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(execution)h(is)f(usually)g(signi\014can)n(t)g(relativ)n(e)f(to)i(the)g (a)n(v)n(erage)450 3596 y(lifetime)g(of)f(pro)r(cesses,)g(implicit)h (non-preemptiv)n(e)e(p)r(olicies)h(require)f(some)h(a)g(priori)f (infor-)450 3695 y(mation)26 b(ab)r(out)h(job)f(lifetimes.)37 b(This)27 b(information)f(is)g(often)h(implemen)n(ted)g(as)f(an)g (eligibilit)n(y)450 3795 y(list)k(that)g(sp)r(eci\014es)g(b)n(y)f(pro)r (cess)g(name)h(whic)n(h)f(pro)r(cesses)g(are)f(w)n(orth)h(migrating)g ([Sv)n(ensson)450 3895 y(1990])d([Zhou)h(et)h(al.)f(1993].)533 3996 y(In)h(con)n(trast,)f(most)h(preemptiv)n(e)g(migration)f(p)r (olicies)h(do)g(not)g(use)g(a)f(priori)g(information,)450 4095 y(since)h(this)h(is)f(often)g(di\016cult)i(to)e(main)n(tain)g(and) g(preemptiv)n(e)g(strategies)e(can)i(p)r(erform)g(w)n(ell)450 4195 y(without)f(it.)37 b(These)26 b(systems)g(use)g(only)g (system-visible)f(data)h(lik)n(e)g(the)h(curren)n(t)e(age)g(of)i(eac)n (h)450 4295 y(pro)r(cess)f(or)h(its)h(memory)f(size.)533 4396 y(This)37 b(pap)r(er)g(examines)f(the)i(p)r(erformance)e(b)r (ene\014ts)i(of)f Fn(preemptiv)m(e)p Ft(,)h Fn(implicit)d Ft(load)450 4496 y(balancing)27 b(strategies)f(that)i(assume)f Fn(no)k(a)h(priori)g(information)26 b Ft(ab)r(out)h(pro)r(cesses.)533 4597 y(W)-7 b(e)28 b(answ)n(er)e(the)i(follo)n(wing)f(t)n(w)n(o)f (questions:)450 4796 y(\(1\))42 b(Is)35 b(preemptiv)n(e)g(migration)f (w)n(orth)n(while,)j(giv)n(en)d(the)i(additional)f(cost)g(\(CPU)g(and)h (la-)598 4896 y(tency\))28 b(asso)r(ciated)e(with)i(migrating)e(an)i (activ)n(e)f(pro)r(cess?)450 5044 y(\(2\))42 b(Whic)n(h)27 b(activ)n(e)g(pro)r(cesses,)f(if)j(an)n(y)-7 b(,)27 b(are)f(w)n(orth)h (migrating?)p eop %%Page: 3 3 3 2 bop 821 250 a Fq(Exploiting)24 b(Pro)r(cess)k(Lifetime)c (Distributions)f(fo)n(r)k(Dynamic)d(Load)i(Balancing)156 b Fp(\001)141 b Fq(3)450 465 y Fx(1.2)41 b(Pro)r(cess)27 b(mo)r(del)450 598 y Ft(In)i(our)f(mo)r(del,)h(pro)r(cesses)f(use)g(t)n (w)n(o)g(resources:)38 b(CPU)28 b(and)h(memory)f(\(w)n(e)h(do)f(not)h (consider)450 698 y(I/O\).)35 b(Th)n(us,)j(w)n(e)d(use)h(\\age")d(to)j (mean)g(CPU)f(age)g(\(the)h(CPU)g(time)g(a)f(pro)r(cess)g(has)g(used) 450 798 y(th)n(us)30 b(far\))h(and)f(\\lifetime")g(to)h(mean)f(CPU)g (lifetime)i(\(the)f(total)f(CPU)g(time)h(from)f(start)g(to)450 897 y(completion\).)36 b(W)-7 b(e)26 b(assume)g(that)g(pro)r(cessors)d (implemen)n(t)j(time-sharing)f(with)h(round-robin)450 997 y(sc)n(heduling;)c(in)f(Section)g(7)f(w)n(e)g(discuss)h(the)g (e\013ect)g(of)f(other)g(lo)r(cal)g(sc)n(heduling)g(p)r(olicies.)35 b(Since)450 1096 y(pro)r(cesses)23 b(ma)n(y)h(b)r(e)i(dela)n(y)n(ed)d (while)j(on)e(the)h(run)g(queue)g(or)f(while)h(migrating,)f(the)h(slo)n (wdo)n(wn)450 1196 y(imp)r(osed)j(on)f(a)g(pro)r(cess)g(is)1236 1385 y(Slo)n(wdo)n(wn)g(of)g(pro)r(cess)g Fm(p)22 b Ft(=)2187 1328 y Fo(wal)t(l-time)p Ft(\()p Fm(p)p Ft(\))p 2170 1365 473 4 v 2170 1441 a Fo(CPU-time)p Ft(\()p Fm(p)p Ft(\))450 1574 y(where)33 b(w)n(all)g(time)h(is)g(the)g(total)f(time)h (a)f(pro)r(cess)f(sp)r(ends)i(running,)h(w)n(aiting)e(in)h(queue,)h(or) 450 1673 y(migrating.)450 1835 y Fx(1.3)41 b(Outline)450 1968 y Ft(The)36 b(e\013ectiv)n(eness)f(of)g(load)g(balancing)g(|)h (either)f(b)n(y)g(remote)g(execution)h(or)e(preemptiv)n(e)450 2068 y(migration)26 b(|)i(dep)r(ends)g(strongly)e(on)i(the)g(nature)f (of)g(the)h(w)n(orkload,)e(including)h(the)h(distri-)450 2167 y(bution)k(of)f(pro)r(cess)f(lifetimes)i(and)f(the)h(arriv)-5 b(al)29 b(pro)r(cess.)47 b(This)31 b(pap)r(er)g(presen)n(ts)f (empirical)450 2267 y(observ)-5 b(ations)30 b(ab)r(out)i(the)g(w)n (orkload)e(on)h(a)h(net)n(w)n(ork)e(of)i(UNIX)g(w)n(orkstations,)f(and) h(uses)f(a)450 2366 y(trace-driv)n(en)f(sim)n(ulation)h(to)g(ev)-5 b(aluate)31 b(the)h(impact)g(of)g(this)f(w)n(orkload)f(on)h(prop)r (osed)g(load)450 2466 y(balancing)c(strategies.)533 2566 y(Section)f(2)h(presen)n(ts)e(a)h(study)h(of)f(the)h(distribution)g(of) f(pro)r(cess)f(lifetimes)i(for)f(a)g(v)-5 b(ariet)n(y)26 b(of)450 2665 y(w)n(orkloads)g(in)j(an)f(academic)g(en)n(vironmen)n(t,) g(including)h(instructional)f(mac)n(hines,)g(researc)n(h)450 2765 y(mac)n(hines,)k(and)g(mac)n(hines)f(used)h(for)f(system)h (administration.)49 b(W)-7 b(e)32 b(\014nd)g(that)g(the)g(distri-)450 2865 y(bution)g(is)g(predictable)f(with)i(go)r(o)r(dness)d(of)i(\014t)h (greater)d(than)i(99\045)f(and)h(consisten)n(t)f(across)450 2964 y(a)h(v)-5 b(ariet)n(y)32 b(of)h(mac)n(hines)f(and)g(w)n (orkloads.)50 b(As)33 b(a)f(rule)h(of)f(th)n(um)n(b,)j(the)e (probabilit)n(y)e(that)i(a)450 3064 y(pro)r(cess)27 b(with)i(CPU)g(age) e(of)i(one)f(second)g(uses)g(more)g(than)h Fm(T)39 b Ft(seconds)28 b(of)h(total)f(CPU)g(time)450 3163 y(is)f(1)p Fm(=T)38 b Ft(\(see)28 b(Figure)f(1\).)533 3263 y(Our)f(measuremen)n (ts)g(are)g(consisten)n(t)h(with)g(those)g(of)g(Leland)f(and)h(Ott)g ([Leland)g(and)g(Ott)450 3363 y(1986],)34 b(but)g(this)g(prior)f(w)n (ork)f(has)h(b)r(een)h(incorp)r(orated)e(in)i(few)h(subsequen)n(t)e (analytic)g(and)450 3462 y(sim)n(ulator)26 b(studies)h(of)f(load)g (balancing.)36 b(This)27 b(omission)f(is)h(unfortunate,)g(since)f(the)h (results)450 3562 y(of)h(these)f(are)g(sensitiv)n(e)g(to)g(the)h (lifetime)h(mo)r(del)f(\(see)f(Section)h(2.2\).)533 3662 y(Our)38 b(observ)-5 b(ations)37 b(of)h(lifetime)h(distributions)g(ha)n (v)n(e)e(the)i(follo)n(wing)e(consequences)g(for)450 3761 y(load)27 b(balancing:)450 3902 y(|They)j(suggest)f(that)h(it)g (is)g(preferable)f(to)g(migrate)g(older)g(pro)r(cesses)g(b)r(ecause)g (these)h(pro-)533 4002 y(cesses)g(ha)n(v)n(e)g(a)g(higher)h(probabilit) n(y)e(of)i(living)g(long)f(enough)h(\(ev)n(en)n(tually)f(using)h (enough)533 4101 y(CPU\))d(to)f(amortize)g(their)g(migration)g(cost.) 450 4216 y(|A)h(functional)f(mo)r(del)h(of)f(the)h(distribution)g(pro)n (vides)e(an)h(analytic)g(to)r(ol)g(for)g(deriving)f(the)533 4315 y(eligibilit)n(y)32 b(of)h(a)f(pro)r(cess)f(for)i(migration)e(as)h (a)g(function)h(of)g(its)f(curren)n(t)g(age,)h(migration)533 4415 y(cost,)27 b(and)h(the)g(loads)e(at)i(its)f(source)g(and)g(target) g(host.)533 4556 y(In)k(Section)g(3)g(w)n(e)g(deriv)n(e)f(a)h (migration)f(eligibilit)n(y)h(criterion)f(that)h(guaran)n(tees)e(that)i (the)450 4655 y(slo)n(wdo)n(wn)f(imp)r(osed)i(on)g(a)f(migran)n(t)g (pro)r(cess)f(is)i(lo)n(w)n(er)e(in)i(exp)r(ectation)g(than)g(it)g(w)n (ould)f(b)r(e)450 4755 y(without)h(migration.)48 b(According)31 b(to)g(this)h(criterion,)g(a)f(pro)r(cess)g(is)g(eligible)h(for)f (migration)450 4855 y(only)c(if)h(its)1313 5034 y(CPU)f(age)22 b Fm(>)1851 4978 y Ft(1)p 1760 5015 225 4 v 1760 5091 a Fm(n)c Fl(\000)g Fm(m)2012 5034 y Fl(\001)h Ft(migration)26 b(cost)p eop %%Page: 4 4 4 3 bop 450 250 a Fq(4)142 b Fp(\001)157 b Fq(M.)27 b(Ha)n (rchol-Balter)d(and)h(A.)h(B.)g(Do)n(wney)450 465 y Ft(where)h Fm(n)h Ft(\(resp)r(ectiv)n(ely)f Fm(m)p Ft(\))g(is)h(the)g(n)n(um)n(b)r (er)f(of)h(pro)r(cesses)e(at)h(the)h(source)f(\(target\))g(host.)533 569 y(In)g(Section)h(5)e(w)n(e)h(use)g(a)g(trace-driv)n(en)e(sim)n (ulation)i(to)g(compare)f(our)h(preemptiv)n(e)f(migra-)450 669 y(tion)j(p)r(olicy)h(with)f(a)g(non-preemptiv)n(e)g(p)r(olicy)g (based)f(on)h(name-lists.)42 b(The)29 b(sim)n(ulator)f(uses)450 768 y(start)f(times)g(and)g(durations)f(from)h(traces)f(of)h(a)g(real)f (system,)h(and)g(migration)f(costs)h(c)n(hosen)450 868 y(from)g(a)g(measured)g(distribution.)533 972 y(W)-7 b(e)35 b(use)g(the)g(sim)n(ulator)e(to)h(run)h(three)f(exp)r(erimen)n (ts:)51 b(\014rst)34 b(w)n(e)h(ev)-5 b(aluate)34 b(the)h(e\013ect)g(of) 450 1071 y(migration)27 b(cost)h(on)g(the)h(relativ)n(e)e(p)r (erformance)g(of)i(the)f(t)n(w)n(o)g(strategies.)38 b(Not)28 b(surprisingly)-7 b(,)450 1171 y(w)n(e)23 b(\014nd)h(that)g(as)f(the)i (cost)e(of)g(preemptiv)n(e)h(migration)e(increases,)h(it)h(b)r(ecomes)g (less)f(e\013ectiv)n(e.)450 1271 y(Nev)n(ertheless,)e(preemptiv)n(e)f (migration)f(p)r(erforms)g(b)r(etter)i(than)g(non-preemptiv)n(e)e (migration)450 1370 y(ev)n(en)30 b(with)i(surprisingly)d(large)h (migration)g(costs,)h(despite)g(sev)n(eral)e(conserv)-5 b(ativ)n(e)30 b(assump-)450 1470 y(tions)d(that)h(giv)n(e)f (non-preemptiv)n(e)g(migration)f(an)h(unfair)h(adv)-5 b(an)n(tage.)533 1573 y(Next)37 b(w)n(e)e(c)n(ho)r(ose)g(a)h(sp)r (eci\014c)g(mo)r(del)h(of)f(preemptiv)n(e)g(and)g(non-preemptiv)n(e)f (migration)450 1673 y(costs)25 b(based)g(on)g(real)f(systems)h(\(see)g (Section)h(4\),)g(and)f(use)g(this)h(mo)r(del)f(to)h(compare)e(the)i(t) n(w)n(o)450 1773 y(migration)35 b(strategies)h(in)g(more)g(detail.)64 b(W)-7 b(e)37 b(\014nd)g(that)g(preemptiv)n(e)f(migration)g(reduces)450 1872 y(the)25 b(mean)f(dela)n(y)g(\(queueing)g(and)g(migration\))g(b)n (y)g(35{50\045,)f(compared)h(to)g(non-preemptiv)n(e)450 1972 y(migration.)39 b(W)-7 b(e)29 b(also)f(prop)r(ose)f(sev)n(eral)g (alternativ)n(e)h(metrics)g(in)n(tended)h(to)g(measure)f(users')450 2072 y(p)r(erception)39 b(of)f(system)h(p)r(erformance.)69 b(By)38 b(these)h(metrics,)i(the)e(additional)g(b)r(ene\014ts)g(of)450 2171 y(preemptiv)n(e)f(migration)g(compared)f(to)i(non-preemptiv)n(e)e (migration)h(app)r(ear)g(ev)n(en)g(more)450 2271 y(signi\014can)n(t.) 533 2374 y(In)31 b(Section)f(5.4)g(w)n(e)g(discuss)g(in)h(detail)g(wh)n (y)f(a)g(simple)h(preemptiv)n(e)f(migration)g(p)r(olicy)g(is)450 2474 y(more)36 b(e\013ectiv)n(e)h(than)h(ev)n(en)e(a)h(w)n(ell-tuned)g (non-preemptiv)n(e)f(migration)g(p)r(olicy)-7 b(.)66 b(In)37 b(Sec-)450 2574 y(tion)31 b(5.5)e(w)n(e)i(use)f(the)h(sim)n (ulator)f(to)g(compare)g(our)f(preemptiv)n(e)i(migration)e(strategy)g (with)450 2673 y(previously)d(prop)r(osed)h(preemptiv)n(e)g (strategies.)533 2777 y(W)-7 b(e)28 b(\014nish)g(with)g(a)g(criticism)f (of)h(our)f(mo)r(del)g(in)h(Section)g(6,)f(a)h(discussion)f(of)g (future)h(w)n(ork)450 2877 y(in)g(Section)f(7)h(and)f(conclusions)g(in) g(Section)h(8.)450 3127 y Fx(1.4)41 b(Related)26 b(w)n(o)n(rk)533 3264 y Ft(1.4.1)41 b Fo(Systems.)h Ft(Although)29 b(sev)n(eral)e (systems)h(ha)n(v)n(e)g(the)h(mec)n(hanism)f(to)h(migrate)f(activ)n(e) 450 3363 y(jobs,)38 b(few)f(ha)n(v)n(e)e(implemen)n(ted)i(implicit)g (load)e(balancing)h Fo(p)l(olicies)p Ft(.)65 b(Most)36 b(systems)f(only)450 3463 y(allo)n(w)22 b(for)g Fo(explicit)i Ft(load)e(balancing.)34 b(That)23 b(is,)h(there)f(is)f(no)h(load)f (balancing)g(p)r(olicy;)i(the)g(user)450 3562 y(decides)35 b(whic)n(h)h(pro)r(cesses)e(to)h(migrate,)i(and)e(when.)61 b(Examples)34 b(include)i(Accen)n(t)g([Za)n(y)n(as)450 3662 y(1987],)41 b(Lo)r(cus)e([Thiel)h(1991],)h(Utopia)e([Zhou)h(et)f (al.)h(1993],)h(DEMOS/MP)d([P)n(o)n(w)n(ell)g(and)450 3762 y(Miller)29 b(1983],)e(V)j([Theimer)e(et)i(al.)e(1985],)g(NEST)h ([Agra)n(w)n(al)e(and)i(Ezzet)f(1987],)g(RHODOS)450 3861 y([De)g(P)n(aoli)e(and)i(Goscinski)e(1995],)g(and)i(MIST)f([Casas)g(et) g(al.)h(1995].)533 3965 y(A)20 b(few)g(systems)f(ha)n(v)n(e)f Fo(implicit)k Ft(load)d(balancing)f(p)r(olicies,)j(ho)n(w)n(ev)n(er)d (they)h(are)g(strictly)g(non-)450 4065 y(preemptiv)n(e)i(p)r(olicies)g (\(activ)n(e)f(pro)r(cesses)g(are)g(only)h(migrated)f(for)h(purp)r (oses)f(other)g(than)i(load)450 4164 y(balancing,)31 b(suc)n(h)g(as)f(preserving)f(w)n(orkstation)g(autonom)n(y\).)47 b(Examples)30 b(include)h(Amo)r(eba)450 4264 y([T)-7 b(anen)n(baum)34 b(et)h(al.)f(1990],)g(Charlotte)g([Artsy)g(and)h(Fink) n(el)f(1989],)g(Sprite)h([Douglis)f(and)450 4364 y(Ousterhout)k(1991],) i(Condor)d([Litzk)n(o)n(w)h(et)h(al.)f(1988],)i(and)f(Mac)n(h)f([Milo)5 b(jicic)38 b(1993].)69 b(In)450 4463 y(general,)41 b(non-preemptiv)n(e) e(load)g(balancing)g(p)r(olicies)g(dep)r(end)h(on)g Fo(a)h(priori)h Ft(information)450 4563 y(ab)r(out)31 b(pro)r(cesses;)h(e.g.,)g (explicit)f(kno)n(wledge)f(ab)r(out)i(the)f(run)n(times)g(of)h(pro)r (cesses)d(or)i(user-)450 4662 y(pro)n(vided)22 b(lists)h(of)g (migratable)f(pro)r(cesses)f([Agra)n(w)n(al)g(and)i(Ezzet)f(1987])g ([Litzk)n(o)n(w)g(and)g(Livn)n(y)450 4762 y(1990])k([Douglis)h(and)g (Ousterhout)g(1991])f([Zhou)h(et)h(al.)f(1993].)533 4866 y(One)j(existing)g(system)g(that)g(has)g(implemen)n(ted)h(implemen)n (ted)g(automated)e(preemptiv)n(e)450 4965 y(load)21 b(balancing)g(is)h (MOSIX)g([Barak)e(et)i(al.)g(1993].)33 b(Our)21 b(results)g(supp)r(ort) h(the)g(MOSIX)g(claim)450 5065 y(that)28 b(their)f(sc)n(heme)h(is)f (e\013ectiv)n(e)h(and)f(robust.)p eop %%Page: 5 5 5 4 bop 821 250 a Fq(Exploiting)24 b(Pro)r(cess)k(Lifetime)c (Distributions)f(fo)n(r)k(Dynamic)d(Load)i(Balancing)156 b Fp(\001)141 b Fq(5)533 465 y Ft(1.4.2)41 b Fo(Studies.)h Ft(Although)32 b(few)g(systems)f(incorp)r(orate)f(migration)h(p)r (olicies,)h(there)g(ha)n(v)n(e)450 565 y(b)r(een)i(man)n(y)g(sim)n (ulation)f(and)h(analytical)f(studies)h(of)g(v)-5 b(arious)33 b(migration)g(p)r(olicies.)56 b(Most)450 665 y(of)35 b(these)h(studies)f(ha)n(v)n(e)f(fo)r(cused)i(on)f(load)g(balancing)f (b)n(y)h(remote)g(execution)g([Livn)n(y)g(and)450 764 y(Melman)24 b(1982])e([W)-7 b(ang)23 b(and)h(Morris)e(1985])g([Casa)n (v)-5 b(an)n(t)22 b(and)h(Kuhl)h(1987])e([Zhou)h(1987])f([Pul-)450 864 y(idas)i(et)g(al.)g(1988])e([Kunz)i(1991])e([Bonomi)h(and)h(Kumar)f (1990])g([Ev)-5 b(ans)23 b(and)h(Butt)g(1993])f([Lin)450 964 y(and)31 b(Ragha)n(v)n(endra)d(1993])h([Mirc)n(handaney)h(et)h(al.) f(1990])f([Zhang)i(et)g(al.)f(1995])f([Zhou)i(and)450 1063 y(F)-7 b(errari)26 b(1987])g([Ha)n(\023)-39 b(c)26 b(and)i(Jin)f(1990])f([Eager)g(et)h(al.)h(1986].)533 1167 y(Only)g(a)f(few)h(studies)g(address)f(preemptiv)n(e)g(migration)g (p)r(olicies)g([Leland)h(and)g(Ott)g(1986])450 1267 y([Krueger)d(and)i (Livn)n(y)g(1988].)35 b(The)27 b(Leland)f(and)h(Ott)h(migration)d(p)r (olicy)i(is)g(also)f(age)g(based,)450 1366 y(but)i(do)r(esn't)g(tak)n (e)f(migration)f(cost)h(in)n(to)h(accoun)n(t.)533 1470 y(Eager)20 b(et.)35 b(al.,[Eager)19 b(et)j(al.)f(1988],)g(conclude)h (that)f(the)h(additional)g(p)r(erformance)e(b)r(ene\014t)450 1570 y(of)27 b(preemptiv)n(e)g(migration)g(is)g(to)r(o)g(small)g (compared)f(with)i(the)g(b)r(ene\014t)g(of)g(non-preemptiv)n(e)450 1669 y(migration)h(to)h(mak)n(e)f(preemptiv)n(e)h(migration)f(w)n(orth) n(while.)43 b(This)30 b(result)g(has)f(b)r(een)i(widely)450 1769 y(cited,)25 b(and)g(in)g(sev)n(eral)d(cases)i(used)g(to)g(justify) i(the)e(decision)g(not)h(to)f(implemen)n(t)h(preemptiv)n(e)450 1869 y(migration,)42 b(as)c(in)i(the)g(Utopia)g(system,)i([Zhou)d(et)h (al.)g(1993].)71 b(Our)39 b(w)n(ork)f(di\013ers)h(from)450 1968 y([Eager)30 b(et)i(al.)g(1988])e(in)j(b)r(oth)f(system)g(mo)r(del) g(and)g(w)n(orkload)e(description.)50 b([Eager)30 b(et)i(al.)450 2068 y(1988])27 b(mo)r(del)i(a)f(serv)n(er)f(farm)i(in)g(whic)n(h)f (incoming)h(jobs)f(ha)n(v)n(e)g(no)g(a\016nit)n(y)h(for)f(a)g (particular)450 2167 y(pro)r(cessor,)c(and)i(th)n(us)g(the)h(cost)f(of) g(initial)g(placemen)n(t)g(\(remote)g(execution\))g(is)g(free.)36 b(This)26 b(is)450 2267 y(di\013eren)n(t)h(from)f(our)g(mo)r(del,)h(a)f (net)n(w)n(ork)f(of)h(w)n(orkstations,)f(in)i(whic)n(h)f(incoming)g (jobs)h(arriv)n(e)450 2367 y(at)h(a)g(particular)f(host)h(and)g(the)h (cost)f(of)g(mo)n(ving)f(them)i(a)n(w)n(a)n(y)-7 b(,)27 b(ev)n(en)g(b)n(y)h(remote)g(execution,)450 2466 y(is)33 b(signi\014can)n(t)g(compared)g(to)g(most)h(pro)r(cess)e(lifetimes.)55 b(Also,)35 b([Eager)d(et)i(al.)f(1988])f(use)h(a)450 2566 y(degenerate)g(h)n(yp)r(erexp)r(onen)n(tial)h(distribution)g(of)h (lifetimes)g(that)g(includes)f(few)h(jobs)f(with)450 2666 y(non-zero)e(lifetimes.)55 b(When)34 b(the)g(co)r(e\016cien)n(t)g (of)f(v)-5 b(ariation)32 b(of)i(this)g(distribution)f(matc)n(hes)450 2765 y(the)28 b(distributions)f(w)n(e)g(observ)n(ed,)f(few)n(er)h(than) h(4\045)f(of)g(the)h(sim)n(ulated)f(pro)r(cesses)f(ha)n(v)n(e)g(non-) 450 2865 y(zero)31 b(lifetimes.)50 b(With)33 b(so)e(few)h(jobs)g(\(and) g(balanced)f(initial)h(placemen)n(t\))g(there)g(is)f(seldom)450 2964 y(an)n(y)25 b(load)g(im)n(balance)g(in)h(the)g(system,)f(and)h(th) n(us)g(little)g(b)r(ene\014t)h(for)e(preemptiv)n(e)g(migration.)450 3064 y(F)-7 b(urthermore,)25 b(the)i([Eager)d(et)j(al.)f(1988])e(pro)r (cess)h(lifetime)i(distribution)g(is)f(exp)r(onen)n(tial)f(for)450 3164 y(jobs)31 b(with)g(non-zero)f(lifetimes,)j(the)e(consequences)f (of)h(whic)n(h)g(w)n(e)g(discuss)f(in)i(Section)f(2.2.)450 3263 y(F)-7 b(or)26 b(a)g(more)g(detailed)g(explanation)g(of)g(this)h (distribution)f(and)h(its)f(e\013ect)h(on)f(the)h(study)-7 b(,)27 b(see)450 3363 y([Do)n(wney)g(and)h(Harc)n(hol-Balter)d(1995].) 533 3467 y(Krueger)e(and)h(Livn)n(y)g(in)n(v)n(estigate)f(the)i(b)r (ene\014ts)g(of)f(supplemen)n(ting)g(non-preemptiv)n(e)g(mi-)450 3566 y(gration)33 b(with)i(preemptiv)n(e)f(migration)g(and)g(\014nd)h (that)g(preemptiv)n(e)f(migration)g(is)g(w)n(orth-)450 3666 y(while.)i(They)26 b(use)f(a)g(h)n(yp)r(erexp)r(onen)n(tial)f (lifetime)i(distribution)g(that)f(appro)n(ximates)f(closely)450 3766 y(the)31 b(distribution)g(w)n(e)f(observ)n(ed;)h(as)f(a)g(result,) h(their)g(\014ndings)f(are)g(largely)f(in)i(accord)e(with)450 3865 y(ours.)61 b(One)36 b(di\013erence)g(b)r(et)n(w)n(een)g(their)g(w) n(ork)f(and)h(ours)f(is)h(that)h(they)f(used)g(a)g(syn)n(thetic)450 3965 y(w)n(orkload)26 b(with)i(P)n(oisson)d(arriv)-5 b(als.)36 b(The)28 b(w)n(orkload)d(w)n(e)j(observ)n(ed,)e(and)h(used)h (in)g(our)f(trace-)450 4064 y(driv)n(en)g(sim)n(ulations,)f(exhibits)i (serial)e(correlation;)f(i.e.)37 b(it)28 b(is)f(more)f(burst)n(y)h (than)g(a)g(P)n(oisson)450 4164 y(pro)r(cess.)59 b(Another)35 b(di\013erence)g(is)g(that)h(their)f(migration)g(p)r(olicy)g(requires)f (sev)n(eral)f(hand-)450 4264 y(tuned)d(parameters.)40 b(In)29 b(Section)h(3.1)e(w)n(e)h(sho)n(w)f(ho)n(w)h(to)g(use)g(the)h (distribution)f(of)g(lifetimes)450 4363 y(to)e(eliminate)h(these)g (parameters.)533 4467 y(Lik)n(e)k(us,)j(Bry)n(an)n(t)c(and)i(Fink)n(el) g(discuss)f(the)i(distribution)f(of)g(pro)r(cess)e(lifetimes)j(and)f (its)450 4567 y(e\013ect)c(on)g(preemptiv)n(e)g(migration)f(p)r(olicy) -7 b(,)29 b(but)g(their)g(h)n(yp)r(othetical)g(distributions)g(are)f (not)450 4666 y(based)d(on)f(system)h(measuremen)n(ts)f([Bry)n(an)n(t)g (and)h(Fink)n(el)g(1981].)35 b(Also)24 b(lik)n(e)h(us,)h(they)f(c)n(ho) r(ose)450 4766 y(migran)n(t)20 b(pro)r(cesses)f(on)i(the)h(basis)e(of)h (exp)r(ected)g(slo)n(wdo)n(wn)f(on)g(the)i(source)d(and)i(target)f (hosts,)450 4866 y(but)30 b(their)g(estimation)f(of)h(those)f(slo)n (wdo)n(wns)f(is)h(v)n(ery)g(di\013eren)n(t)g(from)h(ours.)41 b(In)30 b(particular,)450 4965 y(they)k(use)g(the)g(distribution)h(of)f (pro)r(cess)e(lifetimes)j(to)f(predict)g(a)g(host's)f(future)i(load)e (as)g(a)450 5065 y(function)e(of)f(its)g(curren)n(t)g(load)f(and)i(the) f(ages)f(of)h(the)h(pro)r(cesses)e(running)h(there.)44 b(W)-7 b(e)31 b(ha)n(v)n(e)p eop %%Page: 6 6 6 5 bop 450 250 a Fq(6)142 b Fp(\001)157 b Fq(M.)27 b(Ha)n (rchol-Balter)d(and)h(A.)h(B.)g(Do)n(wney)450 465 y Ft(examined)39 b(this)g(issue)g(and)g(found)h(\(1\))f(that)h(this)f(mo)r(del)h(fails)f (to)g(predict)g(future)h(loads)450 565 y(b)r(ecause)26 b(it)h(ignores)d(future)j(arriv)-5 b(als,)25 b(and)h(\(2\))g(that)h (curren)n(t)e(load)h(is)g(the)h(b)r(est)g(predictor)e(of)450 665 y(future)k(load)e(\(see)h(Section)h(3.1\).)38 b(Th)n(us,)28 b(in)h(our)e(estimates)h(of)g(slo)n(wdo)n(wn,)f(w)n(e)h(assume)g(that) 450 764 y(the)g(future)g(load)f(on)g(a)g(host)h(is)f(equal)g(to)h(the)g (curren)n(t)e(load.)450 943 y Fx(2.)69 b(DISTRIBUTION)27 b(OF)h(LIFETIMES)450 1075 y Ft(The)i(general)e(shap)r(e)i(of)g(the)g (distribution)g(of)g(pro)r(cess)e(lifetimes)j(in)f(an)f(academic)g(en)n (viron-)450 1175 y(men)n(t)f(has)g(b)r(een)g(kno)n(wn)f(for)h(a)f(long) g(time)i([Rosin)e(1965]:)36 b(there)28 b(are)f(man)n(y)g(short)g(jobs)h (and)450 1275 y(a)37 b(few)h(long)f(jobs,)j(and)d(the)h(v)-5 b(ariance)37 b(of)g(the)h(distribution)g(is)f(greater)f(than)i(that)g (of)f(an)450 1374 y(exp)r(onen)n(tial)27 b(distribution.)533 1474 y(In)35 b(1986,)f(Cabrera)e(measured)h(UNIX)j(pro)r(cesses)c(and)j (found)f(that)h(o)n(v)n(er)d(40\045)i(doubled)450 1574 y(their)39 b(curren)n(t)e(age)h([Cabrera)f(1986].)68 b(That)39 b(same)f(y)n(ear,)i(Leland)e(and)h(Ott)g(prop)r(osed)e(a)450 1673 y(functional)25 b(form)g(for)g(the)h(pro)r(cess)e(lifetime)i (distribution,)g(based)f(on)g(measuremen)n(ts)f(of)h(the)450 1773 y(lifetimes)36 b(of)f(9.5)g(million)h(UNIX)g(pro)r(cesses)e(b)r (et)n(w)n(een)h(1984)f(and)h(1985)e([Leland)i(and)h(Ott)450 1872 y(1986].)41 b(They)30 b(conclude)f(that)h(pro)r(cess)f(lifetimes)h (ha)n(v)n(e)f(a)g(UBNE)h(\(used-b)r(etter-than-new-)450 1972 y(in-exp)r(ectation\))h(t)n(yp)r(e)h(of)f(distribution.)49 b(That)31 b(is,)h(the)g(greater)e(the)i(curren)n(t)e(CPU)h(age)g(of)450 2072 y(a)e(pro)r(cess,)f(the)i(greater)d(its)j(exp)r(ected)f(remaining) g(CPU)g(lifetime.)42 b(Sp)r(eci\014cally)-7 b(,)30 b(they)f(\014nd)450 2171 y(that)f(for)g Fm(T)35 b(>)23 b Ft(3)28 b(seconds,)f(the)i (probabilit)n(y)e(of)h(a)f(pro)r(cess's)g(lifetime)i(exceeding)f Fm(T)39 b Ft(seconds)450 2271 y(is)27 b Fm(r)r(T)633 2241 y Fk(k)674 2271 y Ft(,)h(where)f Fl(\000)p Ft(1)p Fm(:)p Ft(25)21 b Fm(<)i(k)j(<)c Fl(\000)p Ft(1)p Fm(:)p Ft(05)k(and)i Fm(r)i Ft(normalizes)c(the)i(distribution.)533 2371 y(In)38 b(con)n(trast,)g(Rommel)g([Rommel)f(1991])f(claims)h(that) g(his)h(measuremen)n(ts)e(sho)n(w)h(that)450 2470 y(\\long)27 b(pro)r(cesses)g(ha)n(v)n(e)h(exp)r(onen)n(tial)g(service)f(times.")40 b(Man)n(y)28 b(subsequen)n(t)g(studies)h(assume)450 2570 y(an)e(exp)r(onen)n(tial)g(lifetime)i(distribution.)533 2669 y(Because)c(of)h(the)h(imp)r(ortance)f(of)g(the)g(pro)r(cess)f (lifetime)i(distribution)g(for)e(load)h(balancing)450 2769 y(p)r(olicies,)c(w)n(e)e(p)r(erformed)g(an)g(indep)r(enden)n(t)h (study)g(of)f(this)h(distribution,)h(and)e(found)h(that)f(the)450 2869 y(functional)j(form)f(prop)r(osed)g(b)n(y)g(Leland)h(and)f(Ott)h (\014ts)g(the)g(observ)n(ed)e(distributions)i(w)n(ell,)g(for)450 2968 y(pro)r(cesses)30 b(with)i(lifetimes)f(greater)f(than)h(1)g (second.)48 b(This)31 b(functional)g(form)g(is)g(consisten)n(t)450 3068 y(across)26 b(a)h(v)-5 b(ariet)n(y)27 b(of)g(mac)n(hines)g(and)h (w)n(orkloads,)d(and)j(although)f(the)h(parameter,)e Fm(k)s Ft(,)i(v)-5 b(aries)450 3168 y(from)27 b(-1.3)g(to)g(-.8,)g(it)h (is)g(generally)e(near)g(-1.)37 b(Th)n(us,)27 b(as)g(a)g Fo(rule)j(of)g(thumb)p Ft(,)450 3313 y(|The)c(probabilit)n(y)f(that)h (a)f(pro)r(cess)g(with)h(age)f(1)g(second)g(uses)h(at)f(least)h Fm(T)36 b Ft(seconds)25 b(of)h(total)533 3412 y(CPU)h(time)i(is)e(ab)r (out)h(1)p Fm(=T)12 b Ft(.)450 3527 y(|The)35 b(probabilit)n(y)f(that)h (a)g(pro)r(cess)e(with)j(age)e Fm(T)46 b Ft(seconds)34 b(uses)g(at)h(least)g(an)f(additional)533 3627 y Fm(T)41 b Ft(seconds)29 b(of)g(CPU)h(time)g(is)f(ab)r(out)h(1)p Fm(=)p Ft(2.)42 b(Th)n(us,)30 b(the)g(median)f(remaining)g(lifetime)i (of)e(a)533 3727 y(pro)r(cess)d(is)i(equal)f(to)g(its)h(curren)n(t)f (age.)533 3872 y(Section)j(2.1)e(describ)r(es)h(our)g(measuremen)n(ts)g (and)g(the)h(distribution)g(of)f(lifetimes)h(w)n(e)f(ob-)450 3971 y(serv)n(ed.)65 b(Section)37 b(2.2)g(discusses)f(other)h(mo)r (dels)g(for)g(the)h(distribution)f(of)h(lifetimes,)i(and)450 4071 y(argues)23 b(that)h(the)h(particular)e(shap)r(e)h(of)g(this)g (distribution)g(is)h(critical)e(for)h(ev)-5 b(aluating)23 b(migra-)450 4170 y(tion)28 b(p)r(olicies.)450 4334 y Fx(2.1)41 b(Lifetime)27 b(distribution)f(when)i(lifetime)f Fm(>)22 b Ft(1)p Fm(s)450 4467 y Ft(T)-7 b(o)36 b(determine)g(the)h (distribution)f(of)g(lifetimes)h(for)f(UNIX)h(pro)r(cesses,)g(w)n(e)f (measured)f(the)450 4567 y(lifetimes)28 b(of)g(o)n(v)n(er)d(one)i (million)h(pro)r(cesses,)e(generated)h(from)g(a)g(v)-5 b(ariet)n(y)26 b(of)i(academic)f(w)n(ork-)450 4666 y(loads,)i (including)g(instructional)g(mac)n(hines,)g(researc)n(h)e(mac)n(hines,) i(and)h(mac)n(hines)e(used)h(for)450 4766 y(system)22 b(administration.)34 b(W)-7 b(e)22 b(obtained)g(our)f(data)g(using)h (the)g(UNIX)h(command)e Fj(lastcomm)p Ft(,)450 4866 y(whic)n(h)28 b(outputs)f(the)h(CPU)g(time)g(used)f(b)n(y)h(eac)n(h)f(completed)g (pro)r(cess.)533 4965 y(Figure)i(1)g(sho)n(ws)f(the)i(distribution)f (of)g(lifetimes)h(from)f(one)g(of)g(the)h(mac)n(hines.)41 b(The)30 b(plot)450 5065 y(sho)n(ws)g(only)i(pro)r(cesses)e(whose)g (lifetimes)j(exceed)e(one)g(second.)48 b(The)32 b(dotted)g(\(hea)n (vy\))f(line)p eop %%Page: 7 7 7 6 bop 821 250 a Fq(Exploiting)24 b(Pro)r(cess)k(Lifetime)c (Distributions)f(fo)n(r)k(Dynamic)d(Load)i(Balancing)156 b Fp(\001)141 b Fq(7)1194 956 y 11840716 11840716 13024788 18945146 27299430 33219788 startTexFig 1194 956 a %%BeginDocument: har1a.ps 50 dict begin % This is a standard prolog for Postscript generated by Tk's canvas % widget. % @(#) prolog.ps 1.2 94/12/09 10:53:18 % The definitions below just define all of the variables used in % any of the procedures here. This is needed for obscure reasons % explained on p. 716 of the Postscript manual (Section H.2.7, % "Initializing Variables," in the section on Encapsulated Postscript). /baseline 0 def /stipimage 0 def /height 0 def /justify 0 def /lineLength 0 def /spacing 0 def /stipple 0 def /strings 0 def /xoffset 0 def /yoffset 0 def /tmpstip null def % Define the array ISOLatin1Encoding (which specifies how characters are % encoded for ISO-8859-1 fonts), if it isn't already present (Postscript % level 2 is supposed to define it, but level 1 doesn't). systemdict /ISOLatin1Encoding known not { /ISOLatin1Encoding [ /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /minus /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /less /equal /greater /question /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /braceleft /bar /braceright /asciitilde /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent /dieresis /space /ring /cedilla /space /hungarumlaut /ogonek /caron /space /exclamdown /cent /sterling /currency /yen /brokenbar /section /dieresis /copyright /ordfeminine /guillemotleft /logicalnot /hyphen /registered /macron /degree /plusminus /twosuperior /threesuperior /acute /mu /paragraph /periodcentered /cedillar /onesuperior /ordmasculine /guillemotright /onequarter /onehalf /threequarters /questiondown /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla /Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis /Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply /Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls /agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla /egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis /eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide /oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis ] def } if % Override the setfont procedure with a new procedure that re-encodes % the font to use the ISO Latin-1 style. The body of this procedure % comes from Section 5.6.1 of the Postscript book. /realsetfont /setfont load def /setfont { dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end % I'm not sure why it's necessary to use "definefont" on this new % font, but it seems to be important; just use the name "Temporary" % for the font. /Temporary exch definefont realsetfont } bind def % StrokeClip % % This procedure converts the current path into a clip area under % the assumption of stroking. It's a bit tricky because some Postscript % interpreters get errors during strokepath for dashed lines. If % this happens then turn off dashes and try again. /StrokeClip { {strokepath} stopped { (This Postscript printer gets limitcheck overflows when) = (stippling dashed lines; lines will be printed solid instead.) = [] 0 setdash strokepath} if clip } bind def % desiredSize EvenPixels closestSize % % The procedure below is used for stippling. Given the optimal size % of a dot in a stipple pattern in the current user coordinate system, % compute the closest size that is an exact multiple of the device's % pixel size. This allows stipple patterns to be displayed without % aliasing effects. /EvenPixels { % Compute exact number of device pixels per stipple dot. dup 0 matrix currentmatrix dtransform dup mul exch dup mul add sqrt % Round to an integer, make sure the number is at least 1, and compute % user coord distance corresponding to this. dup round dup 1 lt {pop 1} if exch div mul } bind def % width height string StippleFill -- % % Given a path already set up and a clipping region generated from % it, this procedure will fill the clipping region with a stipple % pattern. "String" contains a proper image description of the % stipple pattern and "width" and "height" give its dimensions. Each % stipple dot is assumed to be about one unit across in the current % user coordinate system. This procedure trashes the graphics state. /StippleFill { % The following code is needed to work around a NeWSprint bug. /tmpstip 1 index def % Change the scaling so that one user unit in user coordinates % corresponds to the size of one stipple dot. 1 EvenPixels dup scale % Compute the bounding box occupied by the path (which is now % the clipping region), and round the lower coordinates down % to the nearest starting point for the stipple pattern. Be % careful about negative numbers, since the rounding works % differently on them. pathbbox 4 2 roll 5 index div dup 0 lt {1 sub} if cvi 5 index mul 4 1 roll 6 index div dup 0 lt {1 sub} if cvi 6 index mul 3 2 roll % Stack now: width height string y1 y2 x1 x2 % Below is a doubly-nested for loop to iterate across this area % in units of the stipple pattern size, going up columns then % across rows, blasting out a stipple-pattern-sized rectangle at % each position 6 index exch { 2 index 5 index 3 index { % Stack now: width height string y1 y2 x y gsave 1 index exch translate 5 index 5 index true matrix tmpstip imagemask grestore } for pop } for pop pop pop pop pop } bind def % -- AdjustColor -- % Given a color value already set for output by the caller, adjusts % that value to a grayscale or mono value if requested by the CL % variable. /AdjustColor { CL 2 lt { currentgray CL 0 eq { .5 lt {0} {1} ifelse } if setgray } if } bind def % x y strings lineLength spacing xoffset yoffset justify stipple DrawText -- % This procedure does all of the real work of drawing text. The % color and font must already have been set by the caller, and the % following arguments must be on the stack: % % x, y - Coordinates at which to draw text. % strings - An array of strings, one for each line of the text item, % in order from top to bottom. % lineLength - Minimum line length: needed to justify text properly. % spacing - Spacing between lines. % xoffset - Horizontal offset for text bbox relative to x and y: 0 for % nw/w/sw anchor, -0.5 for n/center/s, and -1.0 for ne/e/se. % yoffset - Vertical offset for text bbox relative to x and y: 0 for % nw/n/ne anchor, +0.5 for w/center/e, and +1.0 for sw/s/se. % justify - 0 for left justification, 0.5 for center, 1 for right justify. % stipple - Boolean value indicating whether or not text is to be % drawn in stippled fashion. If text is stippled, % procedure StippleText must have been defined to call % StippleFill in the right way. % % Also, when this procedure is invoked, the color and font must already % have been set for the text. /DrawText { /stipple exch def /justify exch def /yoffset exch def /xoffset exch def /spacing exch def /lineLength exch def /strings exch def % First scan through all of the text to find the widest line (if it's % longer than the "lineLength" argument). strings { stringwidth pop dup lineLength gt {/lineLength exch def} {pop} ifelse newpath } forall % Compute the baseline offset and the actual font height. 0 0 moveto (TXygqPZ) false charpath pathbbox dup /baseline exch def exch pop exch sub /height exch def pop newpath % Translate coordinates first so that the origin is at the upper-left % corner of the text's bounding box. Remember that x and y for % positioning are still on the stack. translate lineLength xoffset mul strings length 1 sub spacing mul height add yoffset mul translate % Now use the baseline and justification information to translate so % that the origin is at the baseline and positioning point for the % first line of text. justify lineLength mul baseline neg translate % Iterate over each of the lines to output it. For each line, % compute its width again so it can be properly justified, then % display it. strings { dup stringwidth pop justify neg mul 0 moveto stipple { % The text is stippled, so turn it into a path and print % by calling StippledText, which in turn calls StippleFill. % Unfortunately, many Postscript interpreters will get % overflow errors if we try to do the whole string at % once, so do it a character at a time. gsave /char (X) def { char 0 3 -1 roll put currentpoint gsave char true charpath clip StippleText grestore char stringwidth translate moveto } forall grestore } {show} ifelse 0 spacing neg translate } forall } bind def /CL 2 def save 306.0 396.0 translate 0.426 0.426 scale -253 -253 translate 0 507 moveto 507 507 lineto 507 0 lineto 0 0 lineto closepath clip newpath gsave 80 447 moveto 400 0 rlineto 0 -380 rlineto -400 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 280 487 [ (Distribution of process lifetimes) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 280 464 [ (\050fraction of processes with duration > T\051) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 495 12 [ (Duration \050T secs.\051) ] 0 20 -1 1 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 65 67 [ (0.0) ] 0 20 -1 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 65 143 [ (0.2) ] 0 20 -1 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 65 219 [ (0.4) ] 0 20 -1 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 65 295 [ (0.6) ] 0 20 -1 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 65 371 [ (0.8) ] 0 20 -1 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 65 447 [ (1.0) ] 0 20 -1 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 80 46.9999999999999 [ (1) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 140 46.9999999999999 [ (2) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 200.87 46.9999999999999 [ (4) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 260.87 46.9999999999999 [ (8) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 320.87 46.9999999999999 [ (16) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 381.739 46.9999999999999 [ (32) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 441.739 46.9999999999999 [ (64) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave matrix currentmatrix 80.5 442.662 translate 0.499999999999993 0.499999999999972 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 82.2217 437.988 translate 0.500000000000007 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 83.0704 431.756 translate 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70.639 lineto 476.783 70.629 lineto 1 setlinewidth 0 setlinecap 1 setlinejoin 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore restore showpage end %%EndDocument endTexFig 1194 2464 a 11840716 11840716 13024788 18945146 27299430 33219788 startTexFig 1194 2464 a %%BeginDocument: har1b.ps 50 dict begin % This is a standard prolog for Postscript generated by Tk's canvas % widget. % @(#) prolog.ps 1.2 94/12/09 10:53:18 % The definitions below just define all of the variables used in % any of the procedures here. This is needed for obscure reasons % explained on p. 716 of the Postscript manual (Section H.2.7, % "Initializing Variables," in the section on Encapsulated Postscript). /baseline 0 def /stipimage 0 def /height 0 def /justify 0 def /lineLength 0 def /spacing 0 def /stipple 0 def /strings 0 def /xoffset 0 def /yoffset 0 def /tmpstip null def % Define the array ISOLatin1Encoding (which specifies how characters are % encoded for ISO-8859-1 fonts), if it isn't already present (Postscript % level 2 is supposed to define it, but level 1 doesn't). systemdict /ISOLatin1Encoding known not { /ISOLatin1Encoding [ /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /minus /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /less /equal /greater /question /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /braceleft /bar /braceright /asciitilde /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent /dieresis /space /ring /cedilla /space /hungarumlaut /ogonek /caron /space /exclamdown /cent /sterling /currency /yen /brokenbar /section /dieresis /copyright /ordfeminine /guillemotleft /logicalnot /hyphen /registered /macron /degree /plusminus /twosuperior /threesuperior /acute /mu /paragraph /periodcentered /cedillar /onesuperior /ordmasculine /guillemotright /onequarter /onehalf /threequarters /questiondown /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla /Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis /Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply /Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls /agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla /egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis /eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide /oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis ] def } if % Override the setfont procedure with a new procedure that re-encodes % the font to use the ISO Latin-1 style. The body of this procedure % comes from Section 5.6.1 of the Postscript book. /realsetfont /setfont load def /setfont { dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end % I'm not sure why it's necessary to use "definefont" on this new % font, but it seems to be important; just use the name "Temporary" % for the font. /Temporary exch definefont realsetfont } bind def % StrokeClip % % This procedure converts the current path into a clip area under % the assumption of stroking. It's a bit tricky because some Postscript % interpreters get errors during strokepath for dashed lines. If % this happens then turn off dashes and try again. /StrokeClip { {strokepath} stopped { (This Postscript printer gets limitcheck overflows when) = (stippling dashed lines; lines will be printed solid instead.) = [] 0 setdash strokepath} if clip } bind def % desiredSize EvenPixels closestSize % % The procedure below is used for stippling. Given the optimal size % of a dot in a stipple pattern in the current user coordinate system, % compute the closest size that is an exact multiple of the device's % pixel size. This allows stipple patterns to be displayed without % aliasing effects. /EvenPixels { % Compute exact number of device pixels per stipple dot. dup 0 matrix currentmatrix dtransform dup mul exch dup mul add sqrt % Round to an integer, make sure the number is at least 1, and compute % user coord distance corresponding to this. dup round dup 1 lt {pop 1} if exch div mul } bind def % width height string StippleFill -- % % Given a path already set up and a clipping region generated from % it, this procedure will fill the clipping region with a stipple % pattern. "String" contains a proper image description of the % stipple pattern and "width" and "height" give its dimensions. Each % stipple dot is assumed to be about one unit across in the current % user coordinate system. This procedure trashes the graphics state. /StippleFill { % The following code is needed to work around a NeWSprint bug. /tmpstip 1 index def % Change the scaling so that one user unit in user coordinates % corresponds to the size of one stipple dot. 1 EvenPixels dup scale % Compute the bounding box occupied by the path (which is now % the clipping region), and round the lower coordinates down % to the nearest starting point for the stipple pattern. Be % careful about negative numbers, since the rounding works % differently on them. pathbbox 4 2 roll 5 index div dup 0 lt {1 sub} if cvi 5 index mul 4 1 roll 6 index div dup 0 lt {1 sub} if cvi 6 index mul 3 2 roll % Stack now: width height string y1 y2 x1 x2 % Below is a doubly-nested for loop to iterate across this area % in units of the stipple pattern size, going up columns then % across rows, blasting out a stipple-pattern-sized rectangle at % each position 6 index exch { 2 index 5 index 3 index { % Stack now: width height string y1 y2 x y gsave 1 index exch translate 5 index 5 index true matrix tmpstip imagemask grestore } for pop } for pop pop pop pop pop } bind def % -- AdjustColor -- % Given a color value already set for output by the caller, adjusts % that value to a grayscale or mono value if requested by the CL % variable. /AdjustColor { CL 2 lt { currentgray CL 0 eq { .5 lt {0} {1} ifelse } if setgray } if } bind def % x y strings lineLength spacing xoffset yoffset justify stipple DrawText -- % This procedure does all of the real work of drawing text. The % color and font must already have been set by the caller, and the % following arguments must be on the stack: % % x, y - Coordinates at which to draw text. % strings - An array of strings, one for each line of the text item, % in order from top to bottom. % lineLength - Minimum line length: needed to justify text properly. % spacing - Spacing between lines. % xoffset - Horizontal offset for text bbox relative to x and y: 0 for % nw/w/sw anchor, -0.5 for n/center/s, and -1.0 for ne/e/se. % yoffset - Vertical offset for text bbox relative to x and y: 0 for % nw/n/ne anchor, +0.5 for w/center/e, and +1.0 for sw/s/se. % justify - 0 for left justification, 0.5 for center, 1 for right justify. % stipple - Boolean value indicating whether or not text is to be % drawn in stippled fashion. If text is stippled, % procedure StippleText must have been defined to call % StippleFill in the right way. % % Also, when this procedure is invoked, the color and font must already % have been set for the text. /DrawText { /stipple exch def /justify exch def /yoffset exch def /xoffset exch def /spacing exch def /lineLength exch def /strings exch def % First scan through all of the text to find the widest line (if it's % longer than the "lineLength" argument). strings { stringwidth pop dup lineLength gt {/lineLength exch def} {pop} ifelse newpath } forall % Compute the baseline offset and the actual font height. 0 0 moveto (TXygqPZ) false charpath pathbbox dup /baseline exch def exch pop exch sub /height exch def pop newpath % Translate coordinates first so that the origin is at the upper-left % corner of the text's bounding box. Remember that x and y for % positioning are still on the stack. translate lineLength xoffset mul strings length 1 sub spacing mul height add yoffset mul translate % Now use the baseline and justification information to translate so % that the origin is at the baseline and positioning point for the % first line of text. justify lineLength mul baseline neg translate % Iterate over each of the lines to output it. For each line, % compute its width again so it can be properly justified, then % display it. strings { dup stringwidth pop justify neg mul 0 moveto stipple { % The text is stippled, so turn it into a path and print % by calling StippledText, which in turn calls StippleFill. % Unfortunately, many Postscript interpreters will get % overflow errors if we try to do the whole string at % once, so do it a character at a time. gsave /char (X) def { char 0 3 -1 roll put currentpoint gsave char true charpath clip StippleText grestore char stringwidth translate moveto } forall grestore } {show} ifelse 0 spacing neg translate } forall } bind def /CL 2 def save 306.0 396.0 translate 0.426 0.426 scale -253 -253 translate 0 507 moveto 507 507 lineto 507 0 lineto 0 0 lineto closepath clip newpath gsave 80 447 moveto 400 0 rlineto 0 -380 rlineto -400 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 280 487 [ (Distribution of process lifetimes \050log plot\051) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 280 464 [ (\050fraction of processes with duration > T\051) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 495 12 [ (Duration \050T secs.\051) ] 0 20 -1 1 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 65 447 [ (1) ] 0 20 -1 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 65 390 [ (1/2) ] 0 20 -1 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 65 332.174 [ (1/4) ] 0 20 -1 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 65 275.174 [ (1/8) ] 0 20 -1 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 65 218.174 [ (1/16) ] 0 20 -1 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 65 160.348 [ (1/32) ] 0 20 -1 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 65 103.348 [ (1/64) ] 0 20 -1 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 80 46.9999999999999 [ (1) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 140 46.9999999999999 [ (2) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 200.87 46.9999999999999 [ (4) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 260.87 46.9999999999999 [ (8) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 320.87 46.9999999999999 [ (16) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 381.739 46.9999999999999 [ (32) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 441.739 46.9999999999999 [ (64) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave matrix currentmatrix 80.5 445.6599 translate 0.499999999999993 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 82.2217 444.6273 translate 0.500000000000007 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 83.0704 443.2303 translate 0.499999999999993 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 84.7426 442.23 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 85.567 441.2601 translate 0.5 0.499999999999972 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 87.1922 440.3638 translate 0.500000000000014 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 87.9939 438.9149 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 89.5783 437.7517 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 90.3522 436.4796 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 91.8913 435.6204 translate 0.500000000000007 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 93.4043 434.497 translate 0.499999999999993 0.499999999999972 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 94.1522 433.1752 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 95.6304 432.0435 translate 0.500000000000007 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 96.3522 431.1183 translate 0.499999999999993 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 97.7957 429.6396 translate 0.499999999999993 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 98.5 428.4583 translate 0.499999999999993 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 99.9 427.4339 translate 0.500000000000007 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 101.283 426.0957 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 101.97 425.0713 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 103.317 423.8487 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 103.978 423.0557 translate 0.499999999999993 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 105.3 421.9983 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 105.952 421.3209 translate 0.499999999999993 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 107.239 420.2883 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 108.509 419.2722 translate 0.500000000000007 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 109.135 418.2726 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 110.378 417.3143 translate 0.500000000000007 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 110.996 416.5709 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 112.204 415.7943 translate 0.499999999999993 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 112.813 414.9517 translate 0.500000000000007 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 114.004 413.7787 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 114.587 412.7957 translate 0.500000000000007 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 115.761 411.92 translate 0.500000000000007 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 116.909 411.0113 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 117.483 410.0861 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 118.613 408.8057 translate 0.500000000000007 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 119.17 407.9878 translate 0.500000000000007 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 120.274 407.09585 translate 0.5 0.499849999999981 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 120.822 405.865 translate 0.499999999999993 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 121.909 404.849 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 122.448 403.957 translate 0.499999999999993 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 123.517 403.188 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 124.57 402.304 translate 0.500000000000014 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 125.091 401.28 translate 0.499999999999986 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 126.126 400.553 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 126.639 399.471 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 127.657 398.405 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 128.161 397.298 translate 0.500000000000021 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 129.161 396.646 translate 0.499999999999986 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 130.152 395.621 translate 0.499999999999986 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 130.639 394.837 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 131.613 394.019 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 132.091 393.259 translate 0.500000000000014 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 133.048 392.466 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 133.526 391.185 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 134.465 390.252 translate 0.5 0.500000000000028 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 135.396 389.574 translate 0.499999999999986 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave matrix currentmatrix 135.857 388.657 translate 0.5 0.5 scale 1 0 moveto 0 0 1 0 360 arc setmatrix 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 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(sample)e(size,)i(they)f(ha)n(v)n(e)f(\014nite)h(mean)g(\(0.4)f (seconds\))g(and)h(co-)450 2865 y(e\016cien)n(t)h(of)g(v)-5 b(ariation)33 b(\(5{7\).)56 b(One)34 b(m)n(ust)g(b)r(e)h(cautious)e (when)i(summarizing)e(long-tailed)450 2965 y(distributions,)28 b(though,)f(b)r(ecause)h(calculated)f(momen)n(ts)h(tend)g(to)g(b)r(e)g (dominated)g(b)n(y)f(a)h(few)450 3064 y(outliers.)53 b(In)33 b(our)f(analyses)g(w)n(e)g(use)h(more)g(robust)f(summary)g (statistics)h(\(order)f(statistics)450 3164 y(lik)n(e)c(the)g(median,)h (or)e(the)h(estimated)g(parameter)f Fm(k)s Ft(\))h(to)g(summarize)g (distributions,)g(rather)450 3264 y(than)g(momen)n(ts.)533 3432 y(2.1.1)41 b Fo(Pr)l(o)l(c)l(ess)34 b(with)f(lifetime)i Fm(<)29 b Ft(1)k Fo(se)l(c)l(ond.)42 b Ft(F)-7 b(or)31 b(pro)r(cesses)f(with)i(lifetimes)g(less)f(than)g(1)450 3531 y(second,)38 b(w)n(e)e(did)g(not)h(\014nd)f(a)g(consisten)n(t)g (functional)g(form;)41 b(ho)n(w)n(ev)n(er,)36 b(for)g(the)h(mac)n (hines)450 3631 y(w)n(e)c(studied)h(these)g(pro)r(cesses)e(had)i(an)f (ev)n(en)g(lo)n(w)n(er)g(hazard)f(rate)h(than)h(those)f(of)h(age)e Fm(>)h Ft(1)450 3731 y(second.)i(That)22 b(is,)i(the)f(probabilit)n(y)f (that)h(a)f(pro)r(cess)g(of)g(age)g Fm(T)34 b(<)23 b Ft(1)f(seconds)g(liv)n(es)g(another)g Fm(T)450 3830 y Ft(seconds)i(is)i(alw)n(a)n(ys)d(greater)g(than)j(1)p Fm(=)p Ft(2.)35 b(Th)n(us)25 b(for)f(jobs)i(with)f(lifetimes)h(less)f (than)h(1)e(second,)450 3930 y(the)k(median)g(remaining)e(lifetime)j (is)e(greater)f(than)i(the)g(curren)n(t)e(age.)450 4132 y Fx(2.2)41 b(Why)28 b(the)f(distribution)g(is)g(critical)450 4266 y Ft(Man)n(y)d(prior)g(studies)h(of)g(pro)r(cess)e(migration)h (assume)g(an)h(exp)r(onen)n(tial)f(distribution)h(of)g(pro-)450 4366 y(cess)c(lifetimes,)i(b)r(oth)f(in)g(analytical)e(pap)r(ers)h ([Lin)h(and)f(Ragha)n(v)n(endra)e(1993])g([Mirc)n(handaney)450 4465 y(et)26 b(al.)f(1990])f([Eager)g(et)h(al.)h(1986])d([Ahmad)j(et)g 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(tly-used)h(mac)n(hine,)f(used)h(primarily)c(for)i(researc)n(h)450 2322 y(on)e(scien)n(ti\014c)h(computing.)33 b(Bugs)24 b(is)f(a)i(hea)n(vily-used)f(mac)n(hine,)g(used)g(primarily)e(for)h(m)n (ultimedia)f(researc)n(h.)450 2405 y(F)-6 b(aith)18 b(is)f(an)h (infrequen)n(tly-used)g(mac)n(hine,)g(used)h(b)r(oth)f(for)f(video)h (applications)h(and)f(system)f(administration.)1194 2809 y 11840716 11840716 13024788 18945146 27299430 33219788 startTexFig 1194 2809 a %%BeginDocument: har2.ps 50 dict begin % This is a standard prolog for Postscript generated by Tk's canvas % widget. % @(#) prolog.ps 1.2 94/12/09 10:53:18 % The definitions below just define all of the variables used in % any of the procedures here. This is needed for obscure reasons % explained on p. 716 of the Postscript manual (Section H.2.7, % "Initializing Variables," in the section on Encapsulated Postscript). /baseline 0 def /stipimage 0 def /height 0 def /justify 0 def /lineLength 0 def /spacing 0 def /stipple 0 def /strings 0 def /xoffset 0 def /yoffset 0 def /tmpstip null def % Define the array ISOLatin1Encoding (which specifies how characters are % encoded for ISO-8859-1 fonts), if it isn't already present (Postscript % level 2 is supposed to define it, but level 1 doesn't). systemdict /ISOLatin1Encoding known not { /ISOLatin1Encoding [ /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /minus /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /less /equal /greater /question /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /braceleft /bar /braceright /asciitilde /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent /dieresis /space /ring /cedilla /space /hungarumlaut /ogonek /caron /space /exclamdown /cent /sterling /currency /yen /brokenbar /section /dieresis /copyright /ordfeminine /guillemotleft /logicalnot /hyphen /registered /macron /degree /plusminus /twosuperior /threesuperior /acute /mu /paragraph /periodcentered /cedillar /onesuperior /ordmasculine /guillemotright /onequarter /onehalf /threequarters /questiondown /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla /Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis /Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply /Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls /agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla /egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis /eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide /oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis ] def } if % Override the setfont procedure with a new procedure that re-encodes % the font to use the ISO Latin-1 style. The body of this procedure % comes from Section 5.6.1 of the Postscript book. /realsetfont /setfont load def /setfont { dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end % I'm not sure why it's necessary to use "definefont" on this new % font, but it seems to be important; just use the name "Temporary" % for the font. /Temporary exch definefont realsetfont } bind def % StrokeClip % % This procedure converts the current path into a clip area under % the assumption of stroking. It's a bit tricky because some Postscript % interpreters get errors during strokepath for dashed lines. If % this happens then turn off dashes and try again. /StrokeClip { {strokepath} stopped { (This Postscript printer gets limitcheck overflows when) = (stippling dashed lines; lines will be printed solid instead.) = [] 0 setdash strokepath} if clip } bind def % desiredSize EvenPixels closestSize % % The procedure below is used for stippling. Given the optimal size % of a dot in a stipple pattern in the current user coordinate system, % compute the closest size that is an exact multiple of the device's % pixel size. This allows stipple patterns to be displayed without % aliasing effects. /EvenPixels { % Compute exact number of device pixels per stipple dot. dup 0 matrix currentmatrix dtransform dup mul exch dup mul add sqrt % Round to an integer, make sure the number is at least 1, and compute % user coord distance corresponding to this. dup round dup 1 lt {pop 1} if exch div mul } bind def % width height string StippleFill -- % % Given a path already set up and a clipping region generated from % it, this procedure will fill the clipping region with a stipple % pattern. "String" contains a proper image description of the % stipple pattern and "width" and "height" give its dimensions. Each % stipple dot is assumed to be about one unit across in the current % user coordinate system. This procedure trashes the graphics state. /StippleFill { % The following code is needed to work around a NeWSprint bug. /tmpstip 1 index def % Change the scaling so that one user unit in user coordinates % corresponds to the size of one stipple dot. 1 EvenPixels dup scale % Compute the bounding box occupied by the path (which is now % the clipping region), and round the lower coordinates down % to the nearest starting point for the stipple pattern. Be % careful about negative numbers, since the rounding works % differently on them. pathbbox 4 2 roll 5 index div dup 0 lt {1 sub} if cvi 5 index mul 4 1 roll 6 index div dup 0 lt {1 sub} if cvi 6 index mul 3 2 roll % Stack now: width height string y1 y2 x1 x2 % Below is a doubly-nested for loop to iterate across this area % in units of the stipple pattern size, going up columns then % across rows, blasting out a stipple-pattern-sized rectangle at % each position 6 index exch { 2 index 5 index 3 index { % Stack now: width height string y1 y2 x y gsave 1 index exch translate 5 index 5 index true matrix tmpstip imagemask grestore } for pop } for pop pop pop pop pop } bind def % -- AdjustColor -- % Given a color value already set for output by the caller, adjusts % that value to a grayscale or mono value if requested by the CL % variable. /AdjustColor { CL 2 lt { currentgray CL 0 eq { .5 lt {0} {1} ifelse } if setgray } if } bind def % x y strings lineLength spacing xoffset yoffset justify stipple DrawText -- % This procedure does all of the real work of drawing text. The % color and font must already have been set by the caller, and the % following arguments must be on the stack: % % x, y - Coordinates at which to draw text. % strings - An array of strings, one for each line of the text item, % in order from top to bottom. % lineLength - Minimum line length: needed to justify text properly. % spacing - Spacing between lines. % xoffset - Horizontal offset for text bbox relative to x and y: 0 for % nw/w/sw anchor, -0.5 for n/center/s, and -1.0 for ne/e/se. % yoffset - Vertical offset for text bbox relative to x and y: 0 for % nw/n/ne anchor, +0.5 for w/center/e, and +1.0 for sw/s/se. % justify - 0 for left justification, 0.5 for center, 1 for right justify. % stipple - Boolean value indicating whether or not text is to be % drawn in stippled fashion. If text is stippled, % procedure StippleText must have been defined to call % StippleFill in the right way. % % Also, when this procedure is invoked, the color and font must already % have been set for the text. /DrawText { /stipple exch def /justify exch def /yoffset exch def /xoffset exch def /spacing exch def /lineLength exch def /strings exch def % First scan through all of the text to find the widest line (if it's % longer than the "lineLength" argument). strings { stringwidth pop dup lineLength gt {/lineLength exch def} {pop} ifelse newpath } forall % Compute the baseline offset and the actual font height. 0 0 moveto (TXygqPZ) false charpath pathbbox dup /baseline exch def exch pop exch sub /height exch def pop newpath % Translate coordinates first so that the origin is at the upper-left % corner of the text's bounding box. Remember that x and y for % positioning are still on the stack. translate lineLength xoffset mul strings length 1 sub spacing mul height add yoffset mul translate % Now use the baseline and justification information to translate so % that the origin is at the baseline and positioning point for the % first line of text. justify lineLength mul baseline neg translate % Iterate over each of the lines to output it. For each line, % compute its width again so it can be properly justified, then % display it. strings { dup stringwidth pop justify neg mul 0 moveto stipple { % The text is stippled, so turn it into a path and print % by calling StippledText, which in turn calls StippleFill. % Unfortunately, many Postscript interpreters will get % overflow errors if we try to do the whole string at % once, so do it a character at a time. gsave /char (X) def { char 0 3 -1 roll put currentpoint gsave char true charpath clip StippleText grestore char stringwidth translate moveto } forall grestore } {show} ifelse 0 spacing neg translate } forall } bind def /CL 2 def save 306.0 396.0 translate 0.426 0.426 scale -253 -253 translate 0 507 moveto 507 507 lineto 507 0 lineto 0 0 lineto closepath clip newpath gsave 80 447 moveto 400 0 rlineto 0 -380 rlineto -400 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 280 487 [ (Observed distribution and two curve fits) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 280 464 [ (\050fraction of processes with duration > T\051) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 495 12 [ (Duration \050T secs.\051) ] 0 20 -1 1 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 263 377 [ (k) ] 0 20 0 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 250 357 [ (T fit) (\050one parameter\051) ] 0 20 0 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 235 267 [ (exponential fit) (\050two parameters\051) ] 0 20 -1 0.5 0 false DrawText 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(onen)n(tial)g(distributions)g(to)h(mo)r(del)g(the)g(distribution)450 4368 y(of)c(lifetimes.)35 b(These)21 b(distributions)g(ma)n(y)g(or)f (ma)n(y)g(not)h(ha)n(v)n(e)f(the)i(righ)n(t)e(b)r(eha)n(vior,)h(dep)r (ending)450 4467 y(on)33 b(ho)n(w)g(accurately)g(they)h(\014t)g(observ) n(ed)e(distributions.)55 b([Krueger)32 b(and)h(Livn)n(y)g(1988])f(use) 450 4567 y(a)h(three-stage)f(h)n(yp)r(erexp)r(onen)n(tial)h(with)h (parameters)e(estimated)i(to)f(\014t)h(observ)n(ed)e(v)-5 b(alues.)450 4666 y(This)26 b(distribution)g(has)f(the)h(appropriate)f (UBNE)g(prop)r(ert)n(y)-7 b(.)36 b(But)26 b(the)g(t)n(w)n(o-stage)e(h)n (yp)r(erex-)450 4766 y(p)r(onen)n(tial)i(distribution)h([Eager)d(et)j (al.)f(1988])e(use)i(is)g(memoryless;)g(the)h(remaining)e(lifetime)450 4866 y(of)d(a)f(job)h(is)g(indep)r(enden)n(t)g(of)g(its)g(age)f(\(for)g (jobs)h(with)g(nonzero)e(lifetimes\).)36 b(According)21 b(to)h(this)450 4965 y(distribution,)g(migration)d(p)r(olicy)h(is)g (irrelev)-5 b(an)n(t;)21 b(all)f(pro)r(cesses)f(are)g(equally)g(go)r(o) r(d)h(candidates)450 5065 y(for)27 b(migration.)36 b(This)27 b(result)h(is)f(clearly)g(in)g(con\015ict)h(with)g(our)f(observ)-5 b(ations.)p eop %%Page: 11 11 11 10 bop 783 250 a Fq(Exploiting)24 b(Pro)r(cess)j(Lifetime)e (Distributions)e(fo)n(r)j(Dynamic)f(Load)g(Balancing)157 b Fp(\001)141 b Fq(11)533 465 y Ft(Assuming)25 b(the)h(wrong)e (lifetime)i(distribution)g(ma)n(y)f(also)f(underestimate)h(the)h(b)r (ene\014ts)g(of)450 565 y(preemptiv)n(e)f(migration.)35 b(The)25 b(hea)n(vy)f(tail)h(of)g(our)f(measured)g(lifetime)i (distribution)g(implies)450 665 y(that)e(a)g(tin)n(y)g(fraction)g(of)g (the)h(jobs)f(require)f(more)g(CPU)h(than)g(all)g(the)h(other)e(jobs)h (com)n(bined.)450 764 y(As)36 b(w)n(e'll)g(discuss)f(in)h(Section)g (5.4,)h(part)f(of)g(the)g(p)r(o)n(w)n(er)f(of)h(preemptiv)n(e)f (migration)g(is)h(its)450 864 y(abilit)n(y)30 b(to)g(iden)n(tify)h (those)f(few)g(hogs.)44 b(In)30 b(a)g(lifetime)h(distribution)g (without)f(suc)n(h)g(a)g(hea)n(vy)450 964 y(tail,)e(preemptiv)n(e)f (migration)f(migh)n(t)i(not)f(b)r(e)h(as)f(e\013ectiv)n(e.)450 1146 y Fx(3.)41 b(MIGRA)-7 b(TION)27 b(POLICY)450 1279 y Ft(A)d(migration)f(p)r(olicy)h(is)h(based)e(on)h(t)n(w)n(o)f (decisions:)35 b(when)24 b(to)g(migrate)f(pro)r(cesses)g(and)h(whic)n (h)450 1379 y(pro)r(cesses)29 b(to)i(migrate.)46 b(The)32 b(\014rst)e(question)h(concerns)f(ho)n(w)g(often)h(or)f(at)h(what)g (times)g(the)450 1478 y(system)f(c)n(hec)n(ks)f(for)g(eligible)h (migran)n(ts.)43 b(W)-7 b(e)30 b(address)f(this)h(issue)g(brie\015y)g (in)g(Section)g(5.1.1.)450 1578 y(The)e(fo)r(cus)f(of)h(this)g(pap)r (er)f(is)g(the)h(second)f(question,)h(also)e(kno)n(wn)h(as)g(the)h Fo(sele)l(ction)i(p)l(olicy)p Ft(:)649 1727 y(Giv)n(en)20 b(that)h(the)g(load)e(at)i(a)f(host)g(is)g(to)r(o)g(high,)i(ho)n(w)e (do)g(w)n(e)g(c)n(ho)r(ose)f Fo(which)j Ft(pro)r(cess)649 1827 y(to)28 b(migrate?)533 1976 y(Our)j(heuristic)h(is)g(to)f(migrate) g(pro)r(cesses)g(that)h(are)f(exp)r(ected)h(to)g(ha)n(v)n(e)f(long)g (remaining)450 2076 y(lifetimes.)37 b(The)28 b(motiv)-5 b(ation)27 b(for)f(this)i(heuristic)f(is)g(t)n(w)n(ofold.)36 b(F)-7 b(rom)27 b(the)g(pro)r(cess's)f(p)r(ersp)r(ec-)450 2176 y(tiv)n(e,)i(migration)f(time)i(has)f(a)g(large)f(impact)h(on)g (resp)r(onse)f(time.)40 b(A)28 b(pro)r(cess)f(w)n(ould)h(c)n(ho)r(ose) 450 2275 y(to)23 b(migrate)f(only)h(if)h(the)g(migration)e(o)n(v)n (erhead)f(could)i(b)r(e)g(amortized)g(o)n(v)n(er)e(a)i(longer)f (lifetime.)450 2375 y(F)-7 b(rom)32 b(the)g(p)r(ersp)r(ectiv)n(e)g(of)g (the)h(source)e(host,)i(it)f(tak)n(es)f(a)h(signi\014can)n(t)g(amoun)n (t)f(of)h(w)n(ork)f(to)450 2475 y(pac)n(k)-5 b(age)27 b(a)g(pro)r(cess)g(for)h(migration.)37 b(The)28 b(host)g(w)n(ould)g (only)f(c)n(ho)r(ose)g(to)h(migrate)f(pro)r(cesses)450 2574 y(that)h(are)e(lik)n(ely)i(to)f(b)r(e)h(more)f(exp)r(ensiv)n(e)g (to)g(run)h(than)g(to)f(migrate.)533 2674 y(Man)n(y)34 b(existing)h(migration)e(p)r(olicies)i(only)g(migrate)f(newb)r(orn)g (pro)r(cesses)f(\(no)i(preemp-)450 2773 y(tion\),)29 b(b)r(ecause)f(these)h(pro)r(cesses)e(ha)n(v)n(e)g(no)h(allo)r(cated)g (memory)g(and)g(th)n(us)h(their)f(migration)450 2873 y(cost)35 b(is)h(lo)n(w.)60 b(The)36 b(idea)f(of)g(migrating)g(newb)r (orn)g(pro)r(cesses)f(migh)n(t)i(also)e(stem)i(from)f(the)450 2973 y(fallacy)g(that)i(pro)r(cess)e(lifetimes)i(ha)n(v)n(e)e(an)g(exp) r(onen)n(tial)h(distribution,)j(implying)d(that)g(all)450 3072 y(pro)r(cesses)d(ha)n(v)n(e)h(equal)g(exp)r(ected)h(remaining)f (lifetimes)i(regardless)c(of)j(their)f(age,)i(so)e(one)450 3172 y(should)27 b(migrate)f(the)h(c)n(heap)r(est)g(pro)r(cesses.)35 b(The)27 b(problem)f(with)i(only)e(migrating)g(newb)r(orn)450 3272 y(pro)r(cesses)f(is)i(that,)g(according)e(to)i(the)g(pro)r(cess)e (lifetime)j(distribution,)f(newