33 b(of)d(short)i(jobs)f(under)h Fx(CS-Central-Que)o (ue)23 b Fy(wher)m(e)31 b Fu(\032)2552 5532 y Ft(S)2640 5518 y Fs(=)38 b(0)p Fu(:)p Fs(9)31 b Fy(and)g Fu(\032)3108 5532 y Ft(L)3190 5518 y Fy(varies.)50 b(Row)30 b(4)120 5631 y(shows)24 b(performance)i(of)e(long)g(jobs)g(under)h Fx(CS-Central-Queu)o(e)17 b Fy(wher)m(e)23 b Fu(\032)2723 5645 y Ft(S)2799 5631 y Fs(=)i(0)p Fu(:)p Fs(9)f Fy(and)g Fu(\032)3240 5645 y Ft(L)3315 5631 y Fy(varies.)1875 5349 y FC(22)p eop %%Page: 23 25 23 24 bop 968 68 a FF(Ho)n(w)24 b(shorts)g(gain)g(from)h(c)o (ycle-stealing)f(\226)g Fe(\032)2563 83 y Ft(L)2643 68 y Fd(=)k(0)p Fe(:)p Fd(5)p 968 103 1904 4 v 81 114 a 8383225 7104430 2894397 11972280 36640440 40521564 startTexFig 81 114 a %%BeginDocument: ../figures/results_rhol5expshorts11.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol5expshorts11.eps %%CreationDate: 07/25/2002 23:16:22 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 44 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 44 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 315 -48 6157 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.5) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4404 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.5) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 731 3859 mt (5) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 598 3014 mt (10) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 598 2168 mt (15) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 598 1323 mt (20) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 598 478 mt (25) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 178 -1691 179 -563 178 -282 179 -169 179 -113 178 -80 179 -61 178 -47 179 -37 178 -31 179 -26 179 -21 178 -19 179 -16 178 -14 179 -13 178 -11 179 -10 178 -8 899 4446 20 MP stroke SO 178 -860 179 -384 179 -218 178 -139 179 -97 178 -71 179 -55 178 -42 179 -35 179 -28 178 -24 179 -20 178 -16 179 -15 178 -13 179 -11 179 -9 178 -8 179 -8 178 -6 179 -6 178 -5 179 -4 1077 4443 24 MP stroke gs 979 2271 4304 2271 MR c np 36 36 1077 4443 FO 36 36 1256 4439 FO 36 36 1434 4434 FO 36 36 1613 4428 FO 36 36 1791 4422 FO 36 36 1970 4414 FO 36 36 2148 4406 FO 36 36 2327 4397 FO 36 36 2506 4386 FO 36 36 2684 4373 FO 36 36 2863 4358 FO 36 36 3041 4342 FO 36 36 3220 4322 FO 36 36 3398 4298 FO 36 36 3577 4270 FO 36 36 3756 4235 FO 36 36 3934 4193 FO 36 36 4113 4138 FO 36 36 4291 4067 FO 36 36 4470 3970 FO 36 36 4648 3831 FO 36 36 4827 3613 FO 36 36 5006 3229 FO 36 36 5184 2369 FO gr DD 178 -741 179 -370 178 -221 179 -147 178 -105 179 -78 179 -61 178 -48 179 -39 178 -32 179 -27 178 -23 179 -19 179 -17 178 -15 179 -12 178 -11 179 -10 178 -9 179 -8 179 -7 178 -6 179 -5 178 -5 179 -5 178 -4 179 -3 1077 4443 28 MP stroke gs 979 2317 5018 2225 MR c np SO 36 36 1077 4443 FO 36 36 1256 4440 FO 36 36 1434 4436 FO 36 36 1613 4431 FO 36 36 1791 4426 FO 36 36 1970 4421 FO 36 36 2148 4415 FO 36 36 2327 4408 FO 36 36 2506 4400 FO 36 36 2684 4391 FO 36 36 2863 4381 FO 36 36 3041 4370 FO 36 36 3220 4358 FO 36 36 3398 4343 FO 36 36 3577 4326 FO 36 36 3756 4307 FO 36 36 3934 4284 FO 36 36 4113 4257 FO 36 36 4291 4225 FO 36 36 4470 4186 FO 36 36 4648 4138 FO 36 36 4827 4077 FO 36 36 5006 3999 FO 36 36 5184 3894 FO 36 36 5363 3747 FO 36 36 5541 3526 FO 36 36 5720 3156 FO 36 36 5898 2415 FO DD gr gr 24 w DD 3343 5104 mt (rhos) s 543 4137 mt -90 rotate (Mean response time short jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.5 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 1369 114 a 8383225 7104430 2894397 11972280 36640440 40521564 startTexFig 1369 114 a %%BeginDocument: ../figures/results_rhol5expshorts110.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol5expshorts110.eps %%CreationDate: 07/25/2002 23:19:24 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 44 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 44 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 315 -48 6157 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.5) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4404 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.5) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3911 mt 952 3911 L 6256 3911 mt 6202 3911 L 731 4000 mt (5) s 899 3207 mt 952 3207 L 6256 3207 mt 6202 3207 L 598 3296 mt (10) s 899 2502 mt 952 2502 L 6256 2502 mt 6202 2502 L 598 2591 mt (15) s 899 1798 mt 952 1798 L 6256 1798 mt 6202 1798 L 598 1887 mt (20) s 899 1093 mt 952 1093 L 6256 1093 mt 6202 1093 L 598 1182 mt (25) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 598 478 mt (30) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 178 -1409 179 -470 178 -235 179 -141 179 -94 178 -67 179 -50 178 -39 179 -32 178 -25 179 -22 179 -18 178 -15 179 -14 178 -11 179 -11 178 -9 179 -8 178 -8 899 4475 20 MP stroke SO 178 -1530 179 -676 179 -374 178 -232 179 -154 178 -105 179 -75 178 -55 179 -42 179 -32 178 -25 179 -21 178 -17 179 -15 178 -12 179 -10 179 -9 178 -8 179 -7 178 -6 179 -5 178 -5 179 -4 1077 4471 24 MP stroke gs 979 954 4304 3616 MR c np 36 36 1077 4471 FO 36 36 1256 4467 FO 36 36 1434 4462 FO 36 36 1613 4457 FO 36 36 1791 4451 FO 36 36 1970 4444 FO 36 36 2148 4436 FO 36 36 2327 4427 FO 36 36 2506 4417 FO 36 36 2684 4405 FO 36 36 2863 4390 FO 36 36 3041 4373 FO 36 36 3220 4352 FO 36 36 3398 4327 FO 36 36 3577 4295 FO 36 36 3756 4253 FO 36 36 3934 4198 FO 36 36 4113 4123 FO 36 36 4291 4018 FO 36 36 4470 3864 FO 36 36 4648 3632 FO 36 36 4827 3258 FO 36 36 5006 2582 FO 36 36 5184 1052 FO gr DD 179 -1029 178 -621 179 -416 178 -297 179 -221 179 -167 178 -127 179 -97 178 -74 179 -56 178 -44 179 -34 179 -27 178 -22 179 -18 178 -16 179 -13 178 -11 179 -10 179 -8 178 -7 179 -7 178 -5 179 -6 178 -4 179 -4 1077 4471 27 MP stroke gs 979 1032 4840 3538 MR c np SO 36 36 1077 4471 FO 36 36 1256 4467 FO 36 36 1434 4463 FO 36 36 1613 4457 FO 36 36 1791 4452 FO 36 36 1970 4445 FO 36 36 2148 4438 FO 36 36 2327 4430 FO 36 36 2506 4420 FO 36 36 2684 4409 FO 36 36 2863 4396 FO 36 36 3041 4380 FO 36 36 3220 4362 FO 36 36 3398 4340 FO 36 36 3577 4313 FO 36 36 3756 4279 FO 36 36 3934 4235 FO 36 36 4113 4179 FO 36 36 4291 4105 FO 36 36 4470 4008 FO 36 36 4648 3881 FO 36 36 4827 3714 FO 36 36 5006 3493 FO 36 36 5184 3196 FO 36 36 5363 2780 FO 36 36 5541 2159 FO 36 36 5720 1130 FO DD gr gr 24 w DD 3343 5104 mt (rhos) s 543 4137 mt -90 rotate (Mean response time short jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.5 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 2656 114 a 8525316 7104430 2170798 11972280 36640440 40521564 startTexFig 2656 114 a %%BeginDocument: ../figures/results_rhol5expshorts101.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol5expshorts101.eps %%CreationDate: 07/25/2002 23:22:33 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 33 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 33 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 181 -48 6291 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.5) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4404 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.5) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 598 3859 mt (50) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 464 3014 mt (100) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 464 2168 mt (150) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 464 1323 mt (200) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 464 478 mt (250) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 178 -1691 179 -563 178 -282 179 -169 179 -113 178 -80 179 -61 178 -47 179 -37 178 -31 179 -26 179 -21 178 -19 179 -16 178 -14 179 -13 178 -11 179 -10 178 -8 899 4446 20 MP stroke SO 178 -763 179 -340 179 -193 178 -124 179 -86 178 -64 179 -48 178 -39 179 -30 179 -26 178 -21 179 -18 178 -15 179 -13 178 -12 179 -9 179 -9 178 -7 179 -7 178 -5 179 -5 178 -4 179 -4 1077 4444 24 MP stroke gs 979 2504 4304 2039 MR c np 36 36 1077 4444 FO 36 36 1256 4440 FO 36 36 1434 4436 FO 36 36 1613 4431 FO 36 36 1791 4426 FO 36 36 1970 4419 FO 36 36 2148 4412 FO 36 36 2327 4403 FO 36 36 2506 4394 FO 36 36 2684 4382 FO 36 36 2863 4369 FO 36 36 3041 4354 FO 36 36 3220 4336 FO 36 36 3398 4315 FO 36 36 3577 4289 FO 36 36 3756 4259 FO 36 36 3934 4220 FO 36 36 4113 4172 FO 36 36 4291 4108 FO 36 36 4470 4022 FO 36 36 4648 3898 FO 36 36 4827 3705 FO 36 36 5006 3365 FO 36 36 5184 2602 FO gr DD 179 -1645 178 -548 179 -273 178 -164 179 -109 178 -77 179 -57 179 -45 178 -35 179 -29 178 -24 179 -19 178 -17 179 -14 179 -12 178 -11 179 -9 178 -8 179 -7 178 -6 179 -5 179 -5 178 -4 179 -3 178 -3 179 -3 178 -2 179 -1 1077 4445 29 MP stroke gs 979 1212 5197 3332 MR c np SO 36 36 1077 4445 FO 36 36 1256 4444 FO 36 36 1434 4442 FO 36 36 1613 4439 FO 36 36 1791 4436 FO 36 36 1970 4433 FO 36 36 2148 4429 FO 36 36 2327 4424 FO 36 36 2506 4419 FO 36 36 2684 4413 FO 36 36 2863 4406 FO 36 36 3041 4398 FO 36 36 3220 4389 FO 36 36 3398 4378 FO 36 36 3577 4366 FO 36 36 3756 4352 FO 36 36 3934 4335 FO 36 36 4113 4316 FO 36 36 4291 4292 FO 36 36 4470 4263 FO 36 36 4648 4228 FO 36 36 4827 4183 FO 36 36 5006 4126 FO 36 36 5184 4049 FO 36 36 5363 3940 FO 36 36 5541 3776 FO 36 36 5720 3503 FO 36 36 5898 2955 FO 36 36 6077 1310 FO DD gr gr 24 w DD 3343 5104 mt (rhos) s 409 4137 mt -90 rotate (Mean response time short jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.5 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 260 1127 a FC(\(a\))23 b(shorts)i(1,)e(longs)i(1)646 b(\(b\))24 b(shorts)h(1,)d(longs)j(10)647 b(\(c\))23 b(shorts)i(10,)e(longs)i(1)950 1353 y FF(Ho)n(w)f(longs)g(suf)n(fer)h (from)f(c)o(ycle-stealing)g(\226)h Fe(\032)2582 1368 y Ft(L)2662 1353 y Fd(=)i(0)p Fe(:)p Fd(5)p 950 1388 1940 4 v 81 1400 a 8454269 7104430 2499706 11972280 36640440 40521564 startTexFig 81 1400 a %%BeginDocument: ../figures/results_rhol5explongs11.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol5explongs11.eps %%CreationDate: 07/25/2002 23:16:23 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 38 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 38 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 248 -48 6224 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.5) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4404 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.5) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 531 4705 mt (1.8) s 899 3559 mt 952 3559 L 6256 3559 mt 6202 3559 L 731 3648 mt (2) s 899 2502 mt 952 2502 L 6256 2502 mt 6202 2502 L 531 2591 mt (2.2) s 899 1445 mt 952 1445 L 6256 1445 mt 6202 1445 L 531 1534 mt (2.4) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 531 478 mt (2.6) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 178 0 179 0 178 0 179 0 179 0 178 0 179 0 178 0 179 0 178 0 179 0 179 0 178 0 179 0 178 0 179 0 178 0 179 0 178 0 899 3559 20 MP stroke SO 178 -56 179 -58 179 -61 178 -65 179 -68 178 -71 179 -75 178 -79 179 -84 179 -89 178 -94 179 -100 178 -107 179 -114 178 -121 179 -130 179 -140 178 -150 179 -163 178 -176 179 -192 178 -208 179 -229 178 -252 899 3559 25 MP stroke gr 24 w gs 801 579 4482 3079 MR c np 36 36 899 3559 FO 36 36 1077 3307 FO 36 36 1256 3078 FO 36 36 1434 2870 FO 36 36 1613 2678 FO 36 36 1791 2502 FO 36 36 1970 2339 FO 36 36 2148 2189 FO 36 36 2327 2049 FO 36 36 2506 1919 FO 36 36 2684 1798 FO 36 36 2863 1684 FO 36 36 3041 1577 FO 36 36 3220 1477 FO 36 36 3398 1383 FO 36 36 3577 1294 FO 36 36 3756 1210 FO 36 36 3934 1131 FO 36 36 4113 1056 FO 36 36 4291 985 FO 36 36 4470 917 FO 36 36 4648 852 FO 36 36 4827 791 FO 36 36 5006 733 FO 36 36 5184 677 FO gr gs 899 389 5358 4228 MR c np DD 179 -151 178 -147 179 -143 178 -139 179 -135 178 -131 179 -126 179 -123 178 -117 179 -113 178 -109 179 -104 178 -99 179 -94 179 -90 178 -84 179 -80 178 -74 179 -70 178 -63 179 -59 179 -52 178 -47 179 -40 178 -34 179 -27 178 -20 179 -13 178 -4 899 3559 30 MP stroke gr DD gs 801 973 5375 2685 MR c np SO 36 36 899 3559 FO 36 36 1077 3555 FO 36 36 1256 3542 FO 36 36 1434 3522 FO 36 36 1613 3495 FO 36 36 1791 3461 FO 36 36 1970 3421 FO 36 36 2148 3374 FO 36 36 2327 3322 FO 36 36 2506 3263 FO 36 36 2684 3200 FO 36 36 2863 3130 FO 36 36 3041 3056 FO 36 36 3220 2976 FO 36 36 3398 2892 FO 36 36 3577 2802 FO 36 36 3756 2708 FO 36 36 3934 2609 FO 36 36 4113 2505 FO 36 36 4291 2396 FO 36 36 4470 2283 FO 36 36 4648 2166 FO 36 36 4827 2043 FO 36 36 5006 1917 FO 36 36 5184 1786 FO 36 36 5363 1651 FO 36 36 5541 1512 FO 36 36 5720 1369 FO 36 36 5898 1222 FO 36 36 6077 1071 FO DD gr gs 899 389 5358 4228 MR c np gr 3343 5104 mt (rhos) s 476 4097 mt -90 rotate (Mean response time long jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.5 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 1378 1400 a 8667404 7104430 1776107 11972280 36640440 40521564 startTexFig 1378 1400 a %%BeginDocument: ../figures/results_rhol5explongs110.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol5explongs110.eps %%CreationDate: 07/25/2002 23:19:25 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 27 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 27 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 114 -48 6358 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5357 0 0 -4227 899 4616 4 MP PP -5357 0 0 4227 5357 0 0 -4227 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L 899 4616 mt 6256 4616 L 899 4616 mt 899 389 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.5) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4404 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.5) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 397 4705 mt (19.8) s 899 3559 mt 952 3559 L 6256 3559 mt 6202 3559 L 598 3648 mt (20) s 899 2502 mt 952 2502 L 6256 2502 mt 6202 2502 L 397 2591 mt (20.2) s 899 1445 mt 952 1445 L 6256 1445 mt 6202 1445 L 397 1534 mt (20.4) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 397 478 mt (20.6) s 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L gs 899 389 5358 4228 MR c np DA 24 w 178 0 179 0 178 0 179 0 179 0 178 0 179 0 178 0 179 0 178 0 179 0 179 0 178 0 179 0 178 0 179 0 178 0 179 0 178 0 899 3559 20 MP stroke SO 178 -56 179 -58 179 -61 178 -65 179 -68 178 -71 179 -75 178 -79 179 -84 179 -89 178 -94 179 -100 178 -107 179 -114 178 -121 179 -130 179 -140 178 -150 179 -163 178 -176 179 -192 178 -208 179 -229 178 -252 899 3559 25 MP stroke gr 24 w gs 801 579 4482 3079 MR c np 36 36 899 3559 FO 36 36 1077 3307 FO 36 36 1256 3078 FO 36 36 1434 2870 FO 36 36 1613 2678 FO 36 36 1791 2502 FO 36 36 1970 2339 FO 36 36 2148 2189 FO 36 36 2327 2049 FO 36 36 2506 1919 FO 36 36 2684 1798 FO 36 36 2863 1684 FO 36 36 3041 1577 FO 36 36 3220 1477 FO 36 36 3398 1383 FO 36 36 3577 1294 FO 36 36 3756 1210 FO 36 36 3934 1131 FO 36 36 4113 1056 FO 36 36 4291 985 FO 36 36 4470 917 FO 36 36 4648 852 FO 36 36 4827 791 FO 36 36 5006 733 FO 36 36 5184 677 FO gr gs 899 389 5358 4228 MR c np DD 179 -173 178 -168 179 -164 178 -158 179 -153 178 -147 179 -139 179 -131 178 -122 179 -113 178 -104 179 -97 178 -89 179 -83 179 -77 178 -72 179 -66 178 -62 179 -57 178 -52 179 -47 179 -43 178 -38 179 -32 178 -28 179 -21 178 -16 179 -10 178 -4 899 3559 30 MP stroke gr DD gs 801 995 5375 2663 MR c np SO 36 36 899 3559 FO 36 36 1077 3555 FO 36 36 1256 3545 FO 36 36 1434 3529 FO 36 36 1613 3508 FO 36 36 1791 3480 FO 36 36 1970 3448 FO 36 36 2148 3410 FO 36 36 2327 3367 FO 36 36 2506 3320 FO 36 36 2684 3268 FO 36 36 2863 3211 FO 36 36 3041 3149 FO 36 36 3220 3083 FO 36 36 3398 3011 FO 36 36 3577 2934 FO 36 36 3756 2851 FO 36 36 3934 2762 FO 36 36 4113 2665 FO 36 36 4291 2561 FO 36 36 4470 2448 FO 36 36 4648 2326 FO 36 36 4827 2195 FO 36 36 5006 2056 FO 36 36 5184 1909 FO 36 36 5363 1756 FO 36 36 5541 1598 FO 36 36 5720 1434 FO 36 36 5898 1266 FO 36 36 6077 1093 FO DD gr gs 899 389 5358 4228 MR c np gr 3343 5104 mt (rhos) s 342 4097 mt -90 rotate (Mean response time long jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.5 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 2701 1400 a 8170093 7104430 3617996 11972280 36640440 40521564 startTexFig 2701 1400 a %%BeginDocument: ../figures/results_rhol5explongs101.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol5explongs101.eps %%CreationDate: 07/25/2002 23:22:33 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 55 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 55 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 448 -48 6024 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5357 0 0 -4227 899 4616 4 MP PP -5357 0 0 4227 5357 0 0 -4227 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L 899 4616 mt 6256 4616 L 899 4616 mt 899 389 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.5) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4404 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.5) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (1) s 899 4012 mt 952 4012 L 6256 4012 mt 6202 4012 L 731 4101 mt (2) s 899 3408 mt 952 3408 L 6256 3408 mt 6202 3408 L 731 3497 mt (3) s 899 2804 mt 952 2804 L 6256 2804 mt 6202 2804 L 731 2893 mt (4) s 899 2200 mt 952 2200 L 6256 2200 mt 6202 2200 L 731 2289 mt (5) s 899 1596 mt 952 1596 L 6256 1596 mt 6202 1596 L 731 1685 mt (6) s 899 992 mt 952 992 L 6256 992 mt 6202 992 L 731 1081 mt (7) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 731 478 mt (8) s 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L gs 899 389 5358 4228 MR c np DA 24 w 178 0 179 0 178 0 179 0 179 0 178 0 179 0 178 0 179 0 178 0 179 0 179 0 178 0 179 0 178 0 179 0 178 0 179 0 178 0 899 4012 20 MP stroke SO 178 -64 179 -67 179 -70 178 -73 179 -78 178 -81 179 -86 178 -91 179 -96 179 -101 178 -108 179 -114 178 -122 179 -130 178 -139 179 -148 179 -160 178 -172 179 -186 178 -201 179 -219 178 -239 179 -261 178 -288 899 4012 25 MP stroke gr 24 w gs 801 620 4482 3491 MR c np 36 36 899 4012 FO 36 36 1077 3724 FO 36 36 1256 3463 FO 36 36 1434 3224 FO 36 36 1613 3005 FO 36 36 1791 2804 FO 36 36 1970 2618 FO 36 36 2148 2446 FO 36 36 2327 2286 FO 36 36 2506 2138 FO 36 36 2684 1999 FO 36 36 2863 1869 FO 36 36 3041 1747 FO 36 36 3220 1633 FO 36 36 3398 1525 FO 36 36 3577 1424 FO 36 36 3756 1328 FO 36 36 3934 1237 FO 36 36 4113 1151 FO 36 36 4291 1070 FO 36 36 4470 992 FO 36 36 4648 919 FO 36 36 4827 849 FO 36 36 5006 782 FO 36 36 5184 718 FO gr gs 899 389 5358 4228 MR c np DD 179 -152 178 -149 179 -146 178 -144 179 -142 178 -138 179 -136 179 -133 178 -130 179 -127 178 -123 179 -121 178 -116 179 -113 179 -108 178 -105 179 -100 178 -95 179 -90 178 -84 179 -78 179 -72 178 -65 179 -57 178 -48 179 -39 178 -30 179 -18 178 -7 899 4012 30 MP stroke gr DD gs 801 1048 5375 3063 MR c np SO 36 36 899 4012 FO 36 36 1077 4005 FO 36 36 1256 3987 FO 36 36 1434 3957 FO 36 36 1613 3918 FO 36 36 1791 3870 FO 36 36 1970 3813 FO 36 36 2148 3748 FO 36 36 2327 3676 FO 36 36 2506 3598 FO 36 36 2684 3514 FO 36 36 2863 3424 FO 36 36 3041 3329 FO 36 36 3220 3229 FO 36 36 3398 3124 FO 36 36 3577 3016 FO 36 36 3756 2903 FO 36 36 3934 2787 FO 36 36 4113 2666 FO 36 36 4291 2543 FO 36 36 4470 2416 FO 36 36 4648 2286 FO 36 36 4827 2153 FO 36 36 5006 2017 FO 36 36 5184 1879 FO 36 36 5363 1737 FO 36 36 5541 1593 FO 36 36 5720 1447 FO 36 36 5898 1298 FO 36 36 6077 1146 FO DD gr gs 899 389 5358 4228 MR c np gr 3343 5104 mt (rhos) s 676 4097 mt -90 rotate (Mean response time long jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.5 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 260 2413 a FC(\(a\))c(shorts)i(1,)e(longs)i(1)646 b(\(b\))24 b(shorts)h(1,)d(longs)j(10)647 b(\(c\))23 b(shorts)i(10,)e(longs)i(1) 968 2638 y FF(Ho)n(w)f(shorts)g(gain)g(from)h(c)o(ycle-stealing)f(\226) g Fe(\032)2563 2653 y Ft(L)2643 2638 y Fd(=)k(0)p Fe(:)p Fd(8)p 968 2673 1904 4 v 81 2685 a 8383225 7104430 2894397 11972280 36640440 40521564 startTexFig 81 2685 a %%BeginDocument: ../figures/results_rhol8expshorts11.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol8expshorts11.eps %%CreationDate: 07/25/2002 23:17:38 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 44 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 44 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 315 -48 6157 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1791 4616 mt 1791 4562 L 1791 389 mt 1791 442 L 1625 4873 mt (0.2) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.4) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3411 4873 mt (0.6) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4304 4873 mt (0.8) s 5363 4616 mt 5363 4562 L 5363 389 mt 5363 442 L 5297 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.2) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 731 3859 mt (5) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 598 3014 mt (10) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 598 2168 mt (15) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 598 1323 mt (20) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 598 478 mt (25) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 223 -1691 223 -563 223 -282 223 -169 224 -113 223 -80 223 -61 223 -47 223 -37 224 -31 223 -26 223 -21 223 -19 223 -16 224 -14 223 -13 223 -11 223 -10 223 -8 899 4446 20 MP stroke SO 223 -1724 224 -606 223 -306 223 -183 223 -122 223 -85 224 -63 223 -49 223 -39 223 -31 223 -26 224 -22 223 -18 223 -16 223 -14 223 -12 224 -10 223 -9 223 -9 223 -7 1122 4440 21 MP stroke gs 1024 991 4661 3548 MR c np 36 36 1122 4440 FO 36 36 1345 4433 FO 36 36 1568 4424 FO 36 36 1791 4415 FO 36 36 2015 4405 FO 36 36 2238 4393 FO 36 36 2461 4379 FO 36 36 2684 4363 FO 36 36 2907 4345 FO 36 36 3131 4323 FO 36 36 3354 4297 FO 36 36 3577 4266 FO 36 36 3800 4227 FO 36 36 4023 4178 FO 36 36 4247 4115 FO 36 36 4470 4030 FO 36 36 4693 3908 FO 36 36 4916 3725 FO 36 36 5139 3419 FO 36 36 5363 2813 FO 36 36 5586 1089 FO gr DD 223 -916 223 -450 224 -263 223 -170 223 -116 223 -84 223 -63 224 -49 223 -38 223 -31 223 -26 223 -21 224 -18 223 -16 223 -14 223 -11 223 -11 224 -9 223 -8 223 -8 223 -6 1122 4440 22 MP stroke gs 1024 2014 4884 2525 MR c np SO 36 36 1122 4440 FO 36 36 1345 4434 FO 36 36 1568 4426 FO 36 36 1791 4418 FO 36 36 2015 4409 FO 36 36 2238 4398 FO 36 36 2461 4387 FO 36 36 2684 4373 FO 36 36 2907 4357 FO 36 36 3131 4339 FO 36 36 3354 4318 FO 36 36 3577 4292 FO 36 36 3800 4261 FO 36 36 4023 4223 FO 36 36 4247 4174 FO 36 36 4470 4111 FO 36 36 4693 4027 FO 36 36 4916 3911 FO 36 36 5139 3741 FO 36 36 5363 3478 FO 36 36 5586 3028 FO 36 36 5809 2112 FO DD gr gr 24 w DD 3343 5104 mt (rhos) s 543 4137 mt -90 rotate (Mean response time short jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.8 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 1369 2685 a 8383225 7104430 2894397 11972280 36640440 40521564 startTexFig 1369 2685 a %%BeginDocument: ../figures/results_rhol8expshorts110.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol8expshorts110.eps %%CreationDate: 07/25/2002 23:21:02 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 44 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 44 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 315 -48 6157 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1791 4616 mt 1791 4562 L 1791 389 mt 1791 442 L 1625 4873 mt (0.2) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.4) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3411 4873 mt (0.6) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4304 4873 mt (0.8) s 5363 4616 mt 5363 4562 L 5363 389 mt 5363 442 L 5297 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.2) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 731 3859 mt (5) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 598 3014 mt (10) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 598 2168 mt (15) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 598 1323 mt (20) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 598 478 mt (25) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 223 -1691 223 -563 223 -282 223 -169 224 -113 223 -80 223 -61 223 -47 223 -37 224 -31 223 -26 223 -21 223 -19 223 -16 224 -14 223 -13 223 -11 223 -10 223 -8 899 4446 20 MP stroke SO 224 -1237 223 -498 223 -250 223 -149 223 -98 224 -70 223 -53 223 -41 223 -32 223 -27 224 -23 223 -19 223 -16 223 -15 223 -12 224 -11 223 -10 223 -9 223 -7 1122 4439 20 MP stroke gs 1024 1764 4438 2774 MR c np 36 36 1122 4439 FO 36 36 1345 4432 FO 36 36 1568 4423 FO 36 36 1791 4413 FO 36 36 2015 4402 FO 36 36 2238 4390 FO 36 36 2461 4375 FO 36 36 2684 4359 FO 36 36 2907 4340 FO 36 36 3131 4317 FO 36 36 3354 4290 FO 36 36 3577 4258 FO 36 36 3800 4217 FO 36 36 4023 4164 FO 36 36 4247 4094 FO 36 36 4470 3996 FO 36 36 4693 3847 FO 36 36 4916 3597 FO 36 36 5139 3099 FO 36 36 5363 1862 FO gr DD 223 -1931 224 -887 223 -417 223 -225 223 -138 223 -94 224 -69 223 -52 223 -41 223 -33 223 -27 224 -23 223 -19 223 -16 223 -15 223 -12 224 -11 223 -10 223 -9 223 -7 1122 4439 21 MP stroke gr 24 w DD gs 1024 305 4661 4233 MR c np SO 36 36 1122 4439 FO 36 36 1345 4432 FO 36 36 1568 4423 FO 36 36 1791 4413 FO 36 36 2015 4402 FO 36 36 2238 4390 FO 36 36 2461 4375 FO 36 36 2684 4359 FO 36 36 2907 4340 FO 36 36 3131 4317 FO 36 36 3354 4290 FO 36 36 3577 4257 FO 36 36 3800 4216 FO 36 36 4023 4164 FO 36 36 4247 4095 FO 36 36 4470 4001 FO 36 36 4693 3863 FO 36 36 4916 3638 FO 36 36 5139 3221 FO 36 36 5363 2334 FO 36 36 5586 403 FO DD gr gs 899 389 5358 4228 MR c np gr 3343 5104 mt (rhos) s 543 4137 mt -90 rotate (Mean response time short jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.8 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 2656 2685 a 8525316 7104430 2170798 11972280 36640440 40521564 startTexFig 2656 2685 a %%BeginDocument: ../figures/results_rhol8expshorts101.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol8expshorts101.eps %%CreationDate: 07/25/2002 23:23:51 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 33 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 33 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 181 -48 6291 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1791 4616 mt 1791 4562 L 1791 389 mt 1791 442 L 1625 4873 mt (0.2) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.4) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3411 4873 mt (0.6) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4304 4873 mt (0.8) s 5363 4616 mt 5363 4562 L 5363 389 mt 5363 442 L 5297 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.2) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 598 3859 mt (50) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 464 3014 mt (100) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 464 2168 mt (150) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 464 1323 mt (200) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 464 478 mt (250) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 223 -1691 223 -563 223 -282 223 -169 224 -113 223 -80 223 -61 223 -47 223 -37 224 -31 223 -26 223 -21 223 -19 223 -16 224 -14 223 -13 223 -11 223 -10 223 -8 899 4446 20 MP stroke SO 223 -1458 224 -517 223 -265 223 -160 223 -108 223 -77 224 -58 223 -46 223 -36 223 -29 223 -25 224 -20 223 -18 223 -15 223 -13 223 -11 224 -10 223 -9 223 -8 223 -6 1122 4440 21 MP stroke gs 1024 1453 4661 3086 MR c np 36 36 1122 4440 FO 36 36 1345 4434 FO 36 36 1568 4426 FO 36 36 1791 4417 FO 36 36 2015 4407 FO 36 36 2238 4396 FO 36 36 2461 4383 FO 36 36 2684 4368 FO 36 36 2907 4350 FO 36 36 3131 4330 FO 36 36 3354 4305 FO 36 36 3577 4276 FO 36 36 3800 4240 FO 36 36 4023 4194 FO 36 36 4247 4136 FO 36 36 4470 4059 FO 36 36 4693 3951 FO 36 36 4916 3791 FO 36 36 5139 3526 FO 36 36 5363 3009 FO 36 36 5586 1551 FO gr DD 223 -1712 223 -569 223 -284 224 -170 223 -112 223 -80 223 -59 223 -46 224 -36 223 -29 223 -24 223 -20 223 -17 224 -14 223 -12 223 -11 223 -9 223 -8 224 -6 223 -6 223 -5 223 -5 1122 4443 23 MP stroke gs 1024 1111 5107 3431 MR c np SO 36 36 1122 4443 FO 36 36 1345 4438 FO 36 36 1568 4433 FO 36 36 1791 4427 FO 36 36 2015 4421 FO 36 36 2238 4413 FO 36 36 2461 4404 FO 36 36 2684 4393 FO 36 36 2907 4381 FO 36 36 3131 4367 FO 36 36 3354 4350 FO 36 36 3577 4330 FO 36 36 3800 4306 FO 36 36 4023 4277 FO 36 36 4247 4241 FO 36 36 4470 4195 FO 36 36 4693 4136 FO 36 36 4916 4056 FO 36 36 5139 3944 FO 36 36 5363 3774 FO 36 36 5586 3490 FO 36 36 5809 2921 FO 36 36 6032 1209 FO DD gr gr 24 w DD 3343 5104 mt (rhos) s 409 4137 mt -90 rotate (Mean response time short jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.8 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 260 3698 a FC(\(a\))23 b(shorts)i(1,)e(longs)i(1)646 b(\(b\))24 b(shorts)h(1,)d(longs)j(10)647 b(\(c\))23 b(shorts)i(10,)e(longs)i(1)950 3924 y FF(Ho)n(w)f(longs)g(suf)n(fer)h (from)f(c)o(ycle-stealing)g(\226)h Fe(\032)2582 3939 y Ft(L)2662 3924 y Fd(=)i(0)p Fe(:)p Fd(8)p 950 3958 1940 4 v 72 3970 a 8454269 7104430 2499706 11972280 36640440 40521564 startTexFig 72 3970 a %%BeginDocument: ../figures/results_rhol8explongs11.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol8explongs11.eps %%CreationDate: 07/25/2002 23:17:39 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 38 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 38 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 248 -48 6224 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5357 0 0 -4227 899 4616 4 MP PP -5357 0 0 4227 5357 0 0 -4227 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L 899 4616 mt 6256 4616 L 899 4616 mt 899 389 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1791 4616 mt 1791 4562 L 1791 389 mt 1791 442 L 1625 4873 mt (0.2) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.4) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3411 4873 mt (0.6) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4304 4873 mt (0.8) s 5363 4616 mt 5363 4562 L 5363 389 mt 5363 442 L 5297 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.2) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 531 4705 mt (4.9) s 899 4012 mt 952 4012 L 6256 4012 mt 6202 4012 L 731 4101 mt (5) s 899 3408 mt 952 3408 L 6256 3408 mt 6202 3408 L 531 3497 mt (5.1) s 899 2804 mt 952 2804 L 6256 2804 mt 6202 2804 L 531 2893 mt (5.2) s 899 2200 mt 952 2200 L 6256 2200 mt 6202 2200 L 531 2289 mt (5.3) s 899 1596 mt 952 1596 L 6256 1596 mt 6202 1596 L 531 1685 mt (5.4) s 899 992 mt 952 992 L 6256 992 mt 6202 992 L 531 1081 mt (5.5) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 531 478 mt (5.6) s 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L gs 899 389 5358 4228 MR c np DA 24 w 223 0 223 0 223 0 223 0 224 0 223 0 223 0 223 0 223 0 224 0 223 0 223 0 223 0 223 0 224 0 223 0 223 0 223 0 223 0 899 4012 20 MP stroke SO 223 -73 224 -78 223 -81 223 -86 223 -91 223 -96 224 -101 223 -108 223 -114 223 -122 223 -130 224 -139 223 -148 223 -160 223 -172 223 -186 224 -201 223 -219 223 -239 223 -261 223 -288 899 4012 22 MP stroke gr 24 w gs 801 821 4884 3290 MR c np 36 36 899 4012 FO 36 36 1122 3724 FO 36 36 1345 3463 FO 36 36 1568 3224 FO 36 36 1791 3005 FO 36 36 2015 2804 FO 36 36 2238 2618 FO 36 36 2461 2446 FO 36 36 2684 2286 FO 36 36 2907 2138 FO 36 36 3131 1999 FO 36 36 3354 1869 FO 36 36 3577 1747 FO 36 36 3800 1633 FO 36 36 4023 1525 FO 36 36 4247 1424 FO 36 36 4470 1328 FO 36 36 4693 1237 FO 36 36 4916 1151 FO 36 36 5139 1070 FO 36 36 5363 992 FO 36 36 5586 919 FO gr gs 899 389 5358 4228 MR c np DD 223 -261 223 -243 223 -223 224 -206 223 -189 223 -175 223 -161 223 -150 224 -139 223 -130 223 -121 223 -112 223 -104 224 -95 223 -86 223 -78 223 -68 223 -59 224 -50 223 -39 223 -28 223 -18 223 -6 899 4012 24 MP stroke gr DD gs 801 1173 5330 2938 MR c np SO 36 36 899 4012 FO 36 36 1122 4006 FO 36 36 1345 3988 FO 36 36 1568 3960 FO 36 36 1791 3921 FO 36 36 2015 3871 FO 36 36 2238 3812 FO 36 36 2461 3744 FO 36 36 2684 3666 FO 36 36 2907 3580 FO 36 36 3131 3485 FO 36 36 3354 3381 FO 36 36 3577 3269 FO 36 36 3800 3148 FO 36 36 4023 3018 FO 36 36 4247 2879 FO 36 36 4470 2729 FO 36 36 4693 2568 FO 36 36 4916 2393 FO 36 36 5139 2204 FO 36 36 5363 1998 FO 36 36 5586 1775 FO 36 36 5809 1532 FO 36 36 6032 1271 FO DD gr gs 899 389 5358 4228 MR c np gr 3343 5104 mt (rhos) s 476 4097 mt -90 rotate (Mean response time long jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.8 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 1369 3970 a 8596360 7104430 1776107 11774935 36640440 40521564 startTexFig 1369 3970 a %%BeginDocument: ../figures/results_rhol8explongs110.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol8explongs110.eps %%CreationDate: 07/25/2002 23:21:03 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 27 179 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 27 179 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 114 -48 6358 5235 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5357 0 0 -4227 899 4616 4 MP PP -5357 0 0 4227 5357 0 0 -4227 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L 899 4616 mt 6256 4616 L 899 4616 mt 899 389 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1791 4616 mt 1791 4562 L 1791 389 mt 1791 442 L 1625 4873 mt (0.2) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.4) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3411 4873 mt (0.6) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4304 4873 mt (0.8) s 5363 4616 mt 5363 4562 L 5363 389 mt 5363 442 L 5297 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.2) s 899 3559 mt 952 3559 L 6256 3559 mt 6202 3559 L 598 3648 mt (50) s 899 917 mt 952 917 L 6256 917 mt 6202 917 L 397 1006 mt (50.5) s 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L gs 899 389 5358 4228 MR c np DA 24 w 223 0 223 0 223 0 223 0 224 0 223 0 223 0 223 0 223 0 224 0 223 0 223 0 223 0 223 0 224 0 223 0 223 0 223 0 223 0 899 3559 20 MP stroke SO 223 -64 224 -68 223 -71 223 -75 223 -80 223 -83 224 -89 223 -94 223 -100 223 -107 223 -114 224 -121 223 -130 223 -140 223 -151 223 -162 224 -176 223 -192 223 -209 223 -228 223 -252 899 3559 22 MP stroke gr 24 w gs 801 755 4884 2903 MR c np 36 36 899 3559 FO 36 36 1122 3307 FO 36 36 1345 3079 FO 36 36 1568 2870 FO 36 36 1791 2678 FO 36 36 2015 2502 FO 36 36 2238 2340 FO 36 36 2461 2189 FO 36 36 2684 2049 FO 36 36 2907 1919 FO 36 36 3131 1798 FO 36 36 3354 1684 FO 36 36 3577 1577 FO 36 36 3800 1477 FO 36 36 4023 1383 FO 36 36 4247 1294 FO 36 36 4470 1211 FO 36 36 4693 1131 FO 36 36 4916 1056 FO 36 36 5139 985 FO 36 36 5363 917 FO 36 36 5586 853 FO gr gs 899 389 5358 4228 MR c np DD 223 -330 223 -296 223 -248 224 -196 223 -158 223 -133 223 -117 223 -104 224 -94 223 -85 223 -77 223 -70 223 -64 224 -57 223 -52 223 -46 223 -40 223 -35 224 -29 223 -22 223 -17 223 -10 223 -4 899 3559 24 MP stroke gr DD gs 801 1177 5330 2481 MR c np SO 36 36 899 3559 FO 36 36 1122 3555 FO 36 36 1345 3545 FO 36 36 1568 3528 FO 36 36 1791 3506 FO 36 36 2015 3477 FO 36 36 2238 3442 FO 36 36 2461 3402 FO 36 36 2684 3356 FO 36 36 2907 3304 FO 36 36 3131 3247 FO 36 36 3354 3183 FO 36 36 3577 3113 FO 36 36 3800 3036 FO 36 36 4023 2951 FO 36 36 4247 2857 FO 36 36 4470 2753 FO 36 36 4693 2636 FO 36 36 4916 2503 FO 36 36 5139 2345 FO 36 36 5363 2149 FO 36 36 5586 1901 FO 36 36 5809 1605 FO 36 36 6032 1275 FO DD gr gs 899 389 5358 4228 MR c np gr 3343 5104 mt (rhos) s 342 4097 mt -90 rotate (Mean response time long jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.8 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 2683 3970 a 8383225 7104430 2894397 11972280 36640440 40521564 startTexFig 2683 3970 a %%BeginDocument: ../figures/results_rhol8explongs101.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol8explongs101.eps %%CreationDate: 07/25/2002 23:23:52 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 44 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 44 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 315 -48 6157 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5357 0 0 -4227 899 4616 4 MP PP -5357 0 0 4227 5357 0 0 -4227 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L 899 4616 mt 6256 4616 L 899 4616 mt 899 389 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1791 4616 mt 1791 4562 L 1791 389 mt 1791 442 L 1625 4873 mt (0.2) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.4) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3411 4873 mt (0.6) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4304 4873 mt (0.8) s 5363 4616 mt 5363 4562 L 5363 389 mt 5363 442 L 5297 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.2) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (5) s 899 3911 mt 952 3911 L 6256 3911 mt 6202 3911 L 731 4000 mt (6) s 899 3207 mt 952 3207 L 6256 3207 mt 6202 3207 L 731 3296 mt (7) s 899 2502 mt 952 2502 L 6256 2502 mt 6202 2502 L 731 2591 mt (8) s 899 1798 mt 952 1798 L 6256 1798 mt 6202 1798 L 731 1887 mt (9) s 899 1093 mt 952 1093 L 6256 1093 mt 6202 1093 L 598 1182 mt (10) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 598 478 mt (11) s 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L gs 899 389 5358 4228 MR c np DA 24 w 223 0 223 0 223 0 223 0 224 0 223 0 223 0 223 0 223 0 224 0 223 0 223 0 223 0 223 0 224 0 223 0 223 0 223 0 223 0 899 4615 20 MP stroke SO 223 -86 224 -90 223 -95 223 -101 223 -105 223 -112 224 -119 223 -125 223 -134 223 -142 223 -151 224 -162 223 -174 223 -186 223 -201 223 -217 224 -234 223 -256 223 -278 223 -305 223 -335 899 4615 22 MP stroke gr 24 w gs 801 909 4884 3805 MR c np 36 36 899 4615 FO 36 36 1122 4280 FO 36 36 1345 3975 FO 36 36 1568 3697 FO 36 36 1791 3441 FO 36 36 2015 3207 FO 36 36 2238 2990 FO 36 36 2461 2789 FO 36 36 2684 2603 FO 36 36 2907 2429 FO 36 36 3131 2267 FO 36 36 3354 2116 FO 36 36 3577 1974 FO 36 36 3800 1840 FO 36 36 4023 1715 FO 36 36 4247 1596 FO 36 36 4470 1484 FO 36 36 4693 1379 FO 36 36 4916 1278 FO 36 36 5139 1183 FO 36 36 5363 1093 FO 36 36 5586 1007 FO gr gs 899 389 5358 4228 MR c np DD 223 -211 223 -207 223 -203 224 -199 223 -194 223 -190 223 -186 223 -182 224 -177 223 -172 223 -166 223 -160 223 -154 224 -147 223 -138 223 -128 223 -118 223 -105 224 -90 223 -75 223 -56 223 -36 223 -12 899 4615 24 MP stroke gr DD gs 801 1211 5330 3503 MR c np SO 36 36 899 4615 FO 36 36 1122 4603 FO 36 36 1345 4567 FO 36 36 1568 4511 FO 36 36 1791 4436 FO 36 36 2015 4346 FO 36 36 2238 4241 FO 36 36 2461 4123 FO 36 36 2684 3995 FO 36 36 2907 3857 FO 36 36 3131 3710 FO 36 36 3354 3556 FO 36 36 3577 3396 FO 36 36 3800 3230 FO 36 36 4023 3058 FO 36 36 4247 2881 FO 36 36 4470 2699 FO 36 36 4693 2513 FO 36 36 4916 2323 FO 36 36 5139 2129 FO 36 36 5363 1930 FO 36 36 5586 1727 FO 36 36 5809 1520 FO 36 36 6032 1309 FO DD gr gs 899 389 5358 4228 MR c np gr 3343 5104 mt (rhos) s 543 4097 mt -90 rotate (Mean response time long jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.8 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 260 4983 a FC(\(a\))c(shorts)i(1,)e(longs)i(1)646 b(\(b\))24 b(shorts)h(1,)d(longs)j(10)647 b(\(c\))23 b(shorts)i(10,)e(longs)i(1) 120 5179 y(Figure)36 b(11:)52 b Fy(Results)36 b(of)g(analysis,)k(in)35 b(the)g(case)h(wher)m(e)f(shorts)i(and)f(longs)g(ar)m(e)f(dr)o(awn)h (fr)l(om)f(e)n(xponential)120 5292 y(distrib)n(utions.)1875 5349 y FC(23)p eop %%Page: 24 26 24 25 bop 968 68 a FF(Ho)n(w)24 b(shorts)g(gain)g(from)h(c)o (ycle-stealing)f(\226)g Fe(\032)2563 83 y Ft(L)2643 68 y Fd(=)k(0)p Fe(:)p Fd(5)p 968 103 1904 4 v 81 114 a 8383225 7104430 2894397 11972280 36640440 40521564 startTexFig 81 114 a %%BeginDocument: ../figures/results_rhol5coxshorts11.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol5coxshorts11.eps %%CreationDate: 07/25/2002 23:25:30 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 44 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 44 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 315 -48 6157 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.5) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4404 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.5) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 731 3859 mt (5) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 598 3014 mt (10) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 598 2168 mt (15) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 598 1323 mt (20) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 598 478 mt (25) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 178 -1691 179 -563 178 -282 179 -169 179 -113 178 -80 179 -61 178 -47 179 -37 178 -31 179 -26 179 -21 178 -19 179 -16 178 -14 179 -13 178 -11 179 -10 178 -8 899 4446 20 MP stroke SO 178 -1238 179 -551 179 -308 178 -195 179 -133 178 -96 179 -71 178 -54 179 -43 179 -34 178 -27 179 -23 178 -19 179 -16 178 -14 179 -12 179 -10 178 -9 179 -8 178 -6 179 -6 178 -5 179 -5 1077 4443 24 MP stroke gs 979 1462 4304 3080 MR c np 36 36 1077 4443 FO 36 36 1256 4438 FO 36 36 1434 4433 FO 36 36 1613 4427 FO 36 36 1791 4421 FO 36 36 1970 4413 FO 36 36 2148 4404 FO 36 36 2327 4394 FO 36 36 2506 4382 FO 36 36 2684 4368 FO 36 36 2863 4352 FO 36 36 3041 4333 FO 36 36 3220 4310 FO 36 36 3398 4283 FO 36 36 3577 4249 FO 36 36 3756 4206 FO 36 36 3934 4152 FO 36 36 4113 4081 FO 36 36 4291 3985 FO 36 36 4470 3852 FO 36 36 4648 3657 FO 36 36 4827 3349 FO 36 36 5006 2798 FO 36 36 5184 1560 FO gr DD 178 -1403 179 -703 178 -422 179 -281 178 -201 179 -149 179 -114 178 -89 179 -70 178 -56 179 -45 178 -37 179 -30 179 -25 178 -20 179 -18 178 -14 179 -13 178 -11 179 -9 179 -9 178 -7 179 -6 178 -6 179 -5 178 -4 179 -4 1077 4443 28 MP stroke gs 979 594 5018 3948 MR c np SO 36 36 1077 4443 FO 36 36 1256 4439 FO 36 36 1434 4435 FO 36 36 1613 4430 FO 36 36 1791 4424 FO 36 36 1970 4418 FO 36 36 2148 4411 FO 36 36 2327 4402 FO 36 36 2506 4393 FO 36 36 2684 4382 FO 36 36 2863 4369 FO 36 36 3041 4355 FO 36 36 3220 4337 FO 36 36 3398 4317 FO 36 36 3577 4292 FO 36 36 3756 4262 FO 36 36 3934 4225 FO 36 36 4113 4180 FO 36 36 4291 4124 FO 36 36 4470 4054 FO 36 36 4648 3965 FO 36 36 4827 3851 FO 36 36 5006 3702 FO 36 36 5184 3501 FO 36 36 5363 3220 FO 36 36 5541 2798 FO 36 36 5720 2095 FO 36 36 5898 692 FO DD gr gr 24 w DD 3343 5104 mt (rhos) s 543 4137 mt -90 rotate (Mean response time short jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.5 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 1369 114 a 8383225 7104430 2894397 11972280 36640440 40521564 startTexFig 1369 114 a %%BeginDocument: ../figures/results_rhol5coxshorts110.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol5coxshorts110.eps %%CreationDate: 07/25/2002 23:29:50 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 44 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 44 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 315 -48 6157 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1791 4616 mt 1791 4562 L 1791 389 mt 1791 442 L 1625 4873 mt (0.2) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.4) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3411 4873 mt (0.6) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4304 4873 mt (0.8) s 5363 4616 mt 5363 4562 L 5363 389 mt 5363 442 L 5297 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.2) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 731 3859 mt (5) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 598 3014 mt (10) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 598 2168 mt (15) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 598 1323 mt (20) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 598 478 mt (25) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 223 -1691 223 -563 223 -282 223 -169 224 -113 223 -80 223 -61 223 -47 223 -37 224 -31 223 -26 223 -21 223 -19 223 -16 224 -14 223 -13 223 -11 223 -10 223 -8 899 4446 20 MP stroke SO 223 -1384 223 -790 224 -428 223 -227 223 -130 223 -82 223 -56 224 -41 223 -32 223 -25 223 -21 223 -17 224 -15 223 -12 223 -11 223 -9 223 -8 224 -7 223 -7 223 -5 223 -5 1122 4442 22 MP stroke gs 1024 1032 4884 3509 MR c np 36 36 1122 4442 FO 36 36 1345 4437 FO 36 36 1568 4432 FO 36 36 1791 4425 FO 36 36 2015 4418 FO 36 36 2238 4410 FO 36 36 2461 4401 FO 36 36 2684 4390 FO 36 36 2907 4378 FO 36 36 3131 4363 FO 36 36 3354 4346 FO 36 36 3577 4325 FO 36 36 3800 4300 FO 36 36 4023 4268 FO 36 36 4247 4227 FO 36 36 4470 4171 FO 36 36 4693 4089 FO 36 36 4916 3959 FO 36 36 5139 3732 FO 36 36 5363 3304 FO 36 36 5586 2514 FO 36 36 5809 1130 FO gr DD 223 -1073 223 -812 223 -570 224 -349 223 -197 223 -115 223 -74 223 -51 224 -39 223 -29 223 -24 223 -19 223 -16 224 -14 223 -12 223 -10 223 -9 223 -8 224 -7 223 -6 223 -5 223 -5 1122 4442 23 MP stroke gs 1024 900 5107 3641 MR c np SO 36 36 1122 4442 FO 36 36 1345 4437 FO 36 36 1568 4432 FO 36 36 1791 4426 FO 36 36 2015 4419 FO 36 36 2238 4411 FO 36 36 2461 4402 FO 36 36 2684 4392 FO 36 36 2907 4380 FO 36 36 3131 4366 FO 36 36 3354 4350 FO 36 36 3577 4331 FO 36 36 3800 4307 FO 36 36 4023 4278 FO 36 36 4247 4239 FO 36 36 4470 4188 FO 36 36 4693 4114 FO 36 36 4916 3999 FO 36 36 5139 3802 FO 36 36 5363 3453 FO 36 36 5586 2883 FO 36 36 5809 2071 FO 36 36 6032 998 FO DD gr gr 24 w DD 3343 5104 mt (rhos) s 543 4137 mt -90 rotate (Mean response time short jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.5 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 2656 114 a 8525316 7104430 2170798 11972280 36640440 40521564 startTexFig 2656 114 a %%BeginDocument: ../figures/results_rhol5coxshorts101.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol5coxshorts101.eps %%CreationDate: 07/25/2002 23:34:18 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 33 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 33 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 181 -48 6291 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.5) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4404 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.5) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 598 3859 mt (50) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 464 3014 mt (100) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 464 2168 mt (150) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 464 1323 mt (200) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 464 478 mt (250) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 178 -1691 179 -563 178 -282 179 -169 179 -113 178 -80 179 -61 178 -47 179 -37 178 -31 179 -26 179 -21 178 -19 179 -16 178 -14 179 -13 178 -11 179 -10 178 -8 899 4446 20 MP stroke SO 178 -801 179 -357 179 -203 178 -130 179 -90 178 -67 179 -51 178 -40 179 -32 179 -27 178 -22 179 -18 178 -16 179 -14 178 -12 179 -10 179 -9 178 -8 179 -7 178 -6 179 -5 178 -5 179 -3 1077 4443 24 MP stroke gs 979 2412 4304 2130 MR c np 36 36 1077 4443 FO 36 36 1256 4440 FO 36 36 1434 4435 FO 36 36 1613 4430 FO 36 36 1791 4424 FO 36 36 1970 4417 FO 36 36 2148 4409 FO 36 36 2327 4400 FO 36 36 2506 4390 FO 36 36 2684 4378 FO 36 36 2863 4364 FO 36 36 3041 4348 FO 36 36 3220 4330 FO 36 36 3398 4308 FO 36 36 3577 4281 FO 36 36 3756 4249 FO 36 36 3934 4209 FO 36 36 4113 4158 FO 36 36 4291 4091 FO 36 36 4470 4001 FO 36 36 4648 3871 FO 36 36 4827 3668 FO 36 36 5006 3311 FO 36 36 5184 2510 FO gr DD 178 -613 179 -306 178 -184 179 -121 178 -87 179 -65 179 -50 178 -39 179 -32 178 -27 179 -22 178 -19 179 -16 179 -14 178 -12 179 -11 178 -9 179 -8 178 -7 179 -7 179 -5 178 -5 179 -5 178 -3 179 -4 178 -3 179 -2 1077 4444 28 MP stroke gs 979 2670 5018 1873 MR c np SO 36 36 1077 4444 FO 36 36 1256 4442 FO 36 36 1434 4439 FO 36 36 1613 4435 FO 36 36 1791 4432 FO 36 36 1970 4427 FO 36 36 2148 4422 FO 36 36 2327 4417 FO 36 36 2506 4410 FO 36 36 2684 4403 FO 36 36 2863 4395 FO 36 36 3041 4386 FO 36 36 3220 4375 FO 36 36 3398 4363 FO 36 36 3577 4349 FO 36 36 3756 4333 FO 36 36 3934 4314 FO 36 36 4113 4292 FO 36 36 4291 4265 FO 36 36 4470 4233 FO 36 36 4648 4194 FO 36 36 4827 4144 FO 36 36 5006 4079 FO 36 36 5184 3992 FO 36 36 5363 3871 FO 36 36 5541 3687 FO 36 36 5720 3381 FO 36 36 5898 2768 FO DD gr gr 24 w DD 3343 5104 mt (rhos) s 409 4137 mt -90 rotate (Mean response time short jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.5 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 260 1127 a FC(\(a\))23 b(shorts)i(1,)e(longs)i(1)646 b(\(b\))24 b(shorts)h(1,)d(longs)j(10)647 b(\(c\))23 b(shorts)i(10,)e(longs)i(1)950 1353 y FF(Ho)n(w)f(longs)g(suf)n(fer)h (from)f(c)o(ycle-stealing)g(\226)h Fe(\032)2582 1368 y Ft(L)2662 1353 y Fd(=)i(0)p Fe(:)p Fd(5)p 950 1388 1940 4 v 68 1400 a 8454269 7104430 2499706 11972280 36640440 40521564 startTexFig 68 1400 a %%BeginDocument: ../figures/results_rhol5coxlongs11.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol5coxlongs11.eps %%CreationDate: 07/25/2002 23:25:30 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 38 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 38 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 248 -48 6224 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5357 0 0 -4227 899 4616 4 MP PP -5357 0 0 4227 5357 0 0 -4227 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L 899 4616 mt 6256 4616 L 899 4616 mt 899 389 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.5) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4404 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.5) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 531 4705 mt (5.4) s 899 4012 mt 952 4012 L 6256 4012 mt 6202 4012 L 531 4101 mt (5.5) s 899 3408 mt 952 3408 L 6256 3408 mt 6202 3408 L 531 3497 mt (5.6) s 899 2804 mt 952 2804 L 6256 2804 mt 6202 2804 L 531 2893 mt (5.7) s 899 2200 mt 952 2200 L 6256 2200 mt 6202 2200 L 531 2289 mt (5.8) s 899 1596 mt 952 1596 L 6256 1596 mt 6202 1596 L 531 1685 mt (5.9) s 899 992 mt 952 992 L 6256 992 mt 6202 992 L 731 1081 mt (6) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 531 478 mt (6.1) s 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L gs 899 389 5358 4228 MR c np DA 24 w 178 0 179 0 178 0 179 0 179 0 178 0 179 0 178 0 179 0 178 0 179 0 179 0 178 0 179 0 178 0 179 0 178 0 179 0 178 0 899 4012 20 MP stroke SO 178 -63 179 -67 179 -70 178 -74 179 -77 178 -82 179 -86 178 -91 179 -95 179 -102 178 -108 179 -114 178 -122 179 -129 178 -139 179 -149 179 -160 178 -172 179 -186 178 -201 179 -219 178 -238 179 -262 178 -287 899 4012 25 MP stroke gr 24 w gs 801 621 4482 3490 MR c np 36 36 899 4012 FO 36 36 1077 3725 FO 36 36 1256 3463 FO 36 36 1434 3225 FO 36 36 1613 3006 FO 36 36 1791 2805 FO 36 36 1970 2619 FO 36 36 2148 2447 FO 36 36 2327 2287 FO 36 36 2506 2138 FO 36 36 2684 1999 FO 36 36 2863 1870 FO 36 36 3041 1748 FO 36 36 3220 1634 FO 36 36 3398 1526 FO 36 36 3577 1424 FO 36 36 3756 1329 FO 36 36 3934 1238 FO 36 36 4113 1152 FO 36 36 4291 1070 FO 36 36 4470 993 FO 36 36 4648 919 FO 36 36 4827 849 FO 36 36 5006 782 FO 36 36 5184 719 FO gr gs 899 389 5358 4228 MR c np DD 179 -182 178 -178 179 -173 178 -168 179 -162 178 -157 179 -151 179 -143 178 -136 179 -130 178 -122 179 -115 178 -108 179 -102 179 -96 178 -90 179 -84 178 -79 179 -73 178 -68 179 -62 179 -56 178 -50 179 -43 178 -37 179 -29 178 -21 179 -14 178 -4 899 4012 30 MP stroke gr DD gs 801 1081 5375 3030 MR c np SO 36 36 899 4012 FO 36 36 1077 4008 FO 36 36 1256 3994 FO 36 36 1434 3973 FO 36 36 1613 3944 FO 36 36 1791 3907 FO 36 36 1970 3864 FO 36 36 2148 3814 FO 36 36 2327 3758 FO 36 36 2506 3696 FO 36 36 2684 3628 FO 36 36 2863 3555 FO 36 36 3041 3476 FO 36 36 3220 3392 FO 36 36 3398 3302 FO 36 36 3577 3206 FO 36 36 3756 3104 FO 36 36 3934 2996 FO 36 36 4113 2881 FO 36 36 4291 2759 FO 36 36 4470 2629 FO 36 36 4648 2493 FO 36 36 4827 2350 FO 36 36 5006 2199 FO 36 36 5184 2042 FO 36 36 5363 1880 FO 36 36 5541 1712 FO 36 36 5720 1539 FO 36 36 5898 1361 FO 36 36 6077 1179 FO DD gr gs 899 389 5358 4228 MR c np gr 3343 5104 mt (rhos) s 476 4097 mt -90 rotate (Mean response time long jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.5 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 1364 1400 a 8667404 7104430 1776107 11972280 36640440 40521564 startTexFig 1364 1400 a %%BeginDocument: ../figures/results_rhol5coxlongs110.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol5coxlongs110.eps %%CreationDate: 07/25/2002 23:29:51 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 27 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 27 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 114 -48 6358 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5357 0 0 -4227 899 4616 4 MP PP -5357 0 0 4227 5357 0 0 -4227 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L 899 4616 mt 6256 4616 L 899 4616 mt 899 389 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.5) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4404 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.5) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 598 4705 mt (55) s 899 4012 mt 952 4012 L 6256 4012 mt 6202 4012 L 397 4101 mt (55.1) s 899 3408 mt 952 3408 L 6256 3408 mt 6202 3408 L 397 3497 mt (55.2) s 899 2804 mt 952 2804 L 6256 2804 mt 6202 2804 L 397 2893 mt (55.3) s 899 2200 mt 952 2200 L 6256 2200 mt 6202 2200 L 397 2289 mt (55.4) s 899 1596 mt 952 1596 L 6256 1596 mt 6202 1596 L 397 1685 mt (55.5) s 899 992 mt 952 992 L 6256 992 mt 6202 992 L 397 1081 mt (55.6) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 397 478 mt (55.7) s 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L gs 899 389 5358 4228 MR c np DA 24 w 178 0 179 0 178 0 179 0 179 0 178 0 179 0 178 0 179 0 178 0 179 0 179 0 178 0 179 0 178 0 179 0 178 0 179 0 178 0 899 4615 20 MP stroke SO 178 -64 179 -67 179 -70 178 -74 179 -77 178 -82 179 -86 178 -90 179 -96 179 -102 178 -107 179 -115 178 -121 179 -130 178 -139 179 -149 179 -160 178 -172 179 -185 178 -202 179 -218 178 -239 179 -262 178 -287 899 4615 25 MP stroke gr 24 w gs 801 1223 4482 3491 MR c np 36 36 899 4615 FO 36 36 1077 4328 FO 36 36 1256 4066 FO 36 36 1434 3827 FO 36 36 1613 3609 FO 36 36 1791 3407 FO 36 36 1970 3222 FO 36 36 2148 3050 FO 36 36 2327 2890 FO 36 36 2506 2741 FO 36 36 2684 2602 FO 36 36 2863 2472 FO 36 36 3041 2351 FO 36 36 3220 2236 FO 36 36 3398 2129 FO 36 36 3577 2027 FO 36 36 3756 1931 FO 36 36 3934 1841 FO 36 36 4113 1755 FO 36 36 4291 1673 FO 36 36 4470 1596 FO 36 36 4648 1522 FO 36 36 4827 1452 FO 36 36 5006 1385 FO 36 36 5184 1321 FO gr gs 899 389 5358 4228 MR c np DD 179 -199 178 -195 179 -190 178 -185 179 -180 178 -173 179 -166 179 -155 178 -142 179 -127 178 -113 179 -103 178 -96 179 -91 179 -84 178 -80 179 -74 178 -69 179 -64 178 -59 179 -54 179 -48 178 -43 179 -37 178 -31 179 -25 178 -18 179 -11 178 -4 899 4615 30 MP stroke gr DD gs 801 1701 5375 3013 MR c np SO 36 36 899 4615 FO 36 36 1077 4611 FO 36 36 1256 4600 FO 36 36 1434 4582 FO 36 36 1613 4557 FO 36 36 1791 4526 FO 36 36 1970 4489 FO 36 36 2148 4446 FO 36 36 2327 4398 FO 36 36 2506 4344 FO 36 36 2684 4285 FO 36 36 2863 4221 FO 36 36 3041 4152 FO 36 36 3220 4078 FO 36 36 3398 3998 FO 36 36 3577 3914 FO 36 36 3756 3823 FO 36 36 3934 3727 FO 36 36 4113 3624 FO 36 36 4291 3511 FO 36 36 4470 3384 FO 36 36 4648 3242 FO 36 36 4827 3087 FO 36 36 5006 2921 FO 36 36 5184 2748 FO 36 36 5363 2568 FO 36 36 5541 2383 FO 36 36 5720 2193 FO 36 36 5898 1998 FO 36 36 6077 1799 FO DD gr gs 899 389 5358 4228 MR c np gr 3343 5104 mt (rhos) s 342 4097 mt -90 rotate (Mean response time long jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.5 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 2688 1400 a 8383225 7104430 2894397 11972280 36640440 40521564 startTexFig 2688 1400 a %%BeginDocument: ../figures/results_rhol5coxlongs101.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol5coxlongs101.eps %%CreationDate: 07/25/2002 23:34:18 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 44 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 44 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 315 -48 6157 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5357 0 0 -4227 899 4616 4 MP PP -5357 0 0 4227 5357 0 0 -4227 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L 899 4616 mt 6256 4616 L 899 4616 mt 899 389 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.5) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4404 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.5) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (5) s 899 3911 mt 952 3911 L 6256 3911 mt 6202 3911 L 731 4000 mt (6) s 899 3207 mt 952 3207 L 6256 3207 mt 6202 3207 L 731 3296 mt (7) s 899 2502 mt 952 2502 L 6256 2502 mt 6202 2502 L 731 2591 mt (8) s 899 1798 mt 952 1798 L 6256 1798 mt 6202 1798 L 731 1887 mt (9) s 899 1093 mt 952 1093 L 6256 1093 mt 6202 1093 L 598 1182 mt (10) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 598 478 mt (11) s 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L gs 899 389 5358 4228 MR c np DA 24 w 178 0 179 0 178 0 179 0 179 0 178 0 179 0 178 0 179 0 178 0 179 0 179 0 178 0 179 0 178 0 179 0 178 0 179 0 178 0 899 4263 20 MP stroke SO 178 -74 179 -78 179 -82 178 -86 179 -90 178 -95 179 -100 178 -106 179 -112 179 -118 178 -126 179 -133 178 -142 179 -152 178 -162 179 -173 179 -187 178 -201 179 -216 178 -235 179 -255 178 -279 179 -305 178 -335 899 4263 25 MP stroke gr 24 w gs 801 323 4482 4039 MR c np 36 36 899 4263 FO 36 36 1077 3928 FO 36 36 1256 3623 FO 36 36 1434 3344 FO 36 36 1613 3089 FO 36 36 1791 2854 FO 36 36 1970 2638 FO 36 36 2148 2437 FO 36 36 2327 2250 FO 36 36 2506 2077 FO 36 36 2684 1915 FO 36 36 2863 1763 FO 36 36 3041 1621 FO 36 36 3220 1488 FO 36 36 3398 1362 FO 36 36 3577 1244 FO 36 36 3756 1132 FO 36 36 3934 1026 FO 36 36 4113 926 FO 36 36 4291 831 FO 36 36 4470 741 FO 36 36 4648 655 FO 36 36 4827 573 FO 36 36 5006 495 FO 36 36 5184 421 FO gr gs 899 389 5358 4228 MR c np DD 179 -187 178 -183 179 -179 178 -175 179 -171 178 -167 179 -163 179 -159 178 -154 179 -149 178 -145 179 -140 178 -135 179 -129 179 -124 178 -119 179 -112 178 -106 179 -100 178 -93 179 -85 179 -78 178 -70 179 -60 178 -52 179 -41 178 -31 179 -19 178 -6 899 4263 30 MP stroke gr DD gs 801 833 5375 3529 MR c np SO 36 36 899 4263 FO 36 36 1077 4257 FO 36 36 1256 4238 FO 36 36 1434 4207 FO 36 36 1613 4166 FO 36 36 1791 4114 FO 36 36 1970 4054 FO 36 36 2148 3984 FO 36 36 2327 3906 FO 36 36 2506 3821 FO 36 36 2684 3728 FO 36 36 2863 3628 FO 36 36 3041 3522 FO 36 36 3220 3410 FO 36 36 3398 3291 FO 36 36 3577 3167 FO 36 36 3756 3038 FO 36 36 3934 2903 FO 36 36 4113 2763 FO 36 36 4291 2618 FO 36 36 4470 2469 FO 36 36 4648 2315 FO 36 36 4827 2156 FO 36 36 5006 1993 FO 36 36 5184 1826 FO 36 36 5363 1655 FO 36 36 5541 1480 FO 36 36 5720 1301 FO 36 36 5898 1118 FO 36 36 6077 931 FO DD gr gs 899 389 5358 4228 MR c np gr 3343 5104 mt (rhos) s 543 4097 mt -90 rotate (Mean response time long jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.5 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 260 2413 a FC(\(a\))c(shorts)i(1,)e(longs)i(1)646 b(\(b\))24 b(shorts)h(1,)d(longs)j(10)647 b(\(c\))23 b(shorts)i(10,)e(longs)i(1) 968 2638 y FF(Ho)n(w)f(shorts)g(gain)g(from)h(c)o(ycle-stealing)f(\226) g Fe(\032)2563 2653 y Ft(L)2643 2638 y Fd(=)k(0)p Fe(:)p Fd(8)p 968 2673 1904 4 v 90 2685 a 8383225 7104430 2894397 11972280 36640440 40521564 startTexFig 90 2685 a %%BeginDocument: ../figures/results_rhol8coxshorts11.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol8coxshorts11.eps %%CreationDate: 07/25/2002 23:27:01 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 44 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 44 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 315 -48 6157 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1791 4616 mt 1791 4562 L 1791 389 mt 1791 442 L 1625 4873 mt (0.2) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.4) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3411 4873 mt (0.6) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4304 4873 mt (0.8) s 5363 4616 mt 5363 4562 L 5363 389 mt 5363 442 L 5297 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.2) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 731 3859 mt (5) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 598 3014 mt (10) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 598 2168 mt (15) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 598 1323 mt (20) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 598 478 mt (25) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 223 -1691 223 -563 223 -282 223 -169 224 -113 223 -80 223 -61 223 -47 223 -37 224 -31 223 -26 223 -21 223 -19 223 -16 224 -14 223 -13 223 -11 223 -10 223 -8 899 4446 20 MP stroke SO 224 -883 223 -407 223 -223 223 -139 223 -93 224 -68 223 -51 223 -40 223 -32 223 -26 224 -22 223 -19 223 -16 223 -13 223 -12 224 -11 223 -9 223 -9 223 -7 1122 4440 20 MP stroke gs 1024 2262 4438 2277 MR c np 36 36 1122 4440 FO 36 36 1345 4433 FO 36 36 1568 4424 FO 36 36 1791 4415 FO 36 36 2015 4404 FO 36 36 2238 4392 FO 36 36 2461 4379 FO 36 36 2684 4363 FO 36 36 2907 4344 FO 36 36 3131 4322 FO 36 36 3354 4296 FO 36 36 3577 4264 FO 36 36 3800 4224 FO 36 36 4023 4173 FO 36 36 4247 4105 FO 36 36 4470 4012 FO 36 36 4693 3873 FO 36 36 4916 3650 FO 36 36 5139 3243 FO 36 36 5363 2360 FO gr DD 223 -1022 224 -533 223 -294 223 -174 223 -113 223 -77 224 -57 223 -43 223 -34 223 -28 223 -22 224 -19 223 -16 223 -14 223 -13 223 -10 224 -10 223 -8 223 -8 223 -6 1122 4440 21 MP stroke gs 1024 1841 4661 2698 MR c np SO 36 36 1122 4440 FO 36 36 1345 4434 FO 36 36 1568 4426 FO 36 36 1791 4418 FO 36 36 2015 4408 FO 36 36 2238 4398 FO 36 36 2461 4385 FO 36 36 2684 4371 FO 36 36 2907 4355 FO 36 36 3131 4336 FO 36 36 3354 4314 FO 36 36 3577 4286 FO 36 36 3800 4252 FO 36 36 4023 4209 FO 36 36 4247 4152 FO 36 36 4470 4075 FO 36 36 4693 3962 FO 36 36 4916 3788 FO 36 36 5139 3494 FO 36 36 5363 2961 FO 36 36 5586 1939 FO DD gr gr 24 w DD 3343 5104 mt (rhos) s 543 4137 mt -90 rotate (Mean response time short jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.8 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 1378 2685 a 8241137 7104430 2894397 11972280 36245749 40521564 startTexFig 1378 2685 a %%BeginDocument: ../figures/results_rhol8coxshorts110.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol8coxshorts110.eps %%CreationDate: 07/25/2002 23:32:46 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 44 182 551 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 44 182 551 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 315 -48 6088 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1970 4616 mt 1970 4562 L 1970 389 mt 1970 442 L 1804 4873 mt (0.2) s 3041 4616 mt 3041 4562 L 3041 389 mt 3041 442 L 2875 4873 mt (0.4) s 4113 4616 mt 4113 4562 L 4113 389 mt 4113 442 L 3947 4873 mt (0.6) s 5184 4616 mt 5184 4562 L 5184 389 mt 5184 442 L 5018 4873 mt (0.8) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6190 4873 mt (1) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3911 mt 952 3911 L 6256 3911 mt 6202 3911 L 731 4000 mt (5) s 899 3207 mt 952 3207 L 6256 3207 mt 6202 3207 L 598 3296 mt (10) s 899 2502 mt 952 2502 L 6256 2502 mt 6202 2502 L 598 2591 mt (15) s 899 1798 mt 952 1798 L 6256 1798 mt 6202 1798 L 598 1887 mt (20) s 899 1093 mt 952 1093 L 6256 1093 mt 6202 1093 L 598 1182 mt (25) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 598 478 mt (30) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 268 -1409 268 -470 268 -235 268 -141 268 -94 267 -67 268 -50 268 -39 268 -32 268 -25 268 -22 268 -18 267 -15 268 -14 268 -11 268 -11 268 -9 268 -8 267 -8 899 4475 20 MP stroke SO 268 -2246 268 -545 268 -228 268 -128 268 -82 268 -59 267 -43 268 -34 268 -28 268 -22 268 -19 268 -16 268 -14 267 -11 268 -11 268 -9 268 -8 268 -7 268 -7 1166 4469 20 MP stroke gr 24 w gs 1068 854 5287 3714 MR c np 36 36 1166 4469 FO 36 36 1434 4462 FO 36 36 1702 4455 FO 36 36 1970 4447 FO 36 36 2238 4438 FO 36 36 2506 4427 FO 36 36 2773 4416 FO 36 36 3041 4402 FO 36 36 3309 4386 FO 36 36 3577 4367 FO 36 36 3845 4345 FO 36 36 4113 4317 FO 36 36 4381 4283 FO 36 36 4648 4240 FO 36 36 4916 4181 FO 36 36 5184 4099 FO 36 36 5452 3971 FO 36 36 5720 3743 FO 36 36 5988 3198 FO 36 36 6256 952 FO gr gs 899 389 5358 4228 MR c np DD 268 -1954 268 -510 268 -219 268 -124 268 -82 268 -58 267 -44 268 -34 268 -28 268 -23 268 -19 268 -16 268 -13 267 -12 268 -11 268 -9 268 -8 268 -7 268 -7 1166 4469 20 MP stroke gr DD gs 1068 1193 5287 3375 MR c np SO 36 36 1166 4469 FO 36 36 1434 4462 FO 36 36 1702 4455 FO 36 36 1970 4447 FO 36 36 2238 4438 FO 36 36 2506 4427 FO 36 36 2773 4415 FO 36 36 3041 4402 FO 36 36 3309 4386 FO 36 36 3577 4367 FO 36 36 3845 4344 FO 36 36 4113 4316 FO 36 36 4381 4282 FO 36 36 4648 4238 FO 36 36 4916 4180 FO 36 36 5184 4098 FO 36 36 5452 3974 FO 36 36 5720 3755 FO 36 36 5988 3245 FO 36 36 6256 1291 FO DD gr gs 899 389 5358 4228 MR c np gr 3343 5104 mt (rhos) s 543 4137 mt -90 rotate (Mean response time short jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.8 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 2647 2685 a 8525316 7104430 2170798 11972280 36640440 40521564 startTexFig 2647 2685 a %%BeginDocument: ../figures/results_rhol8coxshorts101.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol8coxshorts101.eps %%CreationDate: 07/25/2002 23:35:41 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 33 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 33 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 181 -48 6291 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1791 4616 mt 1791 4562 L 1791 389 mt 1791 442 L 1625 4873 mt (0.2) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.4) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3411 4873 mt (0.6) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4304 4873 mt (0.8) s 5363 4616 mt 5363 4562 L 5363 389 mt 5363 442 L 5297 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.2) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 598 3859 mt (50) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 464 3014 mt (100) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 464 2168 mt (150) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 464 1323 mt (200) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 464 478 mt (250) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 223 -1691 223 -563 223 -282 223 -169 224 -113 223 -80 223 -61 223 -47 223 -37 224 -31 223 -26 223 -21 223 -19 223 -16 224 -14 223 -13 223 -11 223 -10 223 -8 899 4446 20 MP stroke SO 223 -1563 224 -553 223 -282 223 -170 223 -114 223 -81 224 -61 223 -47 223 -37 223 -31 223 -25 224 -21 223 -17 223 -16 223 -13 223 -12 224 -10 223 -9 223 -7 223 -7 1122 4440 21 MP stroke gs 1024 1266 4661 3273 MR c np 36 36 1122 4440 FO 36 36 1345 4433 FO 36 36 1568 4426 FO 36 36 1791 4417 FO 36 36 2015 4407 FO 36 36 2238 4395 FO 36 36 2461 4382 FO 36 36 2684 4366 FO 36 36 2907 4349 FO 36 36 3131 4328 FO 36 36 3354 4303 FO 36 36 3577 4272 FO 36 36 3800 4235 FO 36 36 4023 4188 FO 36 36 4247 4127 FO 36 36 4470 4046 FO 36 36 4693 3932 FO 36 36 4916 3762 FO 36 36 5139 3480 FO 36 36 5363 2927 FO 36 36 5586 1364 FO gr DD 223 -2103 223 -698 223 -346 224 -206 223 -135 223 -96 223 -70 223 -53 224 -42 223 -34 223 -28 223 -22 223 -19 224 -16 223 -14 223 -12 223 -10 223 -9 224 -8 223 -6 223 -6 223 -5 1122 4442 23 MP stroke gs 1024 406 5107 4135 MR c np SO 36 36 1122 4442 FO 36 36 1345 4437 FO 36 36 1568 4431 FO 36 36 1791 4425 FO 36 36 2015 4417 FO 36 36 2238 4408 FO 36 36 2461 4398 FO 36 36 2684 4386 FO 36 36 2907 4372 FO 36 36 3131 4356 FO 36 36 3354 4337 FO 36 36 3577 4315 FO 36 36 3800 4287 FO 36 36 4023 4253 FO 36 36 4247 4211 FO 36 36 4470 4158 FO 36 36 4693 4088 FO 36 36 4916 3992 FO 36 36 5139 3857 FO 36 36 5363 3651 FO 36 36 5586 3305 FO 36 36 5809 2607 FO 36 36 6032 504 FO DD gr gr 24 w DD 3343 5104 mt (rhos) s 409 4137 mt -90 rotate (Mean response time short jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.8 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 260 3698 a FC(\(a\))23 b(shorts)i(1,)e(longs)i(1)646 b(\(b\))24 b(shorts)h(1,)d(longs)j(10)647 b(\(c\))23 b(shorts)i(10,)e(longs)i(1)950 3924 y FF(Ho)n(w)f(longs)g(suf)n(fer)h (from)f(c)o(ycle-stealing)g(\226)h Fe(\032)2582 3939 y Ft(L)2662 3924 y Fd(=)i(0)p Fe(:)p Fd(8)p 950 3958 1940 4 v 45 3970 a 8667404 7104430 1776107 11972280 36640440 40521564 startTexFig 45 3970 a %%BeginDocument: ../figures/results_rhol8coxlongs11.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol8coxlongs11.eps %%CreationDate: 07/25/2002 23:27:02 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 27 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 27 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 114 -48 6358 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5357 0 0 -4227 899 4616 4 MP PP -5357 0 0 4227 5357 0 0 -4227 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L 899 4616 mt 6256 4616 L 899 4616 mt 899 389 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1791 4616 mt 1791 4562 L 1791 389 mt 1791 442 L 1625 4873 mt (0.2) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.4) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3411 4873 mt (0.6) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4304 4873 mt (0.8) s 5363 4616 mt 5363 4562 L 5363 389 mt 5363 442 L 5297 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.2) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 397 4705 mt (18.8) s 899 3559 mt 952 3559 L 6256 3559 mt 6202 3559 L 598 3648 mt (19) s 899 2502 mt 952 2502 L 6256 2502 mt 6202 2502 L 397 2591 mt (19.2) s 899 1445 mt 952 1445 L 6256 1445 mt 6202 1445 L 397 1534 mt (19.4) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 397 478 mt (19.6) s 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L gs 899 389 5358 4228 MR c np DA 24 w 223 0 223 0 223 0 223 0 224 0 223 0 223 0 223 0 223 0 224 0 223 0 223 0 223 0 223 0 224 0 223 0 223 0 223 0 223 0 899 3560 20 MP stroke SO 223 -64 224 -68 223 -71 223 -75 223 -80 223 -84 224 -88 223 -95 223 -100 223 -106 223 -114 224 -121 223 -130 223 -140 223 -151 223 -162 224 -176 223 -192 223 -209 223 -228 223 -252 899 3564 22 MP stroke gr 24 w gs 801 760 4884 2903 MR c np 36 36 899 3564 FO 36 36 1122 3312 FO 36 36 1345 3084 FO 36 36 1568 2875 FO 36 36 1791 2683 FO 36 36 2015 2507 FO 36 36 2238 2345 FO 36 36 2461 2194 FO 36 36 2684 2054 FO 36 36 2907 1924 FO 36 36 3131 1803 FO 36 36 3354 1689 FO 36 36 3577 1583 FO 36 36 3800 1483 FO 36 36 4023 1388 FO 36 36 4247 1300 FO 36 36 4470 1216 FO 36 36 4693 1136 FO 36 36 4916 1061 FO 36 36 5139 990 FO 36 36 5363 922 FO 36 36 5586 858 FO gr gs 899 389 5358 4228 MR c np DD 223 -255 223 -234 223 -208 224 -180 223 -158 223 -142 223 -130 223 -120 224 -114 223 -106 223 -99 223 -93 223 -86 224 -80 223 -72 223 -65 223 -58 223 -50 224 -42 223 -34 223 -24 223 -15 223 -5 899 3560 24 MP stroke gr DD gs 801 1092 5330 2567 MR c np SO 36 36 899 3560 FO 36 36 1122 3555 FO 36 36 1345 3540 FO 36 36 1568 3516 FO 36 36 1791 3482 FO 36 36 2015 3440 FO 36 36 2238 3390 FO 36 36 2461 3332 FO 36 36 2684 3267 FO 36 36 2907 3195 FO 36 36 3131 3115 FO 36 36 3354 3029 FO 36 36 3577 2936 FO 36 36 3800 2837 FO 36 36 4023 2731 FO 36 36 4247 2617 FO 36 36 4470 2497 FO 36 36 4693 2367 FO 36 36 4916 2225 FO 36 36 5139 2067 FO 36 36 5363 1887 FO 36 36 5586 1679 FO 36 36 5809 1445 FO 36 36 6032 1190 FO DD gr gs 899 389 5358 4228 MR c np gr 3343 5104 mt (rhos) s 342 4097 mt -90 rotate (Mean response time long jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.8 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 1369 3970 a 8809492 7104430 1184071 11972280 36640440 40521564 startTexFig 1369 3970 a %%BeginDocument: ../figures/results_rhol8coxlongs110.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol8coxlongs110.eps %%CreationDate: 07/25/2002 23:32:47 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 18 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 18 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 0 -48 6472 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5358 0 0 -4227 898 4616 4 MP PP -5358 0 0 4227 5358 0 0 -4227 898 4616 5 MP stroke 4 w DO SO 6 w 0 sg 898 4616 mt 6256 4616 L 898 389 mt 6256 389 L 898 4616 mt 898 389 L 6256 4616 mt 6256 389 L 898 4616 mt 6256 4616 L 898 4616 mt 898 389 L 898 4616 mt 898 4562 L 898 389 mt 898 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 832 4873 mt (0) s 1791 4616 mt 1791 4562 L 1791 389 mt 1791 442 L 1625 4873 mt (0.2) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.4) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3411 4873 mt (0.6) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4304 4873 mt (0.8) s 5363 4616 mt 5363 4562 L 5363 389 mt 5363 442 L 5297 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.2) s 898 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 464 4705 mt (190) s 898 3207 mt 952 3207 L 6256 3207 mt 6202 3207 L 264 3296 mt (190.2) s 898 1798 mt 952 1798 L 6256 1798 mt 6202 1798 L 264 1887 mt (190.4) s 898 389 mt 952 389 L 6256 389 mt 6202 389 L 264 478 mt (190.6) s 898 4616 mt 6256 4616 L 898 389 mt 6256 389 L 898 4616 mt 898 389 L 6256 4616 mt 6256 389 L gs 898 389 5359 4228 MR c np DA 24 w 223 0 223 0 223 0 223 0 224 0 223 0 223 0 223 0 223 0 224 0 223 0 223 0 223 0 223 0 224 0 223 0 223 0 223 0 224 0 898 4614 20 MP stroke SO 223 -86 224 -90 223 -96 223 -100 223 -106 223 -111 224 -119 223 -125 223 -134 223 -142 223 -151 224 -162 223 -174 223 -186 223 -201 223 -217 224 -234 223 -256 223 -278 223 -305 224 -336 898 4614 22 MP stroke gr 24 w gs 800 907 4885 3806 MR c np 36 36 898 4614 FO 36 36 1122 4278 FO 36 36 1345 3973 FO 36 36 1568 3695 FO 36 36 1791 3439 FO 36 36 2015 3205 FO 36 36 2238 2988 FO 36 36 2461 2787 FO 36 36 2684 2601 FO 36 36 2907 2427 FO 36 36 3131 2265 FO 36 36 3354 2114 FO 36 36 3577 1972 FO 36 36 3800 1838 FO 36 36 4023 1713 FO 36 36 4247 1594 FO 36 36 4470 1483 FO 36 36 4693 1377 FO 36 36 4916 1277 FO 36 36 5139 1181 FO 36 36 5363 1091 FO 36 36 5586 1005 FO gr gs 898 389 5359 4228 MR c np DD 223 -455 223 -417 223 -352 224 -244 223 -190 223 -166 223 -150 223 -135 224 -122 223 -112 223 -102 223 -93 223 -84 224 -77 223 -68 223 -61 223 -54 223 -46 224 -38 223 -30 223 -23 223 -13 224 -5 898 4614 24 MP stroke gr DD gs 800 1479 5331 3234 MR c np SO 36 36 898 4614 FO 36 36 1122 4609 FO 36 36 1345 4596 FO 36 36 1568 4573 FO 36 36 1791 4543 FO 36 36 2015 4505 FO 36 36 2238 4459 FO 36 36 2461 4405 FO 36 36 2684 4344 FO 36 36 2907 4276 FO 36 36 3131 4199 FO 36 36 3354 4115 FO 36 36 3577 4022 FO 36 36 3800 3920 FO 36 36 4023 3808 FO 36 36 4247 3686 FO 36 36 4470 3551 FO 36 36 4693 3401 FO 36 36 4916 3235 FO 36 36 5139 3045 FO 36 36 5363 2801 FO 36 36 5586 2449 FO 36 36 5809 2032 FO 36 36 6032 1577 FO DD gr gs 898 389 5359 4228 MR c np gr 3343 5104 mt (rhos) s 209 4097 mt -90 rotate (Mean response time long jobs) s 90 rotate 2577 198 mt (Results: rhol = 0.8 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 2710 3970 a 8383225 7104430 2894397 11972280 36640440 40521564 startTexFig 2710 3970 a %%BeginDocument: ../figures/results_rhol8coxlongs101.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhol8coxlongs101.eps %%CreationDate: 07/25/2002 23:35:42 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 44 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 44 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 315 -48 6157 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4227 5357 0 0 -4227 899 4616 4 MP PP -5357 0 0 4227 5357 0 0 -4227 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L 899 4616 mt 6256 4616 L 899 4616 mt 899 389 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1791 4616 mt 1791 4562 L 1791 389 mt 1791 442 L 1625 4873 mt (0.2) s 2684 4616 mt 2684 4562 L 2684 389 mt 2684 442 L 2518 4873 mt (0.4) s 3577 4616 mt 3577 4562 L 3577 389 mt 3577 442 L 3411 4873 mt (0.6) s 4470 4616 mt 4470 4562 L 4470 389 mt 4470 442 L 4304 4873 mt (0.8) s 5363 4616 mt 5363 4562 L 5363 389 mt 5363 442 L 5297 4873 mt (1) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (1.2) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 598 4705 mt (18) s 899 4012 mt 952 4012 L 6256 4012 mt 6202 4012 L 598 4101 mt (19) s 899 3408 mt 952 3408 L 6256 3408 mt 6202 3408 L 598 3497 mt (20) s 899 2804 mt 952 2804 L 6256 2804 mt 6202 2804 L 598 2893 mt (21) s 899 2200 mt 952 2200 L 6256 2200 mt 6202 2200 L 598 2289 mt (22) s 899 1596 mt 952 1596 L 6256 1596 mt 6202 1596 L 598 1685 mt (23) s 899 992 mt 952 992 L 6256 992 mt 6202 992 L 598 1081 mt (24) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 598 478 mt (25) s 899 4616 mt 6256 4616 L 899 389 mt 6256 389 L 899 4616 mt 899 389 L 6256 4616 mt 6256 389 L gs 899 389 5358 4228 MR c np DA 24 w 223 0 223 0 223 0 223 0 224 0 223 0 223 0 223 0 223 0 224 0 223 0 223 0 223 0 223 0 224 0 223 0 223 0 223 0 223 0 899 4012 20 MP stroke SO 223 -74 224 -77 223 -82 223 -86 223 -90 223 -96 224 -102 223 -107 223 -115 223 -121 223 -130 224 -139 223 -149 223 -160 223 -172 223 -185 224 -202 223 -219 223 -238 223 -262 223 -287 899 4012 22 MP stroke gr 24 w gs 801 821 4884 3290 MR c np 36 36 899 4012 FO 36 36 1122 3725 FO 36 36 1345 3463 FO 36 36 1568 3225 FO 36 36 1791 3006 FO 36 36 2015 2804 FO 36 36 2238 2619 FO 36 36 2461 2447 FO 36 36 2684 2287 FO 36 36 2907 2138 FO 36 36 3131 1999 FO 36 36 3354 1869 FO 36 36 3577 1748 FO 36 36 3800 1633 FO 36 36 4023 1526 FO 36 36 4247 1424 FO 36 36 4470 1328 FO 36 36 4693 1238 FO 36 36 4916 1152 FO 36 36 5139 1070 FO 36 36 5363 993 FO 36 36 5586 919 FO gr gs 899 389 5358 4228 MR c np DD 223 -208 223 -199 223 -191 224 -183 223 -175 223 -167 223 -160 223 -154 224 -147 223 -141 223 -134 223 -128 223 -121 224 -115 223 -107 223 -99 223 -90 223 -80 224 -69 223 -57 223 -42 223 -27 223 -10 899 4012 24 MP stroke gr DD gs 801 1110 5330 3001 MR c np SO 36 36 899 4012 FO 36 36 1122 4002 FO 36 36 1345 3975 FO 36 36 1568 3933 FO 36 36 1791 3876 FO 36 36 2015 3807 FO 36 36 2238 3727 FO 36 36 2461 3637 FO 36 36 2684 3538 FO 36 36 2907 3431 FO 36 36 3131 3316 FO 36 36 3354 3195 FO 36 36 3577 3067 FO 36 36 3800 2933 FO 36 36 4023 2792 FO 36 36 4247 2645 FO 36 36 4470 2491 FO 36 36 4693 2331 FO 36 36 4916 2164 FO 36 36 5139 1989 FO 36 36 5363 1806 FO 36 36 5586 1615 FO 36 36 5809 1416 FO 36 36 6032 1208 FO DD gr gs 899 389 5358 4228 MR c np gr 3343 5104 mt (rhos) s 543 4097 mt -90 rotate (Mean response time long jobs) s 90 rotate 2578 198 mt (Results: rhol = 0.8 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 260 4983 a FC(\(a\))c(shorts)i(1,)e(longs)i(1)646 b(\(b\))24 b(shorts)h(1,)d(longs)j(10)647 b(\(c\))23 b(shorts)i(10,)e(longs)i(1) 120 5179 y(Figure)32 b(12:)45 b Fy(Results)32 b(of)g(analysis,)j(in)d (the)f(case)h(wher)m(e)g(longs)h(ar)m(e)e(dr)o(awn)h(fr)l(om)f(Coxian)h (distrib)n(ution)j(with)120 5292 y(appr)l(opriate)27 b(mean)d(and)g Fu(C)1024 5259 y FE(2)1088 5292 y Fs(=)h(8)p Fy(.)j(Response)d(times)f(ar)m(e)f(shown)i(as)e(a)g(function)j(of)d Fu(\032)2889 5306 y Ft(S)2940 5292 y Fy(.)1875 5349 y FC(24)p eop %%Page: 25 27 25 26 bop 969 68 a FF(Ho)n(w)24 b(shorts)g(gain)g(from)h(c)o (ycle-stealing)e(\226)i Fe(\032)2564 83 y Ft(S)2643 68 y Fd(=)i(1)p Fe(:)p Fd(2)p 969 103 1902 4 v 90 114 a 8383225 7104430 2170798 11972280 36114186 40521564 startTexFig 90 114 a %%BeginDocument: ../figures/results_rhos12coxshorts11.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhos12coxshorts11.eps %%CreationDate: 07/31/2002 13:10:37 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 33 182 549 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 33 182 549 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 181 -48 6191 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1970 4616 mt 1970 4562 L 1970 389 mt 1970 442 L 1804 4873 mt (0.2) s 3041 4616 mt 3041 4562 L 3041 389 mt 3041 442 L 2875 4873 mt (0.4) s 4113 4616 mt 4113 4562 L 4113 389 mt 4113 442 L 3947 4873 mt (0.6) s 5184 4616 mt 5184 4562 L 5184 389 mt 5184 442 L 5018 4873 mt (0.8) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6190 4873 mt (1) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 598 3859 mt (20) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 598 3014 mt (40) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 598 2168 mt (60) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 598 1323 mt (80) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 464 478 mt (100) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np 24 w 268 -2198 268 -539 268 -240 268 -134 268 -85 267 -58 268 -42 268 -32 268 -24 268 -20 268 -16 267 -13 899 4515 13 MP stroke gr 24 w gs 801 1016 3411 3598 MR c np 36 36 899 4515 FO 36 36 1166 4502 FO 36 36 1434 4486 FO 36 36 1702 4466 FO 36 36 1970 4442 FO 36 36 2238 4410 FO 36 36 2506 4368 FO 36 36 2773 4310 FO 36 36 3041 4225 FO 36 36 3309 4091 FO 36 36 3577 3851 FO 36 36 3845 3312 FO 36 36 4113 1114 FO gr gs 899 389 5358 4228 MR c np DD 268 -1583 267 -491 268 -229 268 -128 268 -81 268 -55 268 -39 268 -29 267 -22 268 -17 268 -15 268 -11 268 -10 268 -8 267 -6 899 4549 16 MP stroke gr DD gs 801 1727 4214 2921 MR c np SO 36 36 899 4549 FO 36 36 1166 4543 FO 36 36 1434 4535 FO 36 36 1702 4525 FO 36 36 1970 4514 FO 36 36 2238 4499 FO 36 36 2506 4482 FO 36 36 2773 4460 FO 36 36 3041 4431 FO 36 36 3309 4392 FO 36 36 3577 4337 FO 36 36 3845 4256 FO 36 36 4113 4128 FO 36 36 4381 3899 FO 36 36 4648 3408 FO 36 36 4916 1825 FO DD gr gs 899 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 409 4137 mt -90 rotate (Mean response time short jobs) s 90 rotate 2544 198 mt (Results: rhos = 1.2 ) s SO 6 w 1 sg 0 598 2626 0 0 -598 959 1047 4 MP PP -2626 0 0 598 2626 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 3585 1047 L 959 449 mt 3585 449 L 959 1047 mt 959 449 L 3585 1047 mt 3585 449 L 959 1047 mt 3585 1047 L 959 1047 mt 959 449 L 959 1047 mt 3585 1047 L 959 449 mt 3585 449 L 959 1047 mt 959 449 L 3585 1047 mt 3585 449 L 1627 694 mt (CS-Immed-Disp) s 1627 971 mt (CS-Central-Q) s gs 959 449 2627 599 MR c np 24 w 401 0 1092 613 2 MP stroke gs 1195 515 197 197 MR c np 36 36 1293 613 FO gr DD 401 0 1092 891 2 MP stroke SO gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 1378 114 a 8383225 7104430 2170798 11972280 36114186 40521564 startTexFig 1378 114 a %%BeginDocument: ../figures/results_rhos12coxshorts110.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhos12coxshorts110.eps %%CreationDate: 07/31/2002 13:24:08 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 33 182 549 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 33 182 549 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 181 -48 6191 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1970 4616 mt 1970 4562 L 1970 389 mt 1970 442 L 1804 4873 mt (0.2) s 3041 4616 mt 3041 4562 L 3041 389 mt 3041 442 L 2875 4873 mt (0.4) s 4113 4616 mt 4113 4562 L 4113 389 mt 4113 442 L 3947 4873 mt (0.6) s 5184 4616 mt 5184 4562 L 5184 389 mt 5184 442 L 5018 4873 mt (0.8) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6190 4873 mt (1) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 464 3859 mt (100) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 464 3014 mt (200) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 464 2168 mt (300) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 464 1323 mt (400) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 464 478 mt (500) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np 24 w 268 -2170 268 -517 268 -222 268 -118 268 -72 267 -48 268 -32 268 -24 268 -17 268 -14 268 -10 267 -8 899 4595 13 MP stroke gr 24 w gs 801 1245 3411 3449 MR c np 36 36 899 4595 FO 36 36 1166 4587 FO 36 36 1434 4577 FO 36 36 1702 4563 FO 36 36 1970 4546 FO 36 36 2238 4522 FO 36 36 2506 4490 FO 36 36 2773 4442 FO 36 36 3041 4370 FO 36 36 3309 4252 FO 36 36 3577 4030 FO 36 36 3845 3513 FO 36 36 4113 1343 FO gr gs 899 389 5358 4228 MR c np DD 268 -2410 267 -724 268 -324 268 -176 268 -105 268 -68 268 -47 268 -33 267 -24 268 -19 268 -14 268 -11 268 -9 268 -7 267 -6 899 4602 16 MP stroke gr DD gs 801 527 4214 4174 MR c np SO 36 36 899 4602 FO 36 36 1166 4596 FO 36 36 1434 4589 FO 36 36 1702 4580 FO 36 36 1970 4569 FO 36 36 2238 4555 FO 36 36 2506 4536 FO 36 36 2773 4512 FO 36 36 3041 4479 FO 36 36 3309 4432 FO 36 36 3577 4364 FO 36 36 3845 4259 FO 36 36 4113 4083 FO 36 36 4381 3759 FO 36 36 4648 3035 FO 36 36 4916 625 FO DD gr gs 899 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 409 4137 mt -90 rotate (Mean response time short jobs) s 90 rotate 2544 198 mt (Results: rhos = 1.2 ) s SO 6 w 1 sg 0 598 2626 0 0 -598 959 1047 4 MP PP -2626 0 0 598 2626 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 3585 1047 L 959 449 mt 3585 449 L 959 1047 mt 959 449 L 3585 1047 mt 3585 449 L 959 1047 mt 3585 1047 L 959 1047 mt 959 449 L 959 1047 mt 3585 1047 L 959 449 mt 3585 449 L 959 1047 mt 959 449 L 3585 1047 mt 3585 449 L 1627 694 mt (CS-Immed-Disp) s 1627 971 mt (CS-Central-Q) s gs 959 449 2627 599 MR c np 24 w 401 0 1092 613 2 MP stroke gs 1195 515 197 197 MR c np 36 36 1293 613 FO gr DD 401 0 1092 891 2 MP stroke SO gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 2665 114 a 8383225 7104430 2170798 11972280 36114186 40521564 startTexFig 2665 114 a %%BeginDocument: ../figures/results_rhos12coxshorts101.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhos12coxshorts101.eps %%CreationDate: 07/31/2002 13:37:09 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 33 182 549 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 33 182 549 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 181 -48 6191 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1970 4616 mt 1970 4562 L 1970 389 mt 1970 442 L 1804 4873 mt (0.2) s 3041 4616 mt 3041 4562 L 3041 389 mt 3041 442 L 2875 4873 mt (0.4) s 4113 4616 mt 4113 4562 L 4113 389 mt 4113 442 L 3947 4873 mt (0.6) s 5184 4616 mt 5184 4562 L 5184 389 mt 5184 442 L 5018 4873 mt (0.8) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6190 4873 mt (1) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3911 mt 952 3911 L 6256 3911 mt 6202 3911 L 464 4000 mt (100) s 899 3207 mt 952 3207 L 6256 3207 mt 6202 3207 L 464 3296 mt (200) s 899 2502 mt 952 2502 L 6256 2502 mt 6202 2502 L 464 2591 mt (300) s 899 1798 mt 952 1798 L 6256 1798 mt 6202 1798 L 464 1887 mt (400) s 899 1093 mt 952 1093 L 6256 1093 mt 6202 1093 L 464 1182 mt (500) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 464 478 mt (600) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np 24 w 268 -2214 268 -552 268 -250 268 -141 268 -91 267 -64 268 -46 268 -35 268 -28 268 -22 268 -18 267 -15 899 4448 13 MP stroke gr 24 w gs 801 874 3411 3673 MR c np 36 36 899 4448 FO 36 36 1166 4433 FO 36 36 1434 4415 FO 36 36 1702 4393 FO 36 36 1970 4365 FO 36 36 2238 4330 FO 36 36 2506 4284 FO 36 36 2773 4220 FO 36 36 3041 4129 FO 36 36 3309 3988 FO 36 36 3577 3738 FO 36 36 3845 3186 FO 36 36 4113 972 FO gr gs 899 389 5358 4228 MR c np DD 268 -864 267 -282 268 -138 268 -81 268 -53 268 -36 268 -27 268 -20 267 -16 268 -13 268 -10 268 -9 268 -7 268 -6 267 -5 899 4505 16 MP stroke gr DD gs 801 2840 4214 1764 MR c np SO 36 36 899 4505 FO 36 36 1166 4500 FO 36 36 1434 4494 FO 36 36 1702 4487 FO 36 36 1970 4478 FO 36 36 2238 4468 FO 36 36 2506 4455 FO 36 36 2773 4439 FO 36 36 3041 4419 FO 36 36 3309 4392 FO 36 36 3577 4356 FO 36 36 3845 4303 FO 36 36 4113 4222 FO 36 36 4381 4084 FO 36 36 4648 3802 FO 36 36 4916 2938 FO DD gr gs 899 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 409 4137 mt -90 rotate (Mean response time short jobs) s 90 rotate 2544 198 mt (Results: rhos = 1.2 ) s SO 6 w 1 sg 0 598 2626 0 0 -598 959 1047 4 MP PP -2626 0 0 598 2626 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 3585 1047 L 959 449 mt 3585 449 L 959 1047 mt 959 449 L 3585 1047 mt 3585 449 L 959 1047 mt 3585 1047 L 959 1047 mt 959 449 L 959 1047 mt 3585 1047 L 959 449 mt 3585 449 L 959 1047 mt 959 449 L 3585 1047 mt 3585 449 L 1627 694 mt (CS-Immed-Disp) s 1627 971 mt (CS-Central-Q) s gs 959 449 2627 599 MR c np 24 w 401 0 1092 613 2 MP stroke gs 1195 515 197 197 MR c np 36 36 1293 613 FO gr DD 401 0 1092 891 2 MP stroke SO gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 260 1127 a FC(\(a\))c(shorts)i(1,)e(longs)i(1)646 b(\(b\))24 b(shorts)h(1,)d(longs)j(10)647 b(\(c\))23 b(shorts)i(10,)e(longs)i(1) 951 1353 y FF(Ho)n(w)f(longs)g(suf)n(fer)g(from)h(c)o(ycle-stealing)f (\226)g Fe(\032)2582 1368 y Ft(S)2661 1353 y Fd(=)k(1)p Fe(:)p Fd(2)p 951 1388 1939 4 v 77 1400 a 8383225 7104430 2170798 11972280 36114186 40521564 startTexFig 77 1400 a %%BeginDocument: ../figures/results_rhos12coxlongs11.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhos12coxlongs11.eps %%CreationDate: 07/31/2002 13:10:37 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 33 182 549 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 33 182 549 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 181 -48 6191 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1970 4616 mt 1970 4562 L 1970 389 mt 1970 442 L 1804 4873 mt (0.2) s 3041 4616 mt 3041 4562 L 3041 389 mt 3041 442 L 2875 4873 mt (0.4) s 4113 4616 mt 4113 4562 L 4113 389 mt 4113 442 L 3947 4873 mt (0.6) s 5184 4616 mt 5184 4562 L 5184 389 mt 5184 442 L 5018 4873 mt (0.8) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6190 4873 mt (1) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 598 3859 mt (20) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 598 3014 mt (40) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 598 2168 mt (60) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 598 1323 mt (80) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 464 478 mt (100) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 268 -1903 268 -634 268 -317 268 -191 268 -126 267 -91 268 -68 268 -53 268 -42 268 -35 268 -28 268 -25 267 -21 268 -18 268 -16 268 -14 268 -12 268 -11 267 -10 899 4573 20 MP stroke SO 268 -1902 268 -634 268 -317 268 -191 268 -126 267 -91 268 -68 268 -53 268 -42 268 -35 268 -28 268 -25 267 -21 268 -18 268 -16 268 -14 268 -12 268 -11 267 -10 899 4550 20 MP stroke gr 24 w gs 801 838 5286 3811 MR c np 36 36 899 4550 FO 36 36 1166 4540 FO 36 36 1434 4529 FO 36 36 1702 4517 FO 36 36 1970 4503 FO 36 36 2238 4487 FO 36 36 2506 4469 FO 36 36 2773 4448 FO 36 36 3041 4423 FO 36 36 3309 4395 FO 36 36 3577 4360 FO 36 36 3845 4318 FO 36 36 4113 4265 FO 36 36 4381 4197 FO 36 36 4648 4106 FO 36 36 4916 3980 FO 36 36 5184 3789 FO 36 36 5452 3472 FO 36 36 5720 2838 FO 36 36 5988 936 FO gr gs 899 389 5358 4228 MR c np DD 268 -1903 268 -634 268 -317 268 -192 268 -129 267 -92 268 -69 268 -53 268 -43 268 -35 268 -30 268 -25 267 -21 268 -19 268 -16 268 -14 268 -13 268 -11 267 -11 899 4564 20 MP stroke gr DD gs 801 839 5286 3824 MR c np SO 36 36 899 4564 FO 36 36 1166 4553 FO 36 36 1434 4542 FO 36 36 1702 4529 FO 36 36 1970 4515 FO 36 36 2238 4499 FO 36 36 2506 4480 FO 36 36 2773 4459 FO 36 36 3041 4434 FO 36 36 3309 4404 FO 36 36 3577 4369 FO 36 36 3845 4326 FO 36 36 4113 4273 FO 36 36 4381 4204 FO 36 36 4648 4112 FO 36 36 4916 3983 FO 36 36 5184 3791 FO 36 36 5452 3474 FO 36 36 5720 2840 FO 36 36 5988 937 FO DD gr gs 899 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 409 4097 mt -90 rotate (Mean response time long jobs) s 90 rotate 2544 198 mt (Results: rhos = 1.2 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 1364 1400 a 8596360 7104430 1447198 11972280 36114186 40521564 startTexFig 1364 1400 a %%BeginDocument: ../figures/results_rhos12coxlongs110.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhos12coxlongs110.eps %%CreationDate: 07/31/2002 13:24:09 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 22 182 549 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 22 182 549 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 48 -48 6324 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1970 4616 mt 1970 4562 L 1970 389 mt 1970 442 L 1804 4873 mt (0.2) s 3041 4616 mt 3041 4562 L 3041 389 mt 3041 442 L 2875 4873 mt (0.4) s 4113 4616 mt 4113 4562 L 4113 389 mt 4113 442 L 3947 4873 mt (0.6) s 5184 4616 mt 5184 4562 L 5184 389 mt 5184 442 L 5018 4873 mt (0.8) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6190 4873 mt (1) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 464 3859 mt (200) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 464 3014 mt (400) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 464 2168 mt (600) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 464 1323 mt (800) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 331 478 mt (1000) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 268 -1903 268 -634 268 -317 268 -191 268 -126 267 -91 268 -68 268 -53 268 -42 268 -35 268 -28 268 -25 267 -21 268 -18 268 -16 268 -14 268 -12 268 -11 267 -10 899 4573 20 MP stroke SO 268 -1903 268 -634 268 -317 268 -190 268 -127 267 -91 268 -68 268 -52 268 -43 268 -34 268 -29 268 -24 267 -21 268 -19 268 -15 268 -14 268 -13 268 -11 267 -10 899 4571 20 MP stroke gr 24 w gs 801 858 5286 3812 MR c np 36 36 899 4571 FO 36 36 1166 4561 FO 36 36 1434 4550 FO 36 36 1702 4537 FO 36 36 1970 4523 FO 36 36 2238 4508 FO 36 36 2506 4489 FO 36 36 2773 4468 FO 36 36 3041 4444 FO 36 36 3309 4415 FO 36 36 3577 4381 FO 36 36 3845 4338 FO 36 36 4113 4286 FO 36 36 4381 4218 FO 36 36 4648 4127 FO 36 36 4916 4000 FO 36 36 5184 3810 FO 36 36 5452 3493 FO 36 36 5720 2859 FO 36 36 5988 956 FO gr gs 899 389 5358 4228 MR c np DD 268 -1903 268 -634 268 -317 268 -191 268 -127 267 -90 268 -68 268 -53 268 -43 268 -34 268 -29 268 -25 267 -21 268 -18 268 -16 268 -14 268 -12 268 -11 267 -10 899 4572 20 MP stroke gr DD gs 801 858 5286 3813 MR c np SO 36 36 899 4572 FO 36 36 1166 4562 FO 36 36 1434 4551 FO 36 36 1702 4539 FO 36 36 1970 4525 FO 36 36 2238 4509 FO 36 36 2506 4491 FO 36 36 2773 4470 FO 36 36 3041 4445 FO 36 36 3309 4416 FO 36 36 3577 4382 FO 36 36 3845 4339 FO 36 36 4113 4286 FO 36 36 4381 4218 FO 36 36 4648 4128 FO 36 36 4916 4001 FO 36 36 5184 3810 FO 36 36 5452 3493 FO 36 36 5720 2859 FO 36 36 5988 956 FO DD gr gs 899 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 276 4097 mt -90 rotate (Mean response time long jobs) s 90 rotate 2544 198 mt (Results: rhos = 1.2 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 2679 1400 a 8383225 7104430 2170798 11972280 36114186 40521564 startTexFig 2679 1400 a %%BeginDocument: ../figures/results_rhos12coxlongs101.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhos12coxlongs101.eps %%CreationDate: 07/31/2002 13:37:09 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 33 182 549 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 33 182 549 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 181 -48 6191 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1970 4616 mt 1970 4562 L 1970 389 mt 1970 442 L 1804 4873 mt (0.2) s 3041 4616 mt 3041 4562 L 3041 389 mt 3041 442 L 2875 4873 mt (0.4) s 4113 4616 mt 4113 4562 L 4113 389 mt 4113 442 L 3947 4873 mt (0.6) s 5184 4616 mt 5184 4562 L 5184 389 mt 5184 442 L 5018 4873 mt (0.8) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6190 4873 mt (1) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 598 3859 mt (20) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 598 3014 mt (40) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 598 2168 mt (60) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 598 1323 mt (80) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 464 478 mt (100) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 268 -1903 268 -634 268 -317 268 -191 268 -126 267 -91 268 -68 268 -53 268 -42 268 -35 268 -28 268 -25 267 -21 268 -18 268 -16 268 -14 268 -12 268 -11 267 -10 899 4573 20 MP stroke SO 268 -1902 268 -634 268 -317 268 -190 268 -127 267 -90 268 -68 268 -53 268 -42 268 -35 268 -29 268 -24 267 -21 268 -18 268 -16 268 -14 268 -13 268 -11 267 -10 899 4343 20 MP stroke gr 24 w gs 801 631 5286 3811 MR c np 36 36 899 4343 FO 36 36 1166 4333 FO 36 36 1434 4322 FO 36 36 1702 4309 FO 36 36 1970 4295 FO 36 36 2238 4279 FO 36 36 2506 4261 FO 36 36 2773 4240 FO 36 36 3041 4216 FO 36 36 3309 4187 FO 36 36 3577 4152 FO 36 36 3845 4110 FO 36 36 4113 4057 FO 36 36 4381 3989 FO 36 36 4648 3899 FO 36 36 4916 3772 FO 36 36 5184 3582 FO 36 36 5452 3265 FO 36 36 5720 2631 FO 36 36 5988 729 FO gr gs 899 389 5358 4228 MR c np DD 268 -1903 268 -634 268 -317 268 -205 268 -139 267 -102 268 -78 268 -61 268 -51 268 -42 268 -35 268 -31 267 -26 268 -23 268 -21 268 -18 268 -17 268 -15 267 -13 899 4478 20 MP stroke gr DD gs 801 649 5286 3928 MR c np SO 36 36 899 4478 FO 36 36 1166 4465 FO 36 36 1434 4450 FO 36 36 1702 4433 FO 36 36 1970 4415 FO 36 36 2238 4394 FO 36 36 2506 4371 FO 36 36 2773 4345 FO 36 36 3041 4314 FO 36 36 3309 4279 FO 36 36 3577 4237 FO 36 36 3845 4186 FO 36 36 4113 4125 FO 36 36 4381 4047 FO 36 36 4648 3945 FO 36 36 4916 3806 FO 36 36 5184 3601 FO 36 36 5452 3284 FO 36 36 5720 2650 FO 36 36 5988 747 FO DD gr gs 899 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 409 4097 mt -90 rotate (Mean response time long jobs) s 90 rotate 2544 198 mt (Results: rhos = 1.2 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 260 2413 a FC(\(a\))23 b(shorts)i(1,)e(longs)i(1)646 b(\(b\))24 b(shorts)h(1,)d(longs)j(10)647 b(\(c\))23 b(shorts)i(10,)e(longs)i(1)969 2638 y FF(Ho)n(w)f(shorts)g(gain)g(from) h(c)o(ycle-stealing)e(\226)i Fe(\032)2564 2653 y Ft(S)2643 2638 y Fd(=)i(1)p Fe(:)p Fd(5)p 969 2673 1902 4 v 50 2685 a 8525316 7104430 2170798 11972280 36640440 40521564 startTexFig 50 2685 a %%BeginDocument: ../figures/results_rhos15coxshorts11.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhos15coxshorts11.eps %%CreationDate: 07/31/2002 13:13:35 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 33 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 33 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 181 -48 6291 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1970 4616 mt 1970 4562 L 1970 389 mt 1970 442 L 1804 4873 mt (0.1) s 3041 4616 mt 3041 4562 L 3041 389 mt 3041 442 L 2875 4873 mt (0.2) s 4113 4616 mt 4113 4562 L 4113 389 mt 4113 442 L 3947 4873 mt (0.3) s 5184 4616 mt 5184 4562 L 5184 389 mt 5184 442 L 5018 4873 mt (0.4) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (0.5) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 598 3859 mt (20) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 598 3014 mt (40) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 598 2168 mt (60) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 598 1323 mt (80) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 464 478 mt (100) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np 24 w 536 -3061 536 -434 535 -172 899 4286 4 MP stroke gr 24 w gs 801 521 1804 3864 MR c np 36 36 899 4286 FO 36 36 1434 4114 FO 36 36 1970 3680 FO 36 36 2506 619 FO gr gs 899 389 5358 4228 MR c np DD 536 -1031 536 -334 535 -162 536 -93 536 -60 535 -42 536 -29 536 -23 535 -17 899 4519 10 MP stroke gr DD gs 801 2630 5018 1988 MR c np SO 36 36 899 4519 FO 36 36 1434 4502 FO 36 36 1970 4479 FO 36 36 2506 4450 FO 36 36 3041 4408 FO 36 36 3577 4348 FO 36 36 4113 4255 FO 36 36 4648 4093 FO 36 36 5184 3759 FO 36 36 5720 2728 FO DD gr gs 899 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 409 4137 mt -90 rotate (Mean response time short jobs) s 90 rotate 2544 198 mt (Results: rhos = 1.5 ) s SO 6 w 1 sg 0 598 2626 0 0 -598 959 1047 4 MP PP -2626 0 0 598 2626 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 3585 1047 L 959 449 mt 3585 449 L 959 1047 mt 959 449 L 3585 1047 mt 3585 449 L 959 1047 mt 3585 1047 L 959 1047 mt 959 449 L 959 1047 mt 3585 1047 L 959 449 mt 3585 449 L 959 1047 mt 959 449 L 3585 1047 mt 3585 449 L 1627 694 mt (CS-Immed-Disp) s 1627 971 mt (CS-Central-Q) s gs 959 449 2627 599 MR c np 24 w 401 0 1092 613 2 MP stroke gs 1195 515 197 197 MR c np 36 36 1293 613 FO gr DD 401 0 1092 891 2 MP stroke SO gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 1355 2685 a 8525316 7104430 2170798 11972280 36640440 40521564 startTexFig 1355 2685 a %%BeginDocument: ../figures/results_rhos15coxshorts110.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhos15coxshorts110.eps %%CreationDate: 07/31/2002 13:34:57 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 33 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 33 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 181 -48 6291 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1970 4616 mt 1970 4562 L 1970 389 mt 1970 442 L 1804 4873 mt (0.1) s 3041 4616 mt 3041 4562 L 3041 389 mt 3041 442 L 2875 4873 mt (0.2) s 4113 4616 mt 4113 4562 L 4113 389 mt 4113 442 L 3947 4873 mt (0.3) s 5184 4616 mt 5184 4562 L 5184 389 mt 5184 442 L 5018 4873 mt (0.4) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (0.5) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3911 mt 952 3911 L 6256 3911 mt 6202 3911 L 598 4000 mt (50) s 899 3207 mt 952 3207 L 6256 3207 mt 6202 3207 L 464 3296 mt (100) s 899 2502 mt 952 2502 L 6256 2502 mt 6202 2502 L 464 2591 mt (150) s 899 1798 mt 952 1798 L 6256 1798 mt 6202 1798 L 464 1887 mt (200) s 899 1093 mt 952 1093 L 6256 1093 mt 6202 1093 L 464 1182 mt (250) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 464 478 mt (300) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np 24 w 536 -2719 536 -376 535 -144 899 4506 4 MP stroke gr 24 w gs 801 1169 1804 3436 MR c np 36 36 899 4506 FO 36 36 1434 4362 FO 36 36 1970 3986 FO 36 36 2506 1267 FO gr gs 899 389 5358 4228 MR c np DD 536 -2191 536 -698 535 -330 536 -185 536 -116 535 -76 536 -54 536 -38 535 -28 899 4583 10 MP stroke gr DD gs 801 769 5018 3913 MR c np SO 36 36 899 4583 FO 36 36 1434 4555 FO 36 36 1970 4517 FO 36 36 2506 4463 FO 36 36 3041 4387 FO 36 36 3577 4271 FO 36 36 4113 4086 FO 36 36 4648 3756 FO 36 36 5184 3058 FO 36 36 5720 867 FO DD gr gs 899 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 409 4137 mt -90 rotate (Mean response time short jobs) s 90 rotate 2544 198 mt (Results: rhos = 1.5 ) s SO 6 w 1 sg 0 598 2626 0 0 -598 959 1047 4 MP PP -2626 0 0 598 2626 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 3585 1047 L 959 449 mt 3585 449 L 959 1047 mt 959 449 L 3585 1047 mt 3585 449 L 959 1047 mt 3585 1047 L 959 1047 mt 959 449 L 959 1047 mt 3585 1047 L 959 449 mt 3585 449 L 959 1047 mt 959 449 L 3585 1047 mt 3585 449 L 1627 694 mt (CS-Immed-Disp) s 1627 971 mt (CS-Central-Q) s gs 959 449 2627 599 MR c np 24 w 401 0 1092 613 2 MP stroke gs 1195 515 197 197 MR c np 36 36 1293 613 FO gr DD 401 0 1092 891 2 MP stroke SO gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 2661 2685 a 8738448 7104430 1447198 11972280 36640440 40521564 startTexFig 2661 2685 a %%BeginDocument: ../figures/results_rhos15coxshorts101.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhos15coxshorts101.eps %%CreationDate: 07/31/2002 13:39:11 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 22 182 557 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 22 182 557 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 48 -48 6424 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1970 4616 mt 1970 4562 L 1970 389 mt 1970 442 L 1804 4873 mt (0.1) s 3041 4616 mt 3041 4562 L 3041 389 mt 3041 442 L 2875 4873 mt (0.2) s 4113 4616 mt 4113 4562 L 4113 389 mt 4113 442 L 3947 4873 mt (0.3) s 5184 4616 mt 5184 4562 L 5184 389 mt 5184 442 L 5018 4873 mt (0.4) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6090 4873 mt (0.5) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 464 3859 mt (200) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 464 3014 mt (400) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 464 2168 mt (600) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 464 1323 mt (800) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 331 478 mt (1000) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np 24 w 536 -2551 536 -363 535 -145 899 4286 4 MP stroke gr 24 w gs 801 1129 1804 3256 MR c np 36 36 899 4286 FO 36 36 1434 4141 FO 36 36 1970 3778 FO 36 36 2506 1227 FO gr gs 899 389 5358 4228 MR c np DD 536 -458 536 -152 535 -74 536 -45 536 -29 535 -20 536 -16 536 -11 535 -10 899 4519 10 MP stroke gr DD gs 801 3606 5018 1012 MR c np SO 36 36 899 4519 FO 36 36 1434 4509 FO 36 36 1970 4498 FO 36 36 2506 4482 FO 36 36 3041 4462 FO 36 36 3577 4433 FO 36 36 4113 4388 FO 36 36 4648 4314 FO 36 36 5184 4162 FO 36 36 5720 3704 FO DD gr gs 899 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 276 4137 mt -90 rotate (Mean response time short jobs) s 90 rotate 2544 198 mt (Results: rhos = 1.5 ) s SO 6 w 1 sg 0 598 2626 0 0 -598 959 1047 4 MP PP -2626 0 0 598 2626 0 0 -598 959 1047 5 MP stroke 4 w DO SO 6 w 0 sg 959 1047 mt 3585 1047 L 959 449 mt 3585 449 L 959 1047 mt 959 449 L 3585 1047 mt 3585 449 L 959 1047 mt 3585 1047 L 959 1047 mt 959 449 L 959 1047 mt 3585 1047 L 959 449 mt 3585 449 L 959 1047 mt 959 449 L 3585 1047 mt 3585 449 L 1627 694 mt (CS-Immed-Disp) s 1627 971 mt (CS-Central-Q) s gs 959 449 2627 599 MR c np 24 w 401 0 1092 613 2 MP stroke gs 1195 515 197 197 MR c np 36 36 1293 613 FO gr DD 401 0 1092 891 2 MP stroke SO gs 1195 793 197 197 MR c np 36 36 1293 891 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 260 3698 a FC(\(a\))c(shorts)i(1,)e(longs)i(1)646 b(\(b\))24 b(shorts)h(1,)d(longs)j(10)647 b(\(c\))23 b(shorts)i(10,)e(longs)i(1) 951 3924 y FF(Ho)n(w)f(longs)g(suf)n(fer)g(from)h(c)o(ycle-stealing)f (\226)g Fe(\032)2582 3939 y Ft(S)2661 3924 y Fd(=)k(1)p Fe(:)p Fd(5)p 951 3958 1939 4 v 77 3970 a 8383225 7104430 2170798 11972280 36114186 40521564 startTexFig 77 3970 a %%BeginDocument: ../figures/results_rhos15coxlongs11.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhos15coxlongs11.eps %%CreationDate: 07/31/2002 13:13:35 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 33 182 549 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 33 182 549 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 181 -48 6191 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1970 4616 mt 1970 4562 L 1970 389 mt 1970 442 L 1804 4873 mt (0.2) s 3041 4616 mt 3041 4562 L 3041 389 mt 3041 442 L 2875 4873 mt (0.4) s 4113 4616 mt 4113 4562 L 4113 389 mt 4113 442 L 3947 4873 mt (0.6) s 5184 4616 mt 5184 4562 L 5184 389 mt 5184 442 L 5018 4873 mt (0.8) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6190 4873 mt (1) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 598 3859 mt (20) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 598 3014 mt (40) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 598 2168 mt (60) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 598 1323 mt (80) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 464 478 mt (100) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 268 -1903 268 -634 268 -317 268 -191 268 -126 267 -91 268 -68 268 -53 268 -42 268 -35 268 -28 268 -25 267 -21 268 -18 268 -16 268 -14 268 -12 268 -11 267 -10 899 4573 20 MP stroke SO 268 -1902 268 -634 268 -317 268 -190 268 -127 267 -91 268 -68 268 -52 268 -43 268 -34 268 -29 268 -24 267 -21 268 -18 268 -16 268 -14 268 -13 268 -11 267 -10 899 4548 20 MP stroke gr 24 w gs 801 836 5286 3811 MR c np 36 36 899 4548 FO 36 36 1166 4538 FO 36 36 1434 4527 FO 36 36 1702 4514 FO 36 36 1970 4500 FO 36 36 2238 4484 FO 36 36 2506 4466 FO 36 36 2773 4445 FO 36 36 3041 4421 FO 36 36 3309 4392 FO 36 36 3577 4358 FO 36 36 3845 4315 FO 36 36 4113 4263 FO 36 36 4381 4195 FO 36 36 4648 4104 FO 36 36 4916 3977 FO 36 36 5184 3787 FO 36 36 5452 3470 FO 36 36 5720 2836 FO 36 36 5988 934 FO gr gs 899 389 5358 4228 MR c np DD 268 -1903 268 -634 268 -317 268 -190 268 -127 267 -91 268 -68 268 -53 268 -42 268 -36 268 -30 268 -25 267 -22 268 -18 268 -17 268 -15 268 -13 268 -11 267 -11 899 4560 20 MP stroke gr DD gs 801 839 5286 3820 MR c np SO 36 36 899 4560 FO 36 36 1166 4549 FO 36 36 1434 4538 FO 36 36 1702 4525 FO 36 36 1970 4510 FO 36 36 2238 4493 FO 36 36 2506 4475 FO 36 36 2773 4453 FO 36 36 3041 4428 FO 36 36 3309 4398 FO 36 36 3577 4362 FO 36 36 3845 4320 FO 36 36 4113 4267 FO 36 36 4381 4199 FO 36 36 4648 4108 FO 36 36 4916 3981 FO 36 36 5184 3791 FO 36 36 5452 3474 FO 36 36 5720 2840 FO 36 36 5988 937 FO DD gr gs 899 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 409 4097 mt -90 rotate (Mean response time long jobs) s 90 rotate 2544 198 mt (Results: rhos = 1.5 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 1364 3970 a 8596360 7104430 1447198 11972280 36114186 40521564 startTexFig 1364 3970 a %%BeginDocument: ../figures/results_rhos15coxlongs110.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhos15coxlongs110.eps %%CreationDate: 07/31/2002 13:34:58 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 22 182 549 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 22 182 549 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 48 -48 6324 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1970 4616 mt 1970 4562 L 1970 389 mt 1970 442 L 1804 4873 mt (0.2) s 3041 4616 mt 3041 4562 L 3041 389 mt 3041 442 L 2875 4873 mt (0.4) s 4113 4616 mt 4113 4562 L 4113 389 mt 4113 442 L 3947 4873 mt (0.6) s 5184 4616 mt 5184 4562 L 5184 389 mt 5184 442 L 5018 4873 mt (0.8) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6190 4873 mt (1) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 464 3859 mt (200) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 464 3014 mt (400) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 464 2168 mt (600) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 464 1323 mt (800) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 331 478 mt (1000) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 268 -1903 268 -634 268 -317 268 -191 268 -126 267 -91 268 -68 268 -53 268 -42 268 -35 268 -28 268 -25 267 -21 268 -18 268 -16 268 -14 268 -12 268 -11 267 -10 899 4573 20 MP stroke SO 268 -1903 268 -634 268 -317 268 -190 268 -127 267 -90 268 -68 268 -53 268 -42 268 -35 268 -29 268 -24 267 -21 268 -18 268 -16 268 -14 268 -13 268 -11 267 -10 899 4571 20 MP stroke gr 24 w gs 801 858 5286 3812 MR c np 36 36 899 4571 FO 36 36 1166 4561 FO 36 36 1434 4550 FO 36 36 1702 4537 FO 36 36 1970 4523 FO 36 36 2238 4507 FO 36 36 2506 4489 FO 36 36 2773 4468 FO 36 36 3041 4444 FO 36 36 3309 4415 FO 36 36 3577 4380 FO 36 36 3845 4338 FO 36 36 4113 4285 FO 36 36 4381 4217 FO 36 36 4648 4127 FO 36 36 4916 4000 FO 36 36 5184 3810 FO 36 36 5452 3493 FO 36 36 5720 2859 FO 36 36 5988 956 FO gr gs 899 389 5358 4228 MR c np DD 268 -1903 268 -634 268 -317 268 -190 268 -127 267 -91 268 -68 268 -53 268 -42 268 -35 268 -29 268 -24 267 -21 268 -18 268 -16 268 -14 268 -13 268 -11 267 -10 899 4572 20 MP stroke gr DD gs 801 858 5286 3813 MR c np SO 36 36 899 4572 FO 36 36 1166 4562 FO 36 36 1434 4551 FO 36 36 1702 4538 FO 36 36 1970 4524 FO 36 36 2238 4508 FO 36 36 2506 4490 FO 36 36 2773 4469 FO 36 36 3041 4445 FO 36 36 3309 4416 FO 36 36 3577 4381 FO 36 36 3845 4339 FO 36 36 4113 4286 FO 36 36 4381 4218 FO 36 36 4648 4127 FO 36 36 4916 4000 FO 36 36 5184 3810 FO 36 36 5452 3493 FO 36 36 5720 2859 FO 36 36 5988 956 FO DD gr gs 899 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 276 4097 mt -90 rotate (Mean response time long jobs) s 90 rotate 2544 198 mt (Results: rhos = 1.5 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 2679 3970 a 8383225 7104430 2170798 11972280 36114186 40521564 startTexFig 2679 3970 a %%BeginDocument: ../figures/results_rhos15coxlongs101.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: results_rhos15coxlongs101.eps %%CreationDate: 07/31/2002 13:39:12 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 33 182 549 616 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup string currentfile exch readhexstring pop /bmap xdef pop pop} bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform {bmap} image gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 33 182 549 616 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 181 -48 6191 5208 MR c np 91 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6914 5188 PR 6 w 0 4228 5357 0 0 -4228 899 4616 4 MP PP -5357 0 0 4228 5357 0 0 -4228 899 4616 5 MP stroke 4 w DO SO 6 w 0 sg 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L 899 4616 mt 6256 4616 L 899 4616 mt 899 388 L 899 4616 mt 899 4562 L 899 389 mt 899 442 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 240 FMSR 833 4873 mt (0) s 1970 4616 mt 1970 4562 L 1970 389 mt 1970 442 L 1804 4873 mt (0.2) s 3041 4616 mt 3041 4562 L 3041 389 mt 3041 442 L 2875 4873 mt (0.4) s 4113 4616 mt 4113 4562 L 4113 389 mt 4113 442 L 3947 4873 mt (0.6) s 5184 4616 mt 5184 4562 L 5184 389 mt 5184 442 L 5018 4873 mt (0.8) s 6256 4616 mt 6256 4562 L 6256 389 mt 6256 442 L 6190 4873 mt (1) s 899 4616 mt 952 4616 L 6256 4616 mt 6202 4616 L 731 4705 mt (0) s 899 3770 mt 952 3770 L 6256 3770 mt 6202 3770 L 598 3859 mt (20) s 899 2925 mt 952 2925 L 6256 2925 mt 6202 2925 L 598 3014 mt (40) s 899 2079 mt 952 2079 L 6256 2079 mt 6202 2079 L 598 2168 mt (60) s 899 1234 mt 952 1234 L 6256 1234 mt 6202 1234 L 598 1323 mt (80) s 899 389 mt 952 389 L 6256 389 mt 6202 389 L 464 478 mt (100) s 899 4616 mt 6256 4616 L 899 388 mt 6256 388 L 899 4616 mt 899 388 L 6256 4616 mt 6256 388 L gs 899 389 5358 4228 MR c np DA 24 w 268 -1903 268 -634 268 -317 268 -191 268 -126 267 -91 268 -68 268 -53 268 -42 268 -35 268 -28 268 -25 267 -21 268 -18 268 -16 268 -14 268 -12 268 -11 267 -10 899 4573 20 MP stroke SO 268 -1902 268 -634 268 -317 268 -190 268 -127 267 -90 268 -68 268 -53 268 -42 268 -35 268 -29 268 -24 267 -21 268 -18 268 -16 268 -14 268 -12 268 -12 267 -10 899 4320 20 MP stroke gr 24 w gs 801 608 5286 3811 MR c np 36 36 899 4320 FO 36 36 1166 4310 FO 36 36 1434 4298 FO 36 36 1702 4286 FO 36 36 1970 4272 FO 36 36 2238 4256 FO 36 36 2506 4238 FO 36 36 2773 4217 FO 36 36 3041 4193 FO 36 36 3309 4164 FO 36 36 3577 4129 FO 36 36 3845 4087 FO 36 36 4113 4034 FO 36 36 4381 3966 FO 36 36 4648 3876 FO 36 36 4916 3749 FO 36 36 5184 3559 FO 36 36 5452 3242 FO 36 36 5720 2608 FO 36 36 5988 706 FO gr gs 899 389 5358 4228 MR c np DD 268 -1903 268 -634 268 -317 268 -190 268 -127 267 -91 268 -68 268 -52 268 -43 268 -45 268 -39 268 -33 267 -29 268 -26 268 -23 268 -20 268 -19 268 -16 267 -15 899 4437 20 MP stroke gr DD gs 801 649 5286 3887 MR c np SO 36 36 899 4437 FO 36 36 1166 4422 FO 36 36 1434 4406 FO 36 36 1702 4387 FO 36 36 1970 4367 FO 36 36 2238 4344 FO 36 36 2506 4318 FO 36 36 2773 4289 FO 36 36 3041 4256 FO 36 36 3309 4217 FO 36 36 3577 4172 FO 36 36 3845 4129 FO 36 36 4113 4077 FO 36 36 4381 4009 FO 36 36 4648 3918 FO 36 36 4916 3791 FO 36 36 5184 3601 FO 36 36 5452 3284 FO 36 36 5720 2650 FO 36 36 5988 747 FO DD gr gs 899 389 5358 4228 MR c np gr 3377 5104 mt (rhol) s 409 4097 mt -90 rotate (Mean response time long jobs) s 90 rotate 2544 198 mt (Results: rhos = 1.5 ) s SO 6 w 1 sg 0 875 2626 0 0 -875 959 1324 4 MP PP -2626 0 0 875 2626 0 0 -875 959 1324 5 MP stroke 4 w DO SO 6 w 0 sg 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 959 1324 mt 3585 1324 L 959 1324 mt 959 449 L 959 1324 mt 3585 1324 L 959 449 mt 3585 449 L 959 1324 mt 959 449 L 3585 1324 mt 3585 449 L 1627 694 mt (Dedicated) s 1627 971 mt (CS-Immed-Disp) s 1627 1248 mt (CS-Central-Q) s gs 959 449 2627 876 MR c np DA 24 w 401 0 1092 613 2 MP stroke SO 401 0 1092 890 2 MP stroke gs 1195 792 197 197 MR c np 36 36 1293 890 FO gr DD 401 0 1092 1168 2 MP stroke SO gs 1195 1070 197 197 MR c np 36 36 1293 1168 FO gr 6 w gr end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument endTexFig 260 4983 a FC(\(a\))23 b(shorts)i(1,)e(longs)i(1)646 b(\(b\))24 b(shorts)h(1,)d(longs)j(10)647 b(\(c\))23 b(shorts)i(10,)e(longs)i(1)120 5179 y(Figure)32 b(13:)45 b Fy(Results)32 b(of)g(analysis,)j(in)d(the)f(case)h(wher)m(e)g(longs)h (ar)m(e)e(dr)o(awn)h(fr)l(om)f(Coxian)h(distrib)n(ution)j(with)120 5292 y(appr)l(opriate)27 b(mean)d(and)g Fu(C)1024 5259 y FE(2)1088 5292 y Fs(=)h(8)p Fy(.)j(Response)d(times)f(ar)m(e)f(shown) i(as)e(a)g(function)j(of)d Fu(\032)2889 5306 y Ft(L)2942 5292 y Fy(.)1875 5349 y FC(25)p eop %%Page: 26 28 26 27 bop 120 91 a FC(impro)o(v)o(ement)38 b(for)g(the)f(shorts\).)72 b(F)o(or)36 b(the)h(case)h(of)f(column)i(\(b\),)h(where)e(shorts)g(are) g(shorter)g(than)g(longs,)120 204 y(this)f(penalty)i(drops)f(to)f(only) h(2\045)e(under)i Fx(CS-Central-Queu)o(e)30 b FC(and)38 b(5\045)e(under)i Fx(CS-Immediate-)120 317 y(Dispatch)p FC(.)31 b(F)o(or)24 b(the)i(case)h(of)e(column)i(\(c\),)f(where)g (shorts)h(are)e(longer)j(than)e(longs,)h(the)f(penalty)h(is)f(greater) -5 b(.)120 430 y(This)32 b(is)g(to)g(be)g(e)o(xpected)i(since)g(jobs)e (are)h(not)f(preemptible)j(and)e(a)e(long)i(job)g(may)f(no)n(w)f(get)i (stuck)g(w)o(aiting)120 543 y(behind)24 b(a)e(short)h(job)g(ten)f (times)h(its)f(size.)29 b(It')-5 b(s)23 b(important)h(to)e(observ)o(e,) h(ho)n(we)n(v)o(er)l(,)g(that)g(for)g(all)f(v)n(alues)h(of)g Fu(\032)3514 557 y Ft(S)3564 543 y FC(,)f(the)120 656 y(penalty)30 b(to)f(long)h(jobs)f(is)f(lo)n(w)g(compared)j(with)d(the)h (tremendous)i(performance)g(impro)o(v)o(ement)f(a)n(v)n(ailable)h(to) 120 769 y(short)25 b(jobs.)261 882 y(One)20 b(interesting)j(observ)n (ation)h(is)c(that)g(the)h(penalty)h(to)e(long)h(jobs)g(appears)h(lo)n (wer)f(under)g Fx(CS-Central-)120 995 y(Queue)k FC(than)k(under)g Fx(CS-Immediate-D)o(is)o(pat)o(ch)o FC(.)35 b(At)28 b(\002rst)f(this)i (seems)f(quite)h(contrary)-6 b(,)31 b(since)e(under)120 1108 y Fx(CS-Central-Queu)o(e)14 b FC(it)21 b(seems)h(that)g(more)f (idle)h(time)f(is)h(gi)n(v)o(en)g(to)f(short)h(jobs,)h(thus)f(the)f (long)h(jobs)h(should)120 1220 y(suf)n(fer)h(more.)29 b(The)22 b(reason)j(this)e(is)g(not)h(true)g(is)e(that)i(under)g Fx(CS-Central-Queue)15 b FC(the)24 b(serv)o(ers)g(are)g(renam-)120 1333 y(able.)37 b(This)26 b(means)h(that)f(a)g(long)h(job)f(arri)n (ving)i(to)e(\002nd)g(both)h(serv)o(ers)g(serving)h(short)f(jobs)g (need)g(only)g(w)o(ait)f(for)120 1446 y Fy(the)e(\002r)o(st)g FC(of)g(the)f(tw)o(o)h(serv)o(ers)g(to)g(free)g(up)f(under)i Fx(CS-Central-Queu)o(e)p FC(.)261 1559 y(Considering)g(Figure)f(11)e (ro)n(ws)h(3)f(and)h(4,)f(where)h(we)f(no)n(w)g(\002x)g Fu(\032)2319 1573 y Ft(L)2396 1559 y Fs(=)j(0)p Fu(:)p Fs(8)p FC(,)e(we)f(see)h(that)g(results)h(are)f(lar)n(gely)120 1672 y(similar)32 b(to)e(the)i(case)f Fu(\032)878 1686 y Ft(L)969 1672 y Fs(=)39 b(0)p Fu(:)p Fs(5)p FC(,)33 b(e)o(xcept)f(that)f(the)g(bene\002ts)h(to)f(short)h(jobs)g(are)f(not)g (quite)h(as)f(great)h(and)f(the)120 1785 y(penalty)26 b(to)d(long)i(jobs)f(is)g(also)g(not)g(as)g(high.)30 b(This)23 b(is)h(to)g(be)f(e)o(xpected)j(since)f(no)n(w)e(there)h(are)g (fe)n(wer)g(idle)g(c)o(ycles)120 1898 y(to)i(steal.)37 b(Still)26 b(the)g(performance)j(impro)o(v)o(ement)e(of)f(c)o(ycle)h (stealing)h(o)o(v)o(er)e Fx(Dedicated)76 b FC(serv)o(ers)27 b(is)f(orders)120 2011 y(of)d(magnitude)j(for)e(higher)h Fu(\032)1056 2025 y Ft(S)1107 2011 y FC(.)261 2124 y(Figure)30 b(12)f(is)g(the)g(counterpart)j(to)d(Figure)h(11,)g(where)f(no)n(w)g (long)g(jobs)h(are)f(dra)o(wn)g(from)g(a)g(Coxian)h(dis-)120 2237 y(trib)n(ution)k(with)d(the)g(appropriate)k(mean)c(and)h Fu(C)1701 2204 y FE(2)1779 2237 y Fs(=)39 b(8)p FC(,)33 b(representing)h(higher)f(v)n(ariability)h(in)d(the)g(long)h(jobs)120 2350 y(\(short)d(jobs)g(are)g(still)f(dra)o(wn)h(from)f(an)g(e)o (xponential)j(distrib)n(ution\).)47 b(Increasing)31 b(the)d(v)n (ariability)j(of)d(the)g(long)120 2462 y(job)i(service)h(time)e(does)h (not)f(seem)h(to)f(ha)n(v)o(e)h(much)f(ef)n(fect)h(on)g(the)f(mean)g (bene\002t)h(that)g(c)o(ycle)g(stealing)h(of)n(fers)120 2575 y(to)h(short)h(jobs.)56 b(W)l(ith)33 b(respect)h(to)e(the)g (impact)h(on)g(long)g(jobs,)i(the)d(long)h(jobs)g(end)g(up)f(with)h (higher)g(o)o(v)o(erall)120 2688 y(response)h(times)d(due)h(to)f(their) h(higher)h(v)n(ariability)-6 b(,)36 b(b)n(ut)c(similar)g(absolute)h (increase.)54 b(The)31 b(impact)h(of)g(c)o(ycle)120 2801 y(stealing)26 b(on)f(the)g(long)g(jobs)g(is)g(therefore)i(considerably) h(lessened)e(when)f(the)g(v)n(ariability)i(in)d(long)i(job)f(service) 120 2914 y(times)d(is)g(increased.)30 b(In)22 b(f)o(act,)g(e)n(v)o(en)g (for)g Fu(\032)1452 2928 y Ft(S)1528 2914 y Fs(=)j(1)p FC(,)d(under)h(the)f(case)g(where)g(shorts)h(are)f(shorter)i(than)e (longs)h(\(case)120 3027 y(\(b\)\),)34 b(the)f(penalty)h(to)e(long)h (jobs)g(is)f(less)h(than)f Fs(1\045)g FC(under)h(both)g(c)o(ycle)g (stealing)h(algorithms.)57 b(F)o(or)31 b(the)i(case)120 3140 y(where)25 b(shorts)i(are)e(indistinguishable)31 b(from)25 b(longs)i(\(case)f(\(a\)\),)g(the)f(penalty)i(to)e(longs)i (is)e(still)h(under)g(10\045)f(for)120 3253 y Fx(CS-Immediate-Di)o(sp)o (at)o(ch)16 b FC(and)24 b(under)h(5\045)e(for)h Fx(CS-Central-Que)o(ue) o FC(.)261 3366 y(Until)g(no)n(w)f(we)f(ha)n(v)o(e)i(not)g(considered)j (the)d(case)g(where)f Fu(\032)2127 3381 y Ft(hL)2220 3366 y FC(,)g(the)g(load)i(at)e(the)h(long)g(host,)g(is)f(close)i(to)e (1.)28 b(It)120 3479 y(is)f(interesting)i(to)e(ask)g(what)g(the)g (penalty)h(of)f(c)o(ycle)h(stealing)g(to)f(long)h(jobs)f(looks)h(lik)o (e)f(as)g Fu(\032)3115 3494 y Ft(hL)3234 3479 y FC(gets)g(closer)h(to) 120 3592 y(1.)42 b(T)-7 b(o)27 b(in)l(v)o(estigate)k(this)e(question,)i (we)c(again)i(consider)h(the)f(setup)g(in)f(Figure)g(12,)i(e)o(xcept)f (that)f(this)h(time)f(we)120 3704 y(look)f(at)f(response)i(time)e(as)g (a)g(function)i(of)e Fu(\032)1571 3718 y Ft(L)1623 3704 y FC(,)g(where)g(we)g(\002x)f Fu(\032)2219 3718 y Ft(S)2300 3704 y Fs(=)30 b(1)p Fu(:)p Fs(2)c FC(and)h(later)f Fu(\032)2932 3718 y Ft(S)3013 3704 y Fs(=)k(1)p Fu(:)p Fs(5)c FC(and)h(consider)120 3817 y(the)d(full)g(range)g(of)g Fu(\032)773 3831 y Ft(L)825 3817 y FC(,)e(as)i(sho)n(wn)g(in)f(Figure)h(13.)261 3930 y(T)-7 b(o)21 b(understand)k(these)e(plots,)g(it)e(helps)i(to)f (\002rst)g(recall)h(that)f(Figure)h(7)e(limits)i(the)f(range)h(of)e Fu(\032)3196 3944 y Ft(L)3270 3930 y FC(under)i(which)120 4043 y Fx(CS-Immediate-Di)o(sp)o(at)o(ch)11 b FC(and)19 b Fx(CS-Central-Queu)o(e)11 b FC(are)19 b(stable.)28 b(Speci\002cally)-6 b(,)21 b(Figure)e(7)f(sho)n(ws)120 4156 y(that)30 b(when)f Fu(\032)557 4170 y Ft(S)644 4156 y Fs(=)36 b(1)p Fu(:)p Fs(2)p FC(,)31 b Fx(CS-Immediate-D)o(is)o(pa)o (tc)o(h)22 b FC(is)30 b(only)g(stable)g(for)g Fu(\032)2795 4170 y Ft(L)2883 4156 y Fu(<)36 b(:)p Fs(65)29 b FC(\(approximately\)) 120 4269 y(and)21 b Fx(CS-Central-Queu)o(e)13 b FC(is)20 b(only)i(stable)f(for)g Fu(\032)1829 4283 y Ft(L)1906 4269 y Fu(<)k Fs(0)p Fu(:)p Fs(8)c FC(\(approximately\).)32 b(F)o(or)19 b Fu(\032)2965 4283 y Ft(S)3041 4269 y Fs(=)25 b(1)p Fu(:)p Fs(5)p FC(,)c(the)g(stability)120 4382 y(criteria)30 b(on)f Fu(\032)571 4396 y Ft(L)651 4382 y FC(are)g(e)n(v)o(en)g(more)g (stringent,)j(particularly)g(for)d Fx(CS-Immediate-Di)o(sp)o(at)o(ch)o FC(.)38 b(Figure)29 b(13)120 4495 y(ro)n(w)e(1)h(sho)n(ws)g(the)g(mean) g(response)i(time)e(for)g(the)g(short)h(jobs)g(under)g(the)f(tw)o(o)g (c)o(ycle)g(stealing)i(algorithms)g(as)120 4608 y(a)c(function)i(of)f Fu(\032)663 4622 y Ft(L)715 4608 y FC(,)f(when)g(we)g(\002x)f Fu(\032)1286 4622 y Ft(S)1367 4608 y Fs(=)30 b(1)p Fu(:)p Fs(2)p FC(.)38 b(Observ)o(e)27 b(that)g(as)f(each)h(algorithm)h(nears)f (its)g(stability)h(asymp-)120 4721 y(tote)33 b(with)f(respect)j(to)d Fu(\032)920 4735 y Ft(L)972 4721 y FC(,)i(the)f(response)h(time)f (shoots)h(up)e(to)h(in\002nity)g(\(all)g(graphs)h(ha)n(v)o(e)f(been)h (truncated\).)120 4834 y(Thus,)d(because)h Fx(CS-Central-Queue)22 b FC(has)31 b(a)f(bigger)h(stability)h(re)o(gion,)h(its)d(performance)j (also)d(appears)120 4946 y(f)o(ar)c(superior)h(to)f Fx(CS-Immediate-Di) o(sp)o(at)o(ch)o FC(.)i(Observ)o(e)f(that)f(we)f(couldn')n(t)j(sho)n(w) d(the)h(performance)i(of)120 5059 y Fx(Dedicated)19 b FC(because)25 b(it)e(is)h(unstable)h(o)o(v)o(er)f(the)g(entire)h(re)o (gion.)1875 5349 y(26)p eop %%Page: 27 29 27 28 bop 261 91 a FC(Figure)24 b(13)g(ro)n(w)f(2)h(considers)i(the)e (performance)j(of)c(the)h(long)h(jobs)g(as)e(a)h(function)i(of)d Fu(\032)3074 105 y Ft(L)3149 91 y FC(where)i(we)e(again)120 204 y(\002x)j Fu(\032)289 218 y Ft(S)372 204 y Fs(=)31 b(1)p Fu(:)p Fs(2)p FC(.)40 b(Observ)o(e)27 b(that)h(the)f(prior)h (stability)h(criterion)g(on)f Fu(\032)2300 218 y Ft(L)2378 204 y FC(w)o(as)f(only)g(based)i(on)e(k)o(eeping)i(the)e Fy(short)120 317 y FC(host)f(stable.)34 b(The)25 b(long)g(host,)h(on)f (the)h(other)g(hand,)g(is)e(stable)j(for)e(all)g(v)n(alues)h(of)f Fu(\032)2766 331 y Ft(L)2842 317 y FC(under)i Fx(Dedicated)20 b FC(and)120 430 y(under)29 b(both)f(c)o(ycle)g(stealing)i(algorithms.) 42 b(Figure)28 b(13)g(ro)n(w)f(2)g(sho)n(ws)g(that)h(c)o(ycle)g (stealing)i(does)e(not)g(penalize)120 543 y(the)h(long)h(jobs,)h(e)o (xcept)g(in)e(the)g(case)h(where)f(the)h(short)g(jobs)g(are)f(much)g (longer)i(than)f(the)f(long)h(jobs.)47 b(In)29 b(this)120 656 y(case,)23 b(c)o(ycle)g(stealing)i(penalizes)g(the)e(long)g(jobs)h (for)e(lo)n(wer)h(loads;)h(this)f(penalty)i(goes)e(a)o(w)o(ay)g(for)f (higher)i(loads,)120 769 y(since)h(the)e(short)i(jobs)f(can')n(t)h(get) f(in)f(to)h(steal.)29 b(Results)c(for)e Fu(\032)2049 783 y Ft(S)2125 769 y Fs(=)i(1)p Fu(:)p Fs(5)f FC(are)g(similar)g(in)g (trend.)261 882 y(In)40 b(summary)-6 b(,)44 b(we)39 b(ha)n(v)o(e)i (seen)g(that)f(short)h(jobs)g(are)f(tremendously)j(helped)e(by)f(c)o (ycle)h(stealing,)46 b(and)120 995 y(that)39 b Fx(CS-Central-Queu)o(e) 32 b FC(of)n(fers)39 b(greater)h(impro)o(v)o(ements)g(to)f(short)g (jobs)g(o)o(v)o(er)g Fx(CS-Immediate-)120 1108 y(Dispatch)p FC(.)23 b(W)-7 b(e)17 b(ha)n(v)o(e)i(also)g(seen)g(that,)h(pro)o(vided) g(that)f(short)h(jobs)f(are)f(no)h(longer)h(than)f(long)g(jobs,)h(the)f (impact)120 1220 y(of)g(c)o(ycle)g(stealing)i(to)e(long)h(jobs)f(is)g (ne)o(gligible.)30 b(Ev)o(en)18 b(when)h(the)h(short)g(jobs)f(are)g (actually)i(longer)g(than)e(the)g(long)120 1333 y(jobs,)25 b(the)f(penalty)i(to)e(the)h(long)g(jobs)g(is)f(less,)g(proportionally) -6 b(,)29 b(than)c(the)f(bene\002t)h(to)f(the)h(shorts.)32 b(Furthermore,)120 1446 y(this)38 b(impact)h(is)f(greater)h(under)g Fx(CS-Immediate-Di)o(spa)o(tc)o(h)31 b FC(than)38 b(under)i Fx(CS-Central-Que)o(ue)o FC(.)120 1559 y(Thus)28 b Fx(CS-Central-Que)o (ue)21 b FC(is)27 b(al)o(w)o(ays)i(a)e(better)i(strate)o(gy)h(than)e Fx(CS-Immediate-Dis)o(pa)o(tc)o(h)p FC(,)22 b(and)120 1672 y(both)i(are)g(f)o(ar)g(better)h(than)f Fx(Dedicated)p FC(.)120 1957 y FG(8)119 b(Conclusion)120 2164 y FC(The)24 b(purpose)i(of)e(this)h(paper)g(is)f(to)g(analytically)j(deri)n(v)o(e)e (the)g(bene\002t)f(of)h(c)o(ycle)f(stealing)i(where)f(jobs)g(normally) 120 2277 y(destined)h(for)d(one)h(machine)h(may)e(steal)h(the)g(idle)g (c)o(ycles)g(of)g(another)h(machine)g(\(the)f(\223donor\224)h(machine,) g(a.k.a.)120 2390 y(\223long\224)31 b(host\).)48 b(The)30 b(moti)n(v)n(ation)h(is)e(that)i(the)e(jobs)i(doing)g(the)f(stealing)h (\(the)g(\223bene\002ciaries,)j(a.k.a.)46 b(\223short\224)120 2503 y(jobs\))28 b(will)f(bene\002t)h(immensely)-6 b(,)30 b(while)d(the)h(donor)h(jobs)f(e)o(xperience)i(v)o(ery)d(little)i (penalty)-6 b(,)30 b(since)e(\(primarily\))120 2616 y(only)c(their)g (idle)g(c)o(ycles)g(are)f(stolen.)30 b(The)23 b(paper)h(considers)i(tw) o(o)c(algorithms)k(for)d(c)o(ycle)h(stealing:)31 b(Immediate-)120 2729 y(Dispatch)f(\226)e(where)h(only)h(ne)n(wly)e(arri)n(ving)j(jobs)e (can)g(steal)h(idle)f(c)o(ycles)g(\226)g(and)g(Central-Queue)i(\226)d (where)h(the)120 2842 y(bene\002ciaries)d(include)g(both)e(ne)n(wly)g (arri)n(ving)h(jobs)f(and)g(already)h(queued)h(jobs.)261 2955 y(At)32 b(the)h(onset)g(of)g(the)f(paper)i(we)e(assumed)h(that)h (arri)n(ving)g(jobs)f(had)g(been)g(designated)j(as)c(being)i(either)120 3068 y(\223short\224)25 b(or)e(\223long\224,)h(where)f(\223short\224)i (jobs)f(were)f(the)g(ones)h(permitted)h(to)d(do)i(the)f(stealing.)30 b(Ho)n(we)n(v)o(er)23 b(through-)120 3181 y(out)34 b(the)g(paper)h(we)d (also)j(e)n(v)n(aluate)g(the)f(case)g(where)g(\223short\224)h(and)f (\223long\224)h(jobs)g(are)e(indistinguishable)39 b(\226)34 b(a)120 3293 y(perhaps)j(more)e(applicable)i(case)f(\226)e(as)h(well)f (as)h(the)g(pathological)k(case)c(where)g(\223shorts\224)i(are)e (longer)h(than)120 3406 y(\223longs.)-6 b(\224)261 3519 y(Our)26 b(results)i(sho)n(w)f(that)g(the)g(bene\002ciaries)i(\(the)e (shorts\))h(can)f(bene\002t)g(by)g(an)f(order)i(of)e(magnitude)j(under) 120 3632 y(both)c(c)o(ycle)f(stealing)i(algorithms.)31 b(The)23 b(donors)j(\(the)e(longs\))h(are)f(penalized)i(only)f(by)f(a)f (small)h(percentage,)i(so)120 3745 y(long)21 b(as)g(shorts)h(aren')n(t) g(longer)f(than)h(longs)f(on)g(a)n(v)o(erage.)29 b(Ev)o(en)20 b(when)h(the)g(short)g(jobs)g(are)g(actually)i(longer)e(than)120 3858 y(the)29 b(long)h(jobs,)h(the)e(short)h(jobs)g(bene\002t)f(more)g (than)h(the)f(long)h(jobs)g(are)f(penalized.)48 b(Our)28 b(results)j(also)e(sho)n(w)120 3971 y(that)c Fx(CS-Central-Queue)17 b FC(is)25 b(a)f(superior)j(strate)o(gy)f(to)f Fx(CS-Immediate-Di)o(sp) o(at)o(ch)18 b FC(both)25 b(from)g(the)120 4084 y(perspecti)n(v)o(e)h (of)e(the)f(bene\002t)i(to)e(short)i(jobs)f(and)g(from)f(the)h (perspecti)n(v)o(e)i(of)e(the)f(impact)i(on)e(long)i(jobs.)261 4197 y(This)c(paper)h(presents)h(the)e(\002rst)g(analysis)i(of)d(c)o (ycle)i(stealing.)30 b(The)20 b(analysis)j(is)e(an)g(approximation,)k (since)c(it)120 4310 y(depends)26 b(on)d(approximating)k(a)c(b)n(usy)h (period)h(by)f(a)f(\002nite)g(number)i(of)e(moments.)29 b(The)23 b(analysis)j(can)e(be)f(made)120 4423 y(as)g(precise)h(as)f (desired)h(by)f(using)h(more)e(moments)i(\226)e(in)h(this)g(paper)h(we) e(use)h(three.)29 b(Still,)23 b(e)n(v)o(en)f(with)h(just)g(three)120 4535 y(moments,)j(the)g(analysis)h(agrees)g(well)e(with)g(simulation)j (results.)36 b(Furthermore,)27 b(whereas)f(generating)j(a)c(plot)120 4648 y(of)g(simulation)j(results)f(requires)g(an)f(hour)l(,)g (generating)j(a)c(plot)h(of)f(analytical)j(results)f(requires)g(only)g (a)e(couple)120 4761 y(seconds.)261 4874 y(In)30 b(this)h(paper)h(we)e (mak)o(e)g(the)h(assumption)i(that)e(jobs)g(are)f(not)h(preemptible.)52 b(It)30 b(is)g(interesting)k(to)c(com-)120 4987 y(pare)37 b(our)g(task)g(assignment)i(polic)o(y)f(with)e(other)i(non-preempti)n (v)o(e)i(policies.)69 b(A)36 b(natural)i(non-preempti)n(v)o(e)120 5100 y(polic)o(y)24 b(which)f(comes)g(to)g(mind)g(is)f Fx(M/G/2/SJF)p FC(.)c(Here)k(it)h(is)f(assumed)i(that)f(there)h(is)f(a) f Fy(centr)o(al)i FC(queue)g(where)1875 5349 y(27)p eop %%Page: 28 30 28 29 bop 120 91 a FC(jobs)31 b(are)g(held)g(at)f(the)h(dispatcher)l(,) k(and)30 b(short)i(jobs)f(are)f(al)o(w)o(ays)i(gi)n(v)o(en)e (preference)k(o)o(v)o(er)c(long)h(jobs)g(at)f(both)120 204 y(hosts.)40 b(It)27 b(turns)g(out)h(that)f(from)g(the)g(perspecti)n (v)o(e)j(of)c(both)i(the)f(short)h(and)f(long)h(jobs,)g(the)g Fx(M/G/2/SJF)22 b FC(pol-)120 317 y(ic)o(y)i(sometimes)h(outperforms)i (our)d(c)o(ycle)h(stealing)h(algorithms)g(and)e(sometimes)h(does)g(w)o (orse,)f(depending)j(on)120 430 y(conditions)36 b(lik)o(e)e Fu(\032)746 444 y Ft(S)796 430 y FC(,)h Fu(\032)901 444 y Ft(L)953 430 y FC(,)f(and)f(the)h(job)f(size)g(distrib)n(utions.)61 b(On)32 b(the)i(plus)f(side,)j Fx(M/G/2/SJF)28 b FC(of)n(fers)34 b(the)120 543 y(short)e(jobs)f(tw)o(o)f(serv)o(ers,)k(where)d(both)g (serv)o(ers)h(prioritize)h(in)e(f)o(a)n(v)n(or)h(of)e(shorts.)52 b(On)30 b(the)h(ne)o(gati)n(v)o(e)g(size,)i(be-)120 656 y(cause)24 b Fx(M/G/2/SJF)18 b FC(does)24 b(not)f(of)n(fer)g(a)g (dedicated)i(short)f(serv)o(er)l(,)g(the)g(short)f(jobs)h(sometimes)g (end)f(up)g(getting)120 769 y(stuck)30 b(behind)h(tw)o(o)d(long)i (jobs,)h(one)e(at)g(each)g(host.)46 b(W)l(ith)29 b(respect)i(to)d(the)i (long)f(jobs,)i(on)e(the)g(ne)o(gati)n(v)o(e)h(side,)120 882 y Fx(M/G/2/SJF)20 b FC(penalizes)28 b(long)e(jobs)h(at)e(both)h (serv)o(ers,)h(b)n(ut)f(on)f(the)h(positi)n(v)o(e)h(side,)f(long)g (jobs)g(may)f(bene\002t)h(in)120 995 y(situations)g(where)e Fu(\032)783 1009 y Ft(S)857 995 y FC(is)f(lo)n(w)g(and)h(tw)o(o)f(long) h(jobs)h(end)f(up)f(capturing)j(both)f(hosts.)261 1108 y(A)f(natural)k(follo)n(wup)e(problem)h(to)e(this)h(paper)h(is)e(the)h (situation)i(of)d(tw)o(o)g(hosts,)i(both)f(of)f(which)h(help)g(each)120 1220 y(other)-5 b(.)39 b(That)26 b(is,)h(both)g(hosts)h(are)f(donors)h Fy(and)f FC(bene\002ciaries.)40 b(This)27 b(problem)g(is)g(open)g(as)g (of)f(the)h(time)f(of)h(this)120 1333 y(paper)-5 b(.)120 1626 y FG(9)119 b(A)m(ppendix)120 1833 y FC(This)28 b(section)h (includes)h(the)e(virtual)h(w)o(aiting)g(time)e(analysis)j(used)e(to)g (deri)n(v)o(e)g(the)g(Laplace)h(transform)g(of)f(the)120 1959 y(w)o(aiting)j(time)e(for)h(long)h(jobs)g(under)g Fx(CS-Immediate-D)o(is)o(pa)o(tch)o FC(,)24 b(denoted)32 b(by)e Fu(T)3055 1911 y FE(\()p Ft(L)p FE(\))3042 1986 y Ft(Q)3162 1959 y FC(.)47 b(The)29 b(response)120 2090 y(time)23 b(for)h(long)g(jobs)h Fu(T)858 2057 y FE(\()p Ft(L)p FE(\))987 2090 y FC(is)f(de\002ned)g(as)1555 2307 y Fu(T)1621 2270 y FE(\()p Ft(L)p FE(\))1753 2307 y Fs(=)h Fu(T)1915 2259 y FE(\()p Ft(L)p FE(\))1902 2334 y Ft(Q)2042 2307 y Fs(+)20 b Fu(X)2208 2321 y Ft(L)2260 2307 y Fu(:)120 2541 y FB(Summary)j(of)g(Results)247 2819 y Fj(~)231 2840 y Fl(T)292 2797 y Fi(\()p Fk(L)p Fi(\))280 2864 y Fk(Q)392 2840 y Fj(\()p Fl(s)p Fj(\))84 b(=)739 2784 y Fl(s)18 b Fj(+)g Fl(\025)927 2796 y Fk(S)994 2784 y Fm(\000)1101 2763 y Fj(~)1077 2784 y Fl(X)1146 2796 y Fk(S)1194 2784 y Fj(\()p Fl(s)p Fj(\))p Fl(\025)1345 2796 y Fk(S)p 736 2821 661 4 v 736 2907 a Fl(s)h Fm(\000)f Fl(\025)925 2919 y Fk(L)993 2907 y Fj(+)1100 2886 y(~)1076 2907 y Fl(X)1145 2919 y Fk(L)1195 2907 y Fj(\()p Fl(s)p Fj(\))p Fl(\025)1346 2919 y Fk(L)1406 2840 y Fl(\031)1453 2852 y Fi(0)1491 2840 y Fl(;)222 3085 y(E)5 b Fj([)p Fl(T)372 3042 y Fi(\()p Fk(L)p Fi(\))360 3109 y Fk(Q)473 3085 y Fj(])83 b(=)808 3029 y Fl(\032)851 3041 y Fk(L)p 736 3066 236 4 v 736 3142 a Fj(1)18 b Fm(\000)g Fl(\032)922 3154 y Fk(L)1013 3029 y Fl(E)5 b Fj([)p Fl(X)1178 2999 y Fi(2)1171 3052 y Fk(L)1220 3029 y Fj(])p 992 3066 273 4 v 992 3142 a(2)p Fl(E)g Fj([)p Fl(X)1192 3154 y Fk(L)1241 3142 y Fj(])1292 3085 y(+)1457 3029 y Fl(\032)1500 3041 y Fk(S)p 1385 3066 235 4 v 1385 3142 a Fj(1)18 b(+)g Fl(\032)1571 3154 y Fk(S)1660 3029 y Fl(E)5 b Fj([)p Fl(X)1825 2999 y Fi(2)1818 3052 y Fk(S)1866 3029 y Fj(])p 1639 3066 271 4 v 1639 3142 a(2)p Fl(E)g Fj([)p Fl(X)1839 3154 y Fk(S)1887 3142 y Fj(])1920 3085 y Fl(;)120 3320 y(E)g Fj([\()p Fl(T)302 3276 y Fi(\()p Fk(L)p Fi(\))290 3344 y Fk(Q)403 3320 y Fj(\))435 3285 y Fi(2)473 3320 y Fj(])83 b(=)808 3263 y Fl(\032)851 3275 y Fk(L)p 736 3300 236 4 v 736 3376 a Fj(1)18 b Fm(\000)g Fl(\032)922 3388 y Fk(L)1013 3263 y Fl(E)5 b Fj([)p Fl(X)1178 3233 y Fi(3)1171 3286 y Fk(L)1220 3263 y Fj(])p 992 3300 273 4 v 992 3376 a(3)p Fl(E)g Fj([)p Fl(X)1192 3388 y Fk(L)1241 3376 y Fj(])1292 3320 y(+)1457 3263 y Fl(\032)1500 3275 y Fk(S)p 1385 3300 235 4 v 1385 3376 a Fj(1)18 b(+)g Fl(\032)1571 3388 y Fk(S)1660 3263 y Fl(E)5 b Fj([)p Fl(X)1825 3233 y Fi(3)1818 3286 y Fk(S)1866 3263 y Fj(])p 1639 3300 271 4 v 1639 3376 a(3)p Fl(E)g Fj([)p Fl(X)1839 3388 y Fk(S)1887 3376 y Fj(])1938 3320 y(+)2103 3263 y Fl(\032)2146 3275 y Fk(L)p 2031 3300 236 4 v 2031 3376 a Fj(1)18 b Fm(\000)g Fl(\032)2217 3388 y Fk(L)2287 3263 y Fl(E)5 b Fj([)p Fl(X)2452 3233 y Fi(2)2445 3286 y Fk(L)2494 3263 y Fj(])p 2287 3300 231 4 v 2287 3376 a Fl(E)g Fj([)p Fl(X)2445 3388 y Fk(L)2494 3376 y Fj(])2541 3202 y Fq(\022)2684 3263 y Fl(\032)2727 3275 y Fk(L)p 2612 3300 236 4 v 2612 3376 a Fj(1)18 b Fm(\000)g Fl(\032)2798 3388 y Fk(L)2889 3263 y Fl(E)5 b Fj([)p Fl(X)3054 3233 y Fi(2)3047 3286 y Fk(L)3096 3263 y Fj(])p 2868 3300 273 4 v 2868 3376 a(2)p Fl(E)g Fj([)p Fl(X)3068 3388 y Fk(L)3117 3376 y Fj(])3168 3320 y(+)3333 3263 y Fl(\032)3376 3275 y Fk(L)p 3261 3300 236 4 v 3261 3376 a Fj(1)18 b Fm(\000)g Fl(\032)3447 3388 y Fk(L)3538 3263 y Fl(E)5 b Fj([)p Fl(X)3703 3233 y Fi(2)3696 3286 y Fk(S)3744 3263 y Fj(])p 3517 3300 271 4 v 3517 3376 a(2)p Fl(E)g Fj([)p Fl(X)3717 3388 y Fk(S)3764 3376 y Fj(])3798 3202 y Fq(\023)3872 3320 y Fl(:)120 3546 y Fw(where)1683 3665 y Fl(\031)1730 3677 y Fi(0)1791 3665 y Fj(=)1888 3609 y(1)18 b Fm(\000)g Fl(\032)2074 3621 y Fk(L)p 1888 3646 236 4 v 1889 3722 a Fj(1)g(+)g Fl(\032)2075 3734 y Fk(S)2134 3665 y Fl(;)120 3853 y Fw(represents)h(the)i(fraction)d(of)i(time)h(that)f(the)g(long)g (host)g(is)h(idle.)120 4088 y FB(Analysis)j(of)g(Long)e(Host)120 4243 y Fw(Let)d Fl(W)12 b Fj(\()p Fl(t)p Fj(\))20 b Fw(be)e(the)h (virtual)f(w)o(aiting)g(time)h(at)g(time)g Fl(t)p Fw(.)25 b(That)18 b(is,)i(a)f(job)f(arri)n(v)n(al)g(at)h(time)g Fl(t)g Fw(w)o(ould)f(w)o(ait)h Fl(W)12 b Fj(\()p Fl(t)p Fj(\))20 b Fw(before)d(we)i(start)120 4343 y(processing)g(the)h(job)m (.)k(W)-7 b(e)22 b(follo)n(w)d(the)h(follo)n(wing)f(steps)i(to)f (obtain)f(the)i(moments)e(of)h Fl(W)35 b Fj(=)22 b(lim)2950 4355 y Fk(t)p Fc(!1)3125 4343 y Fl(W)12 b Fj(\()p Fl(t)p Fj(\))p Fw(:)240 4492 y(1.)44 b(Set)21 b(up)f(the)g(dif)n(ferential)f (equation)f(for)1536 4471 y Fj(~)1512 4492 y Fl(W)12 b Fj(\()p Fl(t;)i(s)p Fj(\))p Fw(.)240 4665 y(2.)44 b(Let)21 b Fl(t)i Fm(!)g(1)p Fw(;)e(then,)959 4625 y Fk(d)1013 4610 y Fi(~)994 4625 y Fk(W)9 b Fi(\()p Fk(t;s)p Fi(\))p 959 4646 234 4 v 1046 4694 a Fk(dt)1226 4665 y Fj(=)23 b(0)d Fw(\()1428 4644 y Fj(~)1404 4665 y Fl(W)12 b Fj(\()p Fl(s)p Fj(\))21 b Fw(is)g(e)o(xpressed)e(by)h Fl(\031)2192 4677 y Fi(0)2229 4665 y Fw(\).)240 4828 y(3.)44 b(Ev)n(aluate)681 4807 y Fj(~)656 4828 y Fl(W)12 b Fj(\()p Fl(s)24 b Fj(=)e(0\))f Fw(to)f(obtain)f Fl(\031)1383 4840 y Fi(0)1421 4828 y Fw(.)240 4978 y(4.)44 b(Dif)n(ferentiate)814 4957 y Fj(~)790 4978 y Fl(W)12 b Fj(\()p Fl(s)p Fj(\))21 b Fw(to)g(obtain)e(moments)g (of)h Fl(W)12 b Fw(.)1875 5349 y FC(28)p eop %%Page: 29 31 29 30 bop 720 0 a 18945146 13261598 0 0 19931873 14011514 startTexFig 720 0 a %%BeginDocument: ../figures/vwt.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: vwt.eps %%Creator: fig2dev Version 3.2 Patchlevel 3d %%CreationDate: Fri Jul 26 19:00:33 2002 %%For: osogami@gs57.sp.cs.cmu.edu (Takayuki Osogami) %%BoundingBox: 0 0 303 213 %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def F2psDictbeginF2psDict begin F2psDictbeginF2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 213 moveto 0 0 lineto 303 0 lineto 303 213 lineto closepath clip newpath -33.4 246.2 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /reencdict 12 dict def /ReEncode { reencdict begin /newcodesandnames exch def /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall newfont /FontName newfontname put newcodesandnames aload pop 128 1 255 { newfont /Encoding get exch /.notdef put } for newcodesandnames length 2 idiv { newfont /Encoding get 3 1 roll put } repeat newfontname newfont definefont pop end } def /isovec [ 8#055 /minus 8#200 /grave 8#201 /acute 8#202 /circumflex 8#203 /tilde 8#204 /macron 8#205 /breve 8#206 /dotaccent 8#207 /dieresis 8#210 /ring 8#211 /cedilla 8#212 /hungarumlaut 8#213 /ogonek 8#214 /caron 8#220 /dotlessi 8#230 /oe 8#231 /OE 8#240 /space 8#241 /exclamdown 8#242 /cent 8#243 /sterling 8#244 /currency 8#245 /yen 8#246 /brokenbar 8#247 /section 8#250 /dieresis 8#251 /copyright 8#252 /ordfeminine 8#253 /guillemotleft 8#254 /logicalnot 8#255 /hyphen 8#256 /registered 8#257 /macron 8#260 /degree 8#261 /plusminus 8#262 /twosuperior 8#263 /threesuperior 8#264 /acute 8#265 /mu 8#266 /paragraph 8#267 /periodcentered 8#270 /cedilla 8#271 /onesuperior 8#272 /ordmasculine 8#273 /guillemotright 8#274 /onequarter 8#275 /onehalf 8#276 /threequarters 8#277 /questiondown 8#300 /Agrave 8#301 /Aacute 8#302 /Acircumflex 8#303 /Atilde 8#304 /Adieresis 8#305 /Aring 8#306 /AE 8#307 /Ccedilla 8#310 /Egrave 8#311 /Eacute 8#312 /Ecircumflex 8#313 /Edieresis 8#314 /Igrave 8#315 /Iacute 8#316 /Icircumflex 8#317 /Idieresis 8#320 /Eth 8#321 /Ntilde 8#322 /Ograve 8#323 /Oacute 8#324 /Ocircumflex 8#325 /Otilde 8#326 /Odieresis 8#327 /multiply 8#330 /Oslash 8#331 /Ugrave 8#332 /Uacute 8#333 /Ucircumflex 8#334 /Udieresis 8#335 /Yacute 8#336 /Thorn 8#337 /germandbls 8#340 /agrave 8#341 /aacute 8#342 /acircumflex 8#343 /atilde 8#344 /adieresis 8#345 /aring 8#346 /ae 8#347 /ccedilla 8#350 /egrave 8#351 /eacute 8#352 /ecircumflex 8#353 /edieresis 8#354 /igrave 8#355 /iacute 8#356 /icircumflex 8#357 /idieresis 8#360 /eth 8#361 /ntilde 8#362 /ograve 8#363 /oacute 8#364 /ocircumflex 8#365 /otilde 8#366 /odieresis 8#367 /divide 8#370 /oslash 8#371 /ugrave 8#372 /uacute 8#373 /ucircumflex 8#374 /udieresis 8#375 /yacute 8#376 /thorn 8#377 /ydieresis] def /Times-Roman /Times-Roman-iso isovec ReEncode /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def F2psBegin10setmiterlimit0.060000.06000scF2psBegin 10 setmiterlimit 0.06000 0.06000 sc % % Fig objects follow % % Polyline 15.000 slw n 600 600 m 600 3000 l 1800 3000 l 1800 600 l gs col0 s gr % Polyline 45.000 slw n 600 1200 m 1800 2400 l gs col0 s gr % Polyline n 1200 1800 m 1200 600 l 1800 1200 l gs col0 s gr % Polyline 15.000 slw n 3600 600 m 3600 3000 l 4800 3000 l 4800 600 l gs col0 s gr % Polyline 45.000 slw n 3600 2700 m 3900 3000 l 4800 3000 l gs col0 s gr % Polyline n 3750 2850 m 3750 750 l 4800 1800 l gs col0 s gr % Polyline 60.000 slw n 4200 3000 m 4200 1800 l 4800 2400 l gs col0 s gr % Polyline 15.000 slw gs clippath 4815 3630 m 4815 3570 l 4664 3570 l 4784 3600 l 4664 3630 l cp 3885 3570 m 3885 3630 l 4036 3630 l 3916 3600 l 4036 3570 l cp eoclip n 3900 3600 m 4800 3600 l gs col0 s gr gr % arrowhead 7.500 slw n 4036 3570 m 3916 3600 l 4036 3630 l 4036 3570 l cp gs 0.00 setgray ef gr col0 s % arrowhead n 4664 3630 m 4784 3600 l 4664 3570 l 4664 3630 l cp gs 0.00 setgray ef gr col0 s % Polyline 15.000 slw gs clippath 4815 3330 m 4815 3270 l 4664 3270 l 4784 3300 l 4664 3330 l cp 4185 3270 m 4185 3330 l 4336 3330 l 4216 3300 l 4336 3270 l cp eoclip n 4200 3300 m 4800 3300 l gs col0 s gr gr % arrowhead 7.500 slw n 4336 3270 m 4216 3300 l 4336 3330 l 4336 3270 l cp gs 0.00 setgray ef gr col0 s % arrowhead n 4664 3330 m 4784 3300 l 4664 3270 l 4664 3330 l cp gs 0.00 setgray ef gr col0 s % Polyline 15.000 slw gs clippath 1815 3330 m 1815 3270 l 1664 3270 l 1784 3300 l 1664 3330 l cp 1185 3270 m 1185 3330 l 1336 3330 l 1216 3300 l 1336 3270 l cp eoclip n 1200 3300 m 1800 3300 l gs col0 s gr gr % arrowhead 7.500 slw n 1336 3270 m 1216 3300 l 1336 3330 l 1336 3270 l cp gs 0.00 setgray ef gr col0 s % arrowhead n 1664 3330 m 1784 3300 l 1664 3270 l 1664 3330 l cp gs 0.00 setgray ef gr col0 s /Times-Roman-iso ff 180.00 scf sf 4875 1875 m gs 1 -1 sc (1-arrival) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 1875 1275 m gs 1 -1 sc (1-arrival) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 1875 2475 m gs 1 -1 sc (no arrival) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 4875 2475 m gs 1 -1 sc (i-arrival) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 4875 2700 m gs 1 -1 sc (\(i=1,2\)) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 4875 3000 m gs 1 -1 sc (no arrival) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 4575 3450 m gs 1 -1 sc (t) col0 sh gr /Symbol ff 180.00 scf sf 4350 3450 m gs 1 -1 sc (e D) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 3825 1425 m gs 1 -1 sc (S) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 900 1050 m gs 1 -1 sc (S) col0 sh gr /Times-Roman-iso ff 120.00 scf sf 4425 3450 m gs 1 -1 sc (i) col0 sh gr /Times-Roman-iso ff 120.00 scf sf 3900 1425 m gs 1 -1 sc (1) col0 sh gr /Times-Roman-iso ff 120.00 scf sf 975 1050 m gs 1 -1 sc (1) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 4275 2550 m gs 1 -1 sc (Si) col0 sh gr /Symbol ff 180.00 scf sf 4200 3750 m gs 1 -1 sc (eD) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 4425 3750 m gs 1 -1 sc (t) col0 sh gr /Symbol ff 180.00 scf sf 1350 3450 m gs 1 -1 sc (eD) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 1575 3450 m gs 1 -1 sc (t) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 600 3150 m gs 1 -1 sc (t) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 1650 3150 m gs 1 -1 sc (t+ t) col0 sh gr /Symbol ff 180.00 scf sf 1800 3150 m gs 1 -1 sc (D) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 3600 3150 m gs 1 -1 sc (t) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 4650 3150 m gs 1 -1 sc (t+ t) col0 sh gr /Symbol ff 180.00 scf sf 4800 3150 m gs 1 -1 sc (D) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 4125 4050 m gs 1 -1 sc (\(b\)) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 1125 4050 m gs 1 -1 sc (\(a\)) col0 sh gr F2psBegin10setmiterlimit0.060000.06000scF2psEnd rs %%EndDocument endTexFig 537 1876 a FC(Figure)24 b(14:)29 b(V)-5 b(irtual)24 b(w)o(aiting)g(time:)29 b(relationship)e(between)e Fu(W)13 b Fs(\()p Fu(t)p Fs(\))23 b FC(and)h Fu(W)13 b Fs(\()p Fu(t)20 b Fs(+)g(\001)p Fu(t)p Fs(\))261 2154 y Fw(W)-7 b(e)25 b(\002rst)f(set)h(up)e(a)h(dif)n(ferential)e(equation.)34 b(F)o(or)23 b(this)h(purpose,)f(we)h(carefully)e(e)o(xamine)g(the)i (relationship)e(between)120 2253 y Fl(W)12 b Fj(\()p Fl(t)p Fj(\))21 b Fw(and)f Fl(W)12 b Fj(\()p Fl(t)19 b Fj(+)f(\001)p Fl(t)p Fj(\))p Fw(.)261 2353 y(If)i Fl(W)12 b Fj(\()p Fl(t)p Fj(\))24 b Fm(\025)e Fj(\001)p Fl(t)p Fw(,)768 2582 y Fl(W)12 b Fj(\()p Fl(t)19 b Fj(+)f(\001)p Fl(t)p Fj(\))23 b(=)1264 2465 y Fq(\032)1368 2532 y Fl(W)12 b Fj(\()p Fl(t)p Fj(\))19 b Fm(\000)f Fj(\001)p Fl(t)303 b Fj(with)21 b(probabilit)n(y)g(1)d Fm(\000)g Fl(\025)2848 2544 y Fk(L)2898 2532 y Fj(\001)p Fl(t;)1368 2631 y(W)12 b Fj(\()p Fl(t)p Fj(\))19 b(+)f Fl(X)1723 2643 y Fk(L)1791 2631 y Fm(\000)g Fj(\001)p Fl(t)83 b Fj(with)21 b(probabilit)n(y)g Fl(\025)2705 2643 y Fk(L)2755 2631 y Fj(\001)p Fl(t:)120 2812 y Fw(If)f Fj(0)j Fm(\024)f Fl(W)12 b Fj(\()p Fl(t)p Fj(\))24 b Fl(<)e Fj(\001)p Fl(t)p Fw(,)562 3091 y Fl(W)12 b Fj(\()p Fl(t)18 b Fj(+)g(\001)p Fl(t)p Fj(\))24 b(=)1057 2921 y Fq(8)1057 2996 y(<)1057 3145 y(:)1173 2991 y Fj(0)717 b(with)21 b(probabilit)n(y)g(1)d Fm(\000)g Fl(\025)2724 3003 y Fk(L)2774 2991 y Fj(\001)p Fl(t)g Fm(\000)g Fl(\025)3022 3003 y Fk(S)3071 2991 y Fl(\017)p Fj(\001)p Fl(t;)1173 3090 y(W)12 b Fj(\()p Fl(t)p Fj(\))19 b(+)f Fl(X)1528 3102 y Fk(L)1596 3090 y Fm(\000)g Fl(\017)1713 3102 y Fi(1)1750 3090 y Fj(\001)p Fl(t)83 b Fj(with)21 b(probabilit)n(y)g Fl(\025)2581 3102 y Fk(L)2631 3090 y Fj(\001)p Fl(t;)1173 3190 y(X)1242 3202 y Fk(S)1308 3190 y Fm(\000)d Fl(\017)1425 3202 y Fi(2)1462 3190 y Fj(\001)p Fl(t)371 b Fj(with)21 b(probabilit)n(y)g Fl(\025)2581 3202 y Fk(S)2629 3190 y Fl(\017)p Fj(\001)p Fl(t:)120 3365 y Fw(Note)f(that)g Fl(\017)481 3377 y Fi(1)539 3365 y Fw(and)g Fl(\017)714 3377 y Fi(2)771 3365 y Fw(are)h(random)d(v)n(ariables)h(with)i Fj(0)h Fm(\024)h Fl(\017)1841 3377 y Fi(1)1878 3365 y Fl(;)14 b(\017)1949 3377 y Fi(2)2009 3365 y Fm(\024)22 b Fj(1)p Fw(.)144 3623 y Fj(~)120 3644 y Fl(W)12 b Fj(\()p Fl(t)19 b Fj(+)f(\001)p Fl(t;)c(s)p Fj(\))203 3769 y Fm(\021)83 b Fl(E)5 b Fj([)p Fl(e)479 3734 y Fc(\000)p Fk(sW)k Fi(\()p Fk(t)p Fi(+\001)p Fk(t)p Fi(\))845 3769 y Fj(])203 3940 y(=)351 3827 y Fq(Z)434 3848 y Fc(1)397 4016 y Fk(x)p Fi(=0)536 3940 y Fl(E)c Fj([)p Fl(e)664 3906 y Fc(\000)p Fk(sW)k Fi(\()p Fk(t)p Fi(+\001)p Fk(t)p Fi(\))1031 3940 y Fm(j)p Fl(W)j Fj(\()p Fl(t)p Fj(\))23 b(=)g Fl(x)p Fj(])p Fl(d)p Fj(Pr\()p Fl(W)12 b Fj(\()p Fl(t)p Fj(\))23 b Fm(\024)g Fl(x)p Fj(\))p Fl(;)203 4166 y Fj(=)351 4053 y Fq(Z)434 4074 y Fc(1)397 4242 y Fk(x)p Fi(=\001)p Fk(t)583 4074 y Fq(\020)633 4166 y Fl(e)672 4132 y Fc(\000)p Fk(s)p Fi(\()p Fk(x)p Fc(\000)p Fi(\001)p Fk(t)p Fi(\))980 4166 y Fj(\(1)18 b Fm(\000)g Fl(\025)1203 4178 y Fk(L)1253 4166 y Fj(\001)p Fl(t)p Fj(\))h(+)f Fl(E)5 b Fj([)p Fl(e)1614 4132 y Fc(\000)p Fk(s)p Fi(\()p Fk(x)p Fc(\000)p Fi(\001)p Fk(t)p Fi(+)p Fk(X)1998 4140 y Fb(L)2041 4132 y Fi(\))2071 4166 y Fj(])p Fl(\025)2142 4178 y Fk(L)2193 4166 y Fj(\001)p Fl(t)2292 4074 y Fq(\021)2355 4166 y Fl(d)p Fj(Pr)o(\()p Fl(W)12 b Fj(\()p Fl(t)p Fj(\))24 b Fm(\024)f Fl(x)p Fj(\))351 4408 y(+)430 4295 y Fq(Z)512 4315 y Fi(\001)p Fk(t)475 4483 y(x)p Fi(=0)597 4467 y Fa(+)662 4315 y Fq(\020)711 4408 y Fj(\(1)18 b Fm(\000)h Fl(\025)935 4420 y Fk(L)985 4408 y Fj(\001)p Fl(t)f Fm(\000)g Fl(\025)1233 4420 y Fk(S)1282 4408 y Fl(\017)p Fj(\001)p Fl(t)p Fj(\))g(+)g Fl(E)5 b Fj([)p Fl(e)1676 4373 y Fc(\000)p Fk(s)p Fi(\()p Fk(x)p Fi(+)p Fk(X)1928 4381 y Fb(L)1972 4373 y Fc(\000)p Fk(\017)2052 4381 y Fa(1)2084 4373 y Fi(\001)p Fk(t)p Fi(\))2194 4408 y Fj(])p Fl(\025)2265 4420 y Fk(L)2315 4408 y Fj(\001)p Fl(t)19 b Fj(+)f Fl(E)5 b Fj([)p Fl(e)2644 4373 y Fc(\000)p Fk(s)p Fi(\()p Fk(X)2807 4381 y Fb(S)2849 4373 y Fc(\000)p Fk(\017)2929 4381 y Fa(2)2961 4373 y Fi(\001)p Fk(t)p Fi(\))3071 4408 y Fj(])p Fl(\025)3142 4420 y Fk(S)3190 4408 y Fl(\017)p Fj(\001)p Fl(t)3323 4315 y Fq(\021)3387 4408 y Fl(d)p Fj(Pr)o(\()p Fl(W)12 b Fj(\()p Fl(t)p Fj(\))24 b Fm(\024)e Fl(x)p Fj(\))351 4612 y(+)430 4520 y Fq(\020)479 4612 y Fj(\(1)c Fm(\000)g Fl(\025)702 4624 y Fk(L)752 4612 y Fj(\001)p Fl(t)h Fm(\000)f Fl(\025)1001 4624 y Fk(S)1049 4612 y Fj(\001)p Fl(t)p Fj(\))h(+)f Fl(E)5 b Fj([)p Fl(e)1410 4578 y Fc(\000)p Fk(s)p Fi(\()p Fk(x)p Fi(+)p Fk(X)1662 4586 y Fb(L)1706 4578 y Fc(\000)p Fk(\017)1786 4586 y Fa(1)1818 4578 y Fi(\001)p Fk(t)p Fi(\))1928 4612 y Fj(])p Fl(\025)1999 4624 y Fk(L)2049 4612 y Fj(\001)p Fl(t)18 b Fj(+)g Fl(E)5 b Fj([)p Fl(e)2377 4578 y Fc(\000)p Fk(s)p Fi(\()p Fk(X)2540 4586 y Fb(S)2583 4578 y Fc(\000)p Fk(\017)2663 4586 y Fa(2)2695 4578 y Fi(\001)p Fk(t)p Fi(\))2804 4612 y Fj(])p Fl(\025)2875 4624 y Fk(S)2924 4612 y Fj(\001)p Fl(t)3023 4520 y Fq(\021)3086 4612 y Fj(Pr\()p Fl(W)12 b Fj(\()p Fl(t)p Fj(\))23 b(=)g(0\))p Fl(;)203 4817 y Fj(=)351 4704 y Fq(Z)434 4724 y Fc(1)397 4892 y Fk(x)p Fi(=0)536 4724 y Fq(\020)586 4817 y Fj(1)18 b(+)g(\()p Fl(s)h Fm(\000)f Fl(\025)950 4829 y Fk(L)1018 4817 y Fj(+)g Fl(\025)1149 4829 y Fk(L)1223 4796 y Fj(~)1199 4817 y Fl(X)1268 4829 y Fk(L)1318 4817 y Fj(\()p Fl(s)p Fj(\)\)\001)p Fl(t)h Fj(+)f Fl(o)p Fj(\(\001)p Fl(t)p Fj(\))1857 4724 y Fq(\021)1922 4817 y Fl(e)1961 4782 y Fc(\000)p Fk(sx)2085 4817 y Fl(d)p Fj(Pr\()p Fl(W)12 b Fj(\()p Fl(t)p Fj(\))23 b Fm(\024)g Fl(x)p Fj(\))351 5058 y(+)430 4945 y Fq(Z)512 4965 y Fi(\001)p Fk(t)475 5133 y(x)p Fi(=0)597 5117 y Fa(+)662 4990 y Fq(\010)710 5058 y Fj(1)18 b Fm(\000)g Fj(\()p Fl(\025)933 5070 y Fk(L)1002 5058 y Fj(+)g Fl(\025)1133 5070 y Fk(S)1181 5058 y Fl(\017)p Fj(\)\001)p Fl(t)h Fj(+)f Fl(E)5 b Fj([)p Fl(e)1576 5023 y Fc(\000)p Fk(sx)1701 5058 y Fl(e)1740 5023 y Fc(\000)p Fk(sX)1877 5031 y Fb(L)1925 5058 y Fj(\(1)18 b(+)g Fl(O)r Fj(\(\001)p Fl(t)p Fj(\)\)])p Fl(\025)2431 5070 y Fk(L)2483 5058 y Fj(\001)p Fl(t)h Fj(+)f Fl(E)5 b Fj([)p Fl(e)2812 5023 y Fc(\000)p Fk(sX)2949 5031 y Fb(S)2995 5058 y Fj(\(1)19 b(+)f Fl(O)r Fj(\(\001)p Fl(t)p Fj(\)\)])p Fl(\025)3502 5070 y Fk(S)3552 5058 y Fl(\017)p Fj(\001)p Fl(t)1875 5349 y FC(29)p eop %%Page: 30 32 30 31 bop 715 95 a Fm(\000)794 3 y Fq(\020)843 95 y Fj(1)18 b(+)g(\()p Fl(s)h Fm(\000)f Fl(\025)1207 107 y Fk(L)1275 95 y Fj(+)g Fl(\025)1406 107 y Fk(L)1480 74 y Fj(~)1456 95 y Fl(X)1525 107 y Fk(L)1575 95 y Fj(\()p Fl(s)p Fj(\)\)\001)p Fl(t)h Fj(+)f Fl(o)p Fj(\(\001)p Fl(t)p Fj(\))2114 3 y Fq(\021)2179 95 y Fl(e)2218 61 y Fc(\000)p Fk(sx)2342 3 y Fq(o)2411 95 y Fl(d)p Fj(Pr\()p Fl(W)12 b Fj(\()p Fl(t)p Fj(\))24 b Fm(\024)e Fl(x)p Fj(\))351 257 y(+)430 189 y Fq(\010)477 257 y Fj(\(1)d Fm(\000)f Fl(\025)701 269 y Fk(L)751 257 y Fj(\001)p Fl(t)g Fm(\000)g Fl(\025)999 269 y Fk(S)1048 257 y Fj(\001)p Fl(t)p Fj(\))h(+)f Fl(E)5 b Fj([)p Fl(e)1409 222 y Fc(\000)p Fk(sX)1546 230 y Fb(L)1594 257 y Fj(\(1)19 b(+)f Fl(O)r Fj(\(\001)p Fl(t)p Fj(\)\)])p Fl(\025)2101 269 y Fk(L)2152 257 y Fj(\001)p Fl(t)h Fj(+)f Fl(E)5 b Fj([)p Fl(e)2481 222 y Fc(\000)p Fk(sX)2618 230 y Fb(S)2665 257 y Fj(\(1)18 b(+)g Fl(O)r Fj(\(\001)p Fl(t)p Fj(\)\)])p Fl(\025)3171 269 y Fk(S)3221 257 y Fj(\001)p Fl(t)715 414 y Fm(\000)794 322 y Fq(\020)843 414 y Fj(1)g(+)g(\()p Fl(s)h Fm(\000)f Fl(\025)1207 426 y Fk(L)1275 414 y Fj(+)g Fl(\025)1406 426 y Fk(L)1480 393 y Fj(~)1456 414 y Fl(X)1525 426 y Fk(L)1575 414 y Fj(\()p Fl(s)p Fj(\)\)\001)p Fl(t)h Fj(+)f Fl(o)p Fj(\(\001)p Fl(t)p Fj(\))2114 322 y Fq(\021)q(o)2234 414 y Fj(Pr)o(\()p Fl(W)12 b Fj(\()p Fl(t)p Fj(\))24 b(=)e(0\))p Fl(;)203 634 y Fj(=)351 542 y Fq(\020)400 634 y Fj(1)c(+)g(\()p Fl(s)h Fm(\000)f Fl(\025)764 646 y Fk(L)832 634 y Fj(+)g Fl(\025)963 646 y Fk(L)1037 613 y Fj(~)1014 634 y Fl(X)1083 646 y Fk(L)1132 634 y Fj(\()p Fl(s)p Fj(\)\)\001)p Fl(t)1366 542 y Fq(\021)1455 613 y Fj(~)1430 634 y Fl(W)12 b Fj(\()p Fl(t;)i(s)p Fj(\))19 b(+)1792 521 y Fq(Z)1875 541 y Fi(\001)p Fk(t)1838 709 y(x)p Fi(=0)1960 693 y Fa(+)2025 634 y Fl(O)r Fj(\(\001)p Fl(t)p Fj(\))p Fl(d)p Fj(Pr\()p Fl(W)12 b Fj(\()p Fl(t)p Fj(\))24 b Fm(\024)f Fl(x)p Fj(\))351 838 y(+)430 746 y Fq(\020)479 838 y Fm(\000)p Fl(\025)592 850 y Fk(S)658 838 y Fj(+)765 817 y(~)741 838 y Fl(X)810 850 y Fk(S)858 838 y Fj(\()p Fl(s)p Fj(\))p Fl(\025)1009 850 y Fk(S)1077 838 y Fm(\000)18 b Fl(s)1199 746 y Fq(\021)1262 838 y Fj(\001)p Fl(t)p Fj(Pr)o(\()p Fl(W)12 b Fj(\()p Fl(t)p Fj(\))24 b(=)f(0\))18 b(+)g Fl(o)p Fj(\(\001)p Fl(t)p Fj(\))p Fl(:)378 1167 y Fj(~)354 1188 y Fl(W)12 b Fj(\()p Fl(t)19 b Fj(+)f(\001)p Fl(t;)c(s)p Fj(\))k Fm(\000)941 1167 y Fj(~)916 1188 y Fl(W)12 b Fj(\()p Fl(t;)i(s)p Fj(\))p 354 1226 823 4 v 716 1302 a(\001)p Fl(t)1270 1245 y Fj(=)1417 1152 y Fq(\020)1467 1245 y Fl(s)k Fm(\000)g Fl(\025)1655 1257 y Fk(L)1724 1245 y Fj(+)g Fl(\025)1855 1257 y Fk(L)1929 1224 y Fj(~)1905 1245 y Fl(X)1974 1257 y Fk(L)2023 1245 y Fj(\()p Fl(s)p Fj(\))2126 1152 y Fq(\021)2215 1224 y Fj(~)2190 1245 y Fl(W)12 b Fj(\()p Fl(t;)i(s)p Fj(\))19 b(+)2552 1132 y Fq(Z)2635 1152 y Fi(\001)p Fk(t)2598 1320 y(x)p Fi(=0)2720 1304 y Fa(+)2785 1245 y Fl(O)r Fj(\(1\))p Fl(d)p Fj(Pr\()p Fl(W)12 b Fj(\()p Fl(t)p Fj(\))24 b Fm(\024)e Fl(x)p Fj(\))1417 1472 y(+)1496 1380 y Fq(\020)1545 1472 y Fm(\000)p Fl(\025)1658 1484 y Fk(S)1725 1472 y Fj(+)1832 1451 y(~)1808 1472 y Fl(X)1877 1484 y Fk(S)1925 1472 y Fj(\()p Fl(s)p Fj(\))p Fl(\025)2076 1484 y Fk(S)2143 1472 y Fm(\000)c Fl(s)2265 1380 y Fq(\021)2329 1472 y Fj(Pr)o(\()p Fl(W)12 b Fj(\()p Fl(t)p Fj(\))23 b(=)g(0\))18 b(+)2930 1416 y Fl(o)p Fj(\(\001)p Fl(t)p Fj(\))p 2930 1453 204 4 v 2983 1529 a(\001)p Fl(t)3144 1472 y(:)141 1677 y Fw(Letting)h Fj(\001)p Fl(t)24 b Fm(!)f Fj(0)d Fw(in)g(the)g(abo)o(v)o(e)f(formula,) 412 1863 y Fl(d)480 1842 y Fj(~)455 1863 y Fl(W)13 b Fj(\()p Fl(t;)h(s)p Fj(\))p 412 1900 304 4 v 528 1976 a Fl(dt)809 1919 y Fj(=)956 1827 y Fq(\020)1006 1919 y Fl(s)k Fm(\000)g Fl(\025)1194 1931 y Fk(L)1263 1919 y Fj(+)g Fl(\025)1394 1931 y Fk(L)1468 1898 y Fj(~)1444 1919 y Fl(X)1513 1931 y Fk(L)1563 1919 y Fj(\()p Fl(s)p Fj(\))1666 1827 y Fq(\021)1754 1898 y Fj(~)1730 1919 y Fl(W)12 b Fj(\()p Fl(t;)i(s)p Fj(\))k(+)2091 1827 y Fq(\020)2141 1919 y Fm(\000)p Fl(\025)2254 1931 y Fk(S)2320 1919 y Fj(+)2427 1898 y(~)2404 1919 y Fl(X)2473 1931 y Fk(S)2520 1919 y Fj(\()p Fl(s)p Fj(\))p Fl(\025)2671 1931 y Fk(S)2739 1919 y Fm(\000)g Fl(s)2861 1827 y Fq(\021)2924 1919 y Fj(Pr)o(\()p Fl(W)12 b Fj(\()p Fl(t)p Fj(\))24 b(=)f(0\))p Fl(:)261 2201 y Fw(Let)e Fl(t)i Fm(!)g(1)p Fw(.)i(Then,)903 2161 y Fk(d)957 2146 y Fi(~)938 2161 y Fk(W)9 b Fi(\()p Fk(t;s)p Fi(\))p 903 2182 234 4 v 990 2230 a Fk(dt)1170 2201 y Fm(!)23 b Fj(0)p Fw(.)674 2324 y Fq(\020)723 2417 y Fl(s)c Fm(\000)f Fl(\025)912 2429 y Fk(L)980 2417 y Fj(+)1087 2396 y(~)1063 2417 y Fl(X)1132 2429 y Fk(L)1182 2417 y Fj(\()p Fl(s)p Fj(\))p Fl(\025)1333 2429 y Fk(L)1383 2324 y Fq(\021)1471 2396 y Fj(~)1447 2417 y Fl(W)12 b Fj(\()p Fl(s)p Fj(\))83 b(=)1871 2324 y Fq(\020)1920 2417 y Fl(s)19 b Fj(+)f Fl(\025)2109 2429 y Fk(S)2176 2417 y Fm(\000)2283 2396 y Fj(~)2259 2417 y Fl(X)2328 2429 y Fk(S)2376 2417 y Fj(\()p Fl(s)p Fj(\))p Fl(\025)2527 2429 y Fk(S)2576 2324 y Fq(\021)2639 2417 y Fj(Pr)o(\()p Fl(W)12 b Fj(\()p Fl(t)p Fj(\))24 b(=)f(0\))p Fl(;)1471 2615 y Fj(~)1447 2636 y Fl(W)12 b Fj(\()p Fl(s)p Fj(\))83 b(=)1883 2580 y Fl(s)19 b Fj(+)f Fl(\025)2072 2592 y Fk(S)2139 2580 y Fm(\000)2245 2559 y Fj(~)2222 2580 y Fl(X)2291 2592 y Fk(S)2338 2580 y Fj(\()p Fl(s)p Fj(\))p Fl(\025)2489 2592 y Fk(S)p 1881 2617 661 4 v 1881 2704 a Fl(s)g Fm(\000)g Fl(\025)2069 2716 y Fk(L)2138 2704 y Fj(+)2245 2683 y(~)2221 2704 y Fl(X)2290 2716 y Fk(L)2339 2704 y Fj(\()p Fl(s)p Fj(\))p Fl(\025)2490 2716 y Fk(L)2551 2636 y Fl(\031)2598 2648 y Fi(0)2635 2636 y Fl(;)120 2892 y Fw(where)23 b Fl(\031)394 2904 y Fi(0)461 2892 y Fj(=)29 b(Pr)o(\()p Fl(W)12 b Fj(\()p Fl(t)p Fj(\))30 b(=)e(0\))c Fw(and)f Fj(lim)1341 2904 y Fk(t)p Fc(!1)1540 2871 y Fj(~)1516 2892 y Fl(W)12 b Fj(\()p Fl(t;)i(s)p Fj(\))30 b(=)1924 2871 y(~)1899 2892 y Fl(W)12 b Fj(\()p Fl(s)p Fj(\))p Fw(.)36 b(Ne)o(xt,)24 b(we)g(will)g(obtain)f Fl(\031)2908 2904 y Fi(0)2970 2892 y Fw(by)g(e)n(v)n(aluating)f Fl(W)12 b Fj(\()p Fl(s)p Fj(\))24 b Fw(at)120 2992 y Fl(s)f Fj(=)g(0)p Fw(:)1389 3174 y Fj(1)83 b(=)1686 3153 y(~)1661 3174 y Fl(W)12 b Fj(\(0\))p Fl(;)i(;)1514 3383 y Fj(=)1683 3322 y(1)k Fm(\000)1836 3282 y Fk(d)1889 3267 y Fi(~)1871 3282 y Fk(X)1925 3290 y Fb(S)1967 3282 y Fi(\()p Fk(s)p Fi(\))p 1836 3303 215 4 v 1910 3351 a Fk(ds)2060 3322 y Fl(\025)2108 3334 y Fk(S)p 1681 3364 478 4 v 1681 3468 a Fj(1)g(+)1834 3428 y Fk(d)1887 3413 y Fi(~)1869 3428 y Fk(X)1923 3436 y Fb(L)1967 3428 y Fi(\()p Fk(s)p Fi(\))p 1834 3449 217 4 v 1909 3497 a Fk(ds)2060 3468 y Fl(\025)2108 3480 y Fk(L)2168 3238 y Fq(\014)2168 3288 y(\014)2168 3338 y(\014)2168 3388 y(\014)2168 3437 y(\014)2196 3501 y Fk(s)p Fi(=0)2329 3383 y Fl(\031)2376 3395 y Fi(0)2414 3383 y Fl(;)1514 3653 y Fj(=)1673 3597 y(1)g(+)g Fl(E)5 b Fj([)p Fl(X)1974 3609 y Fk(S)2022 3597 y Fj(])p Fl(\025)2093 3609 y Fk(S)p 1671 3634 472 4 v 1671 3710 a Fj(1)18 b Fm(\000)g Fl(E)5 b Fj([)p Fl(X)1972 3722 y Fk(L)2022 3710 y Fj(])p Fl(\025)2093 3722 y Fk(L)2153 3653 y Fl(\031)2200 3665 y Fi(0)2238 3653 y Fl(:)120 3878 y Fw(The)20 b(second)f(equality)g (is)j(by)d(L)-8 b('Hopital')j(s)20 b(rule.)1505 4106 y Fl(\031)1552 4118 y Fi(0)1673 4106 y Fj(=)1830 4050 y(1)e Fm(\000)g Fl(\025)2021 4062 y Fk(L)2071 4050 y Fl(E)5 b Fj([)p Fl(X)2229 4062 y Fk(L)2279 4050 y Fj(])p 1830 4087 V 1832 4163 a(1)18 b(+)g Fl(\025)2023 4175 y Fk(S)2071 4163 y Fl(E)5 b Fj([)p Fl(X)2229 4175 y Fk(S)2277 4163 y Fj(])2312 4106 y Fl(:)120 4352 y Fw(W)-7 b(e)26 b(will)f(dif)n(ferentiate)861 4331 y Fj(~)837 4352 y Fl(W)12 b Fj(\()p Fl(s)p Fj(\))25 b Fw(and)f(e)n(v)n(aluate)g(at)h Fl(s)31 b Fj(=)f(0)25 b Fw(to)g(obtain)e(the)i(moments)e(of)i Fl(W)12 b Fw(,)25 b(which)f(is)i(the)e(time)h(in)g(queue)120 4467 y Fl(T)181 4424 y Fi(\()p Fk(L)p Fi(\))169 4492 y Fk(Q)302 4467 y Fw(for)20 b(the)g(lar)o(ge)f(jobs.)25 b(Let)1388 4671 y Fl(h)p Fj(\()p Fl(s)p Fj(\))84 b(=)e Fl(s)19 b Fj(+)f Fl(\025)1959 4683 y Fk(S)2026 4671 y Fm(\000)g Fl(\025)2157 4683 y Fk(S)2229 4650 y Fj(~)2205 4671 y Fl(X)2274 4683 y Fk(S)2322 4671 y Fj(\()p Fl(s)p Fj(\))p Fl(:)1394 4795 y(g)s Fj(\()p Fl(s)p Fj(\))83 b(=)f Fl(s)19 b Fm(\000)f Fl(\025)1959 4807 y Fk(L)2027 4795 y Fj(+)g Fl(\025)2158 4807 y Fk(L)2232 4774 y Fj(~)2208 4795 y Fl(X)2277 4807 y Fk(L)2327 4795 y Fj(\()p Fl(s)p Fj(\))p Fl(:)1387 4968 y(f)9 b Fj(\()p Fl(s)p Fj(\))83 b(=)1780 4912 y Fl(h)p Fj(\()p Fl(s)p Fj(\))p 1780 4949 152 4 v 1783 5025 a Fl(g)s Fj(\()p Fl(s)p Fj(\))1942 4968 y Fl(:)1875 5349 y FC(30)p eop %%Page: 31 33 31 32 bop 120 91 a Fw(Then,)1785 304 y Fl(f)9 b Fj(\(0\))83 b(=)2203 248 y(1)p 2181 285 85 4 v 2181 361 a Fl(\031)2228 373 y Fi(0)2276 304 y Fl(;)1527 469 y(h)p Fj(\(0\))23 b(=)g Fl(g)s Fj(\(0\))83 b(=)f(0)p Fl(:)120 652 y Fw(Since)1105 863 y Fl(f)1155 828 y Fc(0)1178 863 y Fj(\(0\))h(=)1525 806 y Fl(h)1573 776 y Fc(00)1615 806 y Fj(\(0\))19 b Fm(\000)f Fl(f)9 b Fj(\(0\))p Fl(g)2022 776 y Fc(00)2063 806 y Fj(\(0\))p 1525 844 645 4 v 1740 920 a(2)p Fl(g)1825 896 y Fc(0)1848 920 y Fj(\(0\))2179 863 y Fl(;)1086 1092 y(f)1136 1058 y Fc(00)1178 1092 y Fj(\(0\))83 b(=)1525 1036 y Fl(h)1573 1006 y Fc(000)1634 1036 y Fj(\(0\))19 b Fm(\000)f Fj(3)p Fl(f)1934 1006 y Fc(0)1956 1036 y Fj(\(0\))p Fl(g)2105 1006 y Fc(00)2147 1036 y Fj(\(0\))h Fm(\000)f Fl(f)9 b Fj(\(0\))p Fl(g)2554 1006 y Fc(000)2615 1036 y Fj(\(0\))p 1525 1073 1196 4 v 2016 1149 a(3)p Fl(g)2101 1125 y Fc(0)2123 1149 y Fj(\(0\))2731 1092 y Fl(;)120 1318 y Fw(and)1413 1500 y Fl(h)p Fj(\()p Fl(s)p Fj(\))83 b(=)g Fl(s)18 b Fj(+)g Fl(\025)1983 1512 y Fk(S)2050 1500 y Fm(\000)g Fl(\025)2181 1512 y Fk(S)2253 1479 y Fj(~)2229 1500 y Fl(X)2298 1512 y Fk(S)2346 1500 y Fj(\()p Fl(s)p Fj(\))p Fl(;)1389 1625 y(h)1437 1591 y Fc(0)1460 1625 y Fj(\()p Fl(s)p Fj(\))84 b(=)f(1)18 b Fm(\000)g Fl(\025)1986 1637 y Fk(S)2058 1604 y Fj(~)2034 1625 y Fl(X)2110 1591 y Fc(0)2103 1645 y Fk(S)2151 1625 y Fj(\()p Fl(s)p Fj(\))p Fl(;)1370 1749 y(h)1418 1715 y Fc(00)1460 1749 y Fj(\()p Fl(s)p Fj(\))84 b(=)f Fm(\000)p Fl(\025)1908 1761 y Fk(S)1979 1728 y Fj(~)1956 1749 y Fl(X)2032 1715 y Fc(00)2025 1770 y Fk(S)2073 1749 y Fj(\()p Fl(s)p Fj(\))p Fl(;)1351 1874 y(h)1399 1840 y Fc(000)1460 1874 y Fj(\()p Fl(s)p Fj(\))h(=)f Fm(\000)p Fl(\025)1908 1886 y Fk(S)1979 1853 y Fj(~)1956 1874 y Fl(X)2032 1840 y Fc(000)2025 1895 y Fk(S)2093 1874 y Fj(\()p Fl(s)p Fj(\))p Fl(;)1418 1999 y(g)s Fj(\()p Fl(s)p Fj(\))g(=)g Fl(s)18 b Fm(\000)g Fl(\025)1983 2011 y Fk(L)2052 1999 y Fj(+)g Fl(\025)2183 2011 y Fk(L)2256 1978 y Fj(~)2233 1999 y Fl(X)2302 2011 y Fk(L)2351 1999 y Fj(\()p Fl(s)p Fj(\))p Fl(;)1395 2123 y(g)1438 2089 y Fc(0)1460 2123 y Fj(\()p Fl(s)p Fj(\))84 b(=)f(1)18 b(+)g Fl(\025)1986 2135 y Fk(L)2059 2102 y Fj(~)2036 2123 y Fl(X)2112 2089 y Fc(0)2105 2144 y Fk(L)2154 2123 y Fj(\()p Fl(s)p Fj(\))p Fl(;)1375 2248 y(g)1418 2213 y Fc(00)1460 2248 y Fj(\()p Fl(s)p Fj(\))84 b(=)f Fl(\025)1843 2260 y Fk(L)1917 2227 y Fj(~)1893 2248 y Fl(X)1969 2213 y Fc(00)1962 2268 y Fk(L)2011 2248 y Fj(\()p Fl(s)p Fj(\))p Fl(;)1356 2372 y(g)1399 2338 y Fc(000)1460 2372 y Fj(\()p Fl(s)p Fj(\))h(=)f Fl(\025)1843 2384 y Fk(L)1917 2351 y Fj(~)1893 2372 y Fl(X)1969 2338 y Fc(000)1962 2393 y Fk(L)2030 2372 y Fj(\()p Fl(s)p Fj(\))p Fl(;)1387 2497 y(h)1435 2462 y Fc(0)1458 2497 y Fj(\(0\))g(=)g(1)18 b(+)g Fl(\032)1981 2509 y Fk(S)2029 2497 y Fl(;)1368 2621 y(h)1416 2587 y Fc(00)1458 2621 y Fj(\(0\))83 b(=)g Fm(\000)p Fl(\025)1908 2633 y Fk(S)1956 2621 y Fl(E)5 b Fj([)p Fl(X)2121 2587 y Fi(2)2114 2642 y Fk(S)2162 2621 y Fj(])p Fl(;)1348 2746 y(h)1396 2711 y Fc(000)1458 2746 y Fj(\(0\))83 b(=)g Fl(\025)1843 2758 y Fk(S)1891 2746 y Fl(E)5 b Fj([)p Fl(X)2056 2711 y Fi(3)2049 2766 y Fk(S)2097 2746 y Fj(])p Fl(;)1392 2870 y(g)1435 2836 y Fc(0)1458 2870 y Fj(\(0\))83 b(=)g(1)18 b Fm(\000)g Fl(\032)1981 2882 y Fk(L)2030 2870 y Fl(;)c(;)1373 2995 y(g)1416 2961 y Fc(00)1458 2995 y Fj(\(0\))83 b(=)g Fl(\025)1843 3007 y Fk(L)1893 2995 y Fl(E)5 b Fj([)p Fl(X)2058 2961 y Fi(2)2051 3015 y Fk(L)2100 2995 y Fj(])1354 3119 y Fl(g)1397 3085 y Fc(000)1458 3119 y Fj(\(0\))83 b(=)g Fm(\000)p Fl(\025)1908 3131 y Fk(L)1957 3119 y Fl(E)5 b Fj([)p Fl(X)2122 3085 y Fi(3)2115 3140 y Fk(L)2165 3119 y Fj(])p Fl(;)120 3302 y Fw(we)21 b(ha)n(v)o(e)670 3534 y Fl(f)720 3500 y Fc(0)743 3534 y Fj(\(0\))83 b(=)1089 3465 y Fm(\000)p Fl(\025)1202 3477 y Fk(S)1250 3465 y Fl(E)5 b Fj([)p Fl(X)1415 3434 y Fi(2)1408 3487 y Fk(S)1456 3465 y Fj(])19 b Fm(\000)1610 3432 y Fi(1)p 1591 3446 72 4 v 1591 3493 a Fk(\031)1630 3501 y Fa(0)1672 3465 y Fl(\025)1720 3477 y Fk(L)1770 3465 y Fl(E)5 b Fj([)p Fl(X)1935 3434 y Fi(2)1928 3487 y Fk(L)1978 3465 y Fj(])p 1089 3515 912 4 v 1374 3591 a(2\(1)18 b Fm(\000)g Fl(\032)1634 3603 y Fk(L)1684 3591 y Fj(\))2011 3534 y Fl(;)651 3830 y(f)701 3796 y Fc(00)743 3830 y Fj(\(0\))83 b(=)1089 3755 y Fl(\025)1137 3767 y Fk(S)1186 3755 y Fl(E)5 b Fj([)p Fl(X)1351 3725 y Fi(3)1344 3778 y Fk(S)1392 3755 y Fj(])18 b Fm(\000)g Fj(3)1568 3697 y Fc(\000)p Fk(\025)1659 3705 y Fb(S)1701 3697 y Fk(E)s Fi([)p Fk(X)1831 3672 y Fa(2)1826 3713 y Fb(S)1868 3697 y Fi(])p Fc(\000)1968 3674 y Fa(1)p 1948 3683 67 4 v 1948 3717 a Fb(\031)1983 3729 y Fa(0)2025 3697 y Fk(\025)2064 3705 y Fb(L)2108 3697 y Fk(E)s Fi([)p Fk(X)2238 3672 y Fa(2)2233 3713 y Fb(L)2277 3697 y Fi(])p 1568 3736 729 4 v 1808 3783 a(2\(1)p Fc(\000)p Fk(\032)1986 3791 y Fb(L)2030 3783 y Fi(\))2306 3755 y Fl(\025)2354 3767 y Fk(L)2404 3755 y Fl(E)5 b Fj([)p Fl(X)2569 3725 y Fi(2)2562 3778 y Fk(L)2612 3755 y Fj(])18 b(+)2766 3722 y Fi(1)p 2746 3736 72 4 v 2746 3783 a Fk(\031)2785 3791 y Fa(0)2828 3755 y Fl(\025)2876 3767 y Fk(L)2926 3755 y Fl(E)5 b Fj([)p Fl(X)3091 3725 y Fi(3)3084 3778 y Fk(L)3133 3755 y Fj(])p 1089 3811 2068 4 v 1952 3887 a(3\(1)18 b Fm(\000)g Fl(\032)2212 3899 y Fk(L)2261 3887 y Fj(\))3166 3830 y Fl(:)222 4196 y(E)5 b Fj([)p Fl(T)372 4153 y Fi(\()p Fk(L)p Fi(\))360 4220 y Fk(Q)473 4196 y Fj(])83 b(=)f Fm(\000)p Fl(f)841 4161 y Fc(0)864 4196 y Fj(\(0\))p Fl(\031)1017 4208 y Fi(0)1054 4196 y Fl(;)579 4388 y Fj(=)808 4332 y Fl(\032)851 4344 y Fk(L)p 736 4369 236 4 v 736 4445 a Fj(1)18 b Fm(\000)g Fl(\032)922 4457 y Fk(L)1013 4332 y Fl(E)5 b Fj([)p Fl(X)1178 4302 y Fi(2)1171 4355 y Fk(L)1220 4332 y Fj(])p 992 4369 273 4 v 992 4445 a(2)p Fl(E)g Fj([)p Fl(X)1192 4457 y Fk(L)1241 4445 y Fj(])1292 4388 y(+)1457 4332 y Fl(\032)1500 4344 y Fk(S)p 1385 4369 235 4 v 1385 4445 a Fj(1)18 b(+)g Fl(\032)1571 4457 y Fk(S)1660 4332 y Fl(E)5 b Fj([)p Fl(X)1825 4302 y Fi(2)1818 4355 y Fk(S)1866 4332 y Fj(])p 1639 4369 271 4 v 1639 4445 a(2)p Fl(E)g Fj([)p Fl(X)1839 4457 y Fk(S)1887 4445 y Fj(])1920 4388 y Fl(;)120 4586 y(E)g Fj([\()p Fl(T)302 4543 y Fi(\()p Fk(L)p Fi(\))290 4610 y Fk(Q)403 4586 y Fj(\))435 4552 y Fi(2)473 4586 y Fj(])83 b(=)f Fl(f)776 4552 y Fc(00)818 4586 y Fj(\(0\))p Fl(\031)971 4598 y Fi(0)1009 4586 y Fl(;)579 4779 y Fj(=)808 4722 y Fl(\032)851 4734 y Fk(L)p 736 4759 236 4 v 736 4836 a Fj(1)18 b Fm(\000)g Fl(\032)922 4848 y Fk(L)1013 4722 y Fl(E)5 b Fj([)p Fl(X)1178 4692 y Fi(3)1171 4745 y Fk(L)1220 4722 y Fj(])p 992 4759 273 4 v 992 4836 a(3)p Fl(E)g Fj([)p Fl(X)1192 4848 y Fk(L)1241 4836 y Fj(])1292 4779 y(+)1457 4722 y Fl(\032)1500 4734 y Fk(S)p 1385 4759 235 4 v 1385 4836 a Fj(1)18 b(+)g Fl(\032)1571 4848 y Fk(S)1660 4722 y Fl(E)5 b Fj([)p Fl(X)1825 4692 y Fi(3)1818 4745 y Fk(S)1866 4722 y Fj(])p 1639 4759 271 4 v 1639 4836 a(3)p Fl(E)g Fj([)p Fl(X)1839 4848 y Fk(S)1887 4836 y Fj(])1938 4779 y(+)2103 4722 y Fl(\032)2146 4734 y Fk(L)p 2031 4759 236 4 v 2031 4836 a Fj(1)18 b Fm(\000)g Fl(\032)2217 4848 y Fk(L)2287 4722 y Fl(E)5 b Fj([)p Fl(X)2452 4692 y Fi(2)2445 4745 y Fk(L)2494 4722 y Fj(])p 2287 4759 231 4 v 2287 4836 a Fl(E)g Fj([)p Fl(X)2445 4848 y Fk(L)2494 4836 y Fj(])2541 4662 y Fq(\022)2684 4722 y Fl(\032)2727 4734 y Fk(L)p 2612 4759 236 4 v 2612 4836 a Fj(1)18 b Fm(\000)g Fl(\032)2798 4848 y Fk(L)2889 4722 y Fl(E)5 b Fj([)p Fl(X)3054 4692 y Fi(2)3047 4745 y Fk(L)3096 4722 y Fj(])p 2868 4759 273 4 v 2868 4836 a(2)p Fl(E)g Fj([)p Fl(X)3068 4848 y Fk(L)3117 4836 y Fj(])3168 4779 y(+)3333 4722 y Fl(\032)3376 4734 y Fk(L)p 3261 4759 236 4 v 3261 4836 a Fj(1)18 b Fm(\000)g Fl(\032)3447 4848 y Fk(L)3538 4722 y Fl(E)5 b Fj([)p Fl(X)3703 4692 y Fi(2)3696 4745 y Fk(S)3744 4722 y Fj(])p 3517 4759 271 4 v 3517 4836 a(2)p Fl(E)g Fj([)p Fl(X)3717 4848 y Fk(S)3764 4836 y Fj(])3798 4662 y Fq(\023)3872 4779 y Fl(:)1875 5349 y FC(31)p eop %%Page: 32 34 32 33 bop 120 91 a FG(Refer)n(ences)165 298 y FC([1])47 b(The)23 b(PSC')-5 b(s)22 b(Cray)i(J90')-5 b(s.)34 b(http://www)-6 b(.psc.edu/machines/cr)q(ay/)q(j90)q(/j9)q(0.h)q(tml,)28 b(1998.)165 449 y([2])47 b(Supercomputing)31 b(at)c(the)g(N)m(AS)f(f)o (acility)-6 b(.)47 b(http://www)-6 b(.nas.nasa.go)o(v/T)g(echnolo)q(gy) q(/Supe)q(rco)q(mpu)q(tin)q(g/,)317 562 y(1998.)165 712 y([3])47 b(S.)30 b(Asmussen.)61 b(Queueing)34 b(simulation)g(in)e(hea)n (vy)h(traf)n(\002c.)60 b Fy(Mathematics)34 b(of)e(Oper)o(ations)i (Resear)m(c)o(h)p FC(,)317 825 y(17\(1\),)24 b(1992.)165 975 y([4])47 b(S.)34 b(Asmussen.)71 b(Phase-type)37 b(distrib)n(utions) i(and)d(related)h(point)f(processes:)55 b(Fitting)36 b(and)f(recent)i(ad-)317 1088 y(v)n(ances.)i(In)25 b(S.)f(R.)f(Chakra)n (v)n(arthy)28 b(and)d(A.)f(S.)g(Alf)o(a,)h(editors,)h Fy(Matrix-Analytic)i(Methods)f(in)e(Stoc)o(hastic)317 1201 y(Models)p FC(,)f(pages)h(137\226149.)g(Marcel)g(Dekk)o(er)l(,)f (1997.)165 1351 y([5])47 b(F)-7 b(.)21 b(Bonomi)i(and)g(A.)f(K)o(umar) -5 b(.)30 b(Adapti)n(v)o(e)24 b(optimal)g(load)f(balancing)j(in)d(a)f (nonhomogeneous)27 b(multiserv)o(er)317 1464 y(system)33 b(with)e(a)h(central)h(job)g(scheduler)-5 b(.)63 b Fy(IEEE)30 b(T)-5 b(r)o(ansactions)34 b(on)e(Computer)o(s)p FC(,)k (39\(10\):1232\2261250,)317 1577 y(October)24 b(1990.)165 1727 y([6])47 b(T)-7 b(.)26 b(Brisco.)45 b(DNS)25 b(support)k(for)f (load)g(balancing.)47 b(RFC)25 b(1794,)k(USC/Information)g(Sciences)f (Institute.)317 1840 y(A)-7 b(v)n(ailable)25 b(at)e (ftp://ds.internic.net/)q(rfc)q(/rfc)q(17)q(94)q(.txt.,)28 b(April)c(1995.)165 1990 y([7])47 b(D.M.Dias,)20 b(W)-8 b(.)19 b(Kish,)h(R.)g(Mukherjee,)j(and)e(R.)e(T)-6 b(e)n(w)o(ari.)26 b(A)19 b(scalable)k(and)e(highly)h(a)n(v)n(ailable)h(Web)e(serv)o(er)-5 b(.)317 2103 y(In)33 b Fy(Pr)l(oceedings)i(of)e(the)g(41st)g(IEEE)e (Computer)j(Society)g(International)j(Confer)m(ence)e(\(COMPCON\))317 2216 y('96)p FC(,)24 b(pages)g(85\22692,)h(February)g(1996.)165 2366 y([8])47 b(A.)23 b(Ephremides,)j(P)-10 b(.)23 b(V)-10 b(araiya,)25 b(and)g(J.)f(W)-7 b(alrand.)38 b(A)23 b(simple)i(dynamic)h (routing)h(problem.)37 b Fy(IEEE)23 b(T)-5 b(r)o(ans-)317 2479 y(actions)25 b(on)f(A)n(utomatic)h(Contr)l(ol)p FC(,)f(A)l(C-25\(4\):690\226693,)k(1980.)165 2630 y([9])47 b(D.)26 b(Feitelson,)k(L.)c(Rudolph,)j(U.)d(Schwie)o(gelshohn,)31 b(K.)26 b(Se)n(vcik,)j(and)e(P)-10 b(.)26 b(W)-7 b(ong.)46 b(Theory)28 b(and)g(practice)317 2742 y(in)34 b(parallel)j(job)e (scheduling.)71 b(In)35 b Fy(Pr)l(oceedings)i(of)e(IPPS/SPDP)e('97)i(W) -8 b(orkshop.)35 b(Lectur)m(e)g(Notes)g(in)317 2855 y(Computer)24 b(Science)o(,)h(vol.)f(1291)p FC(,)g(pages)h(1\22634,)f(April)g(1997.) 120 3006 y([10])47 b(M.)18 b(Harchol-Balter)-5 b(.)27 b(T)-7 b(ask)19 b(assignment)j(with)e(unkno)n(wn)g(duration.)27 b Fy(J)n(ournal)21 b(of)f(the)g(A)m(CM)p FC(,)d(49\(2\),)k(2002.)120 3156 y([11])47 b(M.)28 b(Harchol-Balter)l(,)34 b(M.)29 b(Cro)o(v)o(ella,)i(and)f(C.)f(Murta.)53 b(On)29 b(choosing)j(a)e(task) g(assignment)i(polic)o(y)f(for)f(a)317 3269 y(distrib)n(uted)24 b(serv)o(er)e(system.)29 b Fy(IEEE)19 b(J)n(ournal)j(of)f(P)-7 b(ar)o(allel)22 b(and)f(Distrib)n(uted)j(Computing)p FC(,)f(59:204)f(\226)f(228,)317 3382 y(1999.)120 3532 y([12])47 b(G.)18 b(Hunt,)i(G.)e(Goldszmidt,)k(R.)c(King,)i(and)g(R.)e (Mukherjee.)26 b(Netw)o(ork)20 b(dispatcher:)30 b(A)18 b(connection)23 b(router)317 3645 y(for)e(scalable)i(internet)g (services.)30 b(In)21 b Fy(Pr)l(oceedings)i(of)e(the)g(7th)h (International)j(WWW)19 b(Confer)m(ence)p FC(,)k(April)317 3758 y(1998.)120 3908 y([13])47 b(V)-12 b(.)25 b(S.)f(Iyengar)l(,)k(L.) c(H.)h(T)m(re)n(villyan,)j(and)e(P)-10 b(.)24 b(Bose.)41 b(Representati)n(v)o(e)29 b(traces)e(for)f(processor)j(models)d(with) 317 4021 y(in\002nite)19 b(cache.)k(In)c Fy(Pr)l(oceedings)i(of)d(the)h (International)j(Symposium)e(on)e(High-P)-7 b(erformance)21 b(Computer)317 4134 y(Ar)m(c)o(hitectur)m(e)k(\(HPCA\))p FC(,)c(pages)k(62\22672,)g(February)g(1996.)120 4284 y([14])47 b(M.)32 b(A.)g(Johnson)j(and)f(M.)e(F)-7 b(.)32 b(T)-7 b(aaf)n(fe.)64 b(An)33 b(in)l(v)o(estigation)k(of)c (phase-distrib)n(ution)39 b(moment-matching)317 4397 y(algorithms)26 b(for)d(use)h(in)g(queueing)i(models.)34 b Fy(Queueing)25 b(Systems)p FC(,)f(8:129\226147,)j(1991.)120 4547 y([15])47 b(A.)32 b(Lang)i(and)h(J.)e(L.)f(Arthur)-5 b(.)67 b(P)o(arameter)34 b(approximation)j(for)d(phase-type)j(distrib)n (utions.)71 b(In)33 b(S.)g(R.)317 4660 y(Chakra)n(v)n(arthy)g(and)e(A.) e(S.)g(Alf)o(a,)j(editors,)h Fy(Matrix-Analytic)h(Methods)e(in)e(Stoc)o (hastic)j(Models)p FC(,)g(pages)317 4773 y(151\226206.)26 b(Marcel)e(Dekk)o(er)l(,)g(1997.)120 4923 y([16])47 b(G.)21 b(Latouche)j(and)g(V)-12 b(.)21 b(Ramasw)o(ami.)32 b Fy(Intr)l(oduction)26 b(to)d(Matrix)g(Analytic)h(Methods)g(in)f(Stoc)o (hastic)i(Mod-)317 5036 y(eling)p FC(.)34 b(ASA-SIAM,)21 b(Philadelphia,)26 b(1999.)1875 5349 y(32)p eop %%Page: 33 35 33 34 bop 120 91 a FC([17])47 b(C.)3063 b(Leiser)n(-)317 204 y(son.)63 b(The)32 b(Pleiades)i(alpha)g(cluster)g(at)f(M.I.T)-7 b(..)61 b(Documentation)35 b(at:)48 b(//http://bonanza.lcs.mit.ed)q (u/,)317 317 y(1998.)120 467 y([18])f(C.)37 b(Leiserson.)82 b(The)38 b(Xolas)g(supercomputing)43 b(project)d(at)e(M.I.T)-7 b(..)78 b(Documentation)42 b(a)n(v)n(ailable)e(at:)317 580 y(http://xolas.lcs.mit.edu,)28 b(1998.)120 731 y([19])47 b(J.)26 b(D.)g(C.)f(Little.)45 b(A)26 b(proof)i(of)f(the)g(queuing)j (formula)e Fu(L)j Fs(=)h Fu(\025W)13 b FC(.)43 b Fy(Oper)o(ations)29 b(Resear)m(c)o(h)p FC(,)f(9:383\226387,)317 844 y(1961.)120 994 y([20])47 b(M.)22 b(F)-7 b(.)22 b(Neuts.)33 b Fy(Matrix-Geometric) 27 b(Solutions)f(in)d(Stoc)o(hastic)j(Models)p FC(.)120 1144 y([21])47 b(E.)33 b(W)-8 b(.)33 b(P)o(arsons)i(and)g(K.)e(C.)h(Se) n(vcik.)69 b(Implementing)37 b(multiprocessor)h(scheduling)f (disciplines.)72 b(In)317 1257 y Fy(Pr)l(oceedings)38 b(of)e(IPPS/SPDP)f('97)h(W)-8 b(orkshop.)37 b(Lectur)m(e)g(Notes)f(in)g (Computer)h(Science)o(,)j(vol.)c(1459)p FC(,)317 1370 y(pages)25 b(166\226182,)g(April)f(1997.)120 1520 y([22])47 b(K.)24 b(W)-8 b(.)24 b(Ross)i(and)h(D.)d(D.)g(Y)-9 b(ao.)40 b(Optimal)26 b(load)h(balancing)h(and)f(scheduling)h(in)e(a)g(distrib)n (uted)j(computer)317 1633 y(system.)34 b Fy(J)n(ournal)25 b(of)f(the)f(A)m(CM)p FC(,)f(38\(3\):676\226690,)28 b(July)c(1991.)120 1783 y([23])47 b(B.)20 b(Schroeder)k(and)f(M.)e(Harchol-Balter)-5 b(.)32 b(Ev)n(aluation)24 b(of)e(task)h(assignment)h(policies)g(for)e (supercomput-)317 1896 y(ing)g(serv)o(ers:)30 b(The)22 b(case)h(for)f(load)h(unbalancing)j(and)d(f)o(airness.)32 b(In)22 b Fy(Pr)l(oceedings)j(of)d FC(HPDC)e(2000,)j(pages)317 2009 y(211\226219,)j(2000.)120 2159 y([24])47 b(J.)30 b(Sethuraman)i(and)g(M.)d(S.)h(Squillante.)58 b(Optimal)31 b(scheduling)j(in)d(multiclass)i(multiserv)o(er)f(systems.)317 2272 y(T)-6 b(echnical)25 b(report,)f(IBM)f(Research)i(Di)n(vision,)f (1998.)120 2423 y([25])47 b(M.)22 b(S.)f(Squillante,)k(D.)d(D.)f(Y)-9 b(ao,)23 b(and)g(L.)f(Zhang.)32 b(W)-7 b(eb)23 b(traf)n(\002c)g (modeling)i(and)e(web)g(serv)o(er)h(performance)317 2535 y(analysis.)35 b(T)-6 b(echnical)25 b(report,)g(IBM)d(Research)j(Di)n (vision,)f(October)h(1998.)120 2686 y([26])47 b(H.)19 b(T)-7 b(akagi.)27 b Fy(Queueing)22 b(Analysis)g(\226)e(A)f(F)-10 b(oundation)24 b(of)c(P)-7 b(erformance)22 b(Evaluation)p FC(,)h(v)n(olume)f(1:)27 b(V)-10 b(acation)317 2799 y(and)24 b(Priority)g(Systems,)g(P)o(art)f(1.)33 b(North)24 b(Holland,)g(1991.) 120 2949 y([27])47 b(W)-8 b(.)22 b(Whitt.)33 b(Planning)25 b(queueing)h(simulations.)36 b Fy(Mana)o(g)o(ement)26 b(Science)p FC(,)f(35\(11\),)g(1989.)120 3099 y([28])47 b(W)-8 b(.)18 b(W)l(inston.)26 b(Optimality)20 b(of)g(the)f(shortest)j (line)e(discipline.)27 b Fy(J)n(ournal)21 b(of)e(Applied)i(Pr)l (obability)p FC(,)h(14:181\226)317 3212 y(189,)i(1977.)120 3362 y([29])47 b(R.)22 b(W)-8 b(.)22 b(W)-7 b(olf)n(f.)33 b Fy(Stoc)o(hastic)26 b(Modeling)f(and)f(the)g(Theory)g(of)g(Queues)p FC(.)34 b(Prentice)25 b(Hall,)e(1989.)1875 5349 y(33)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF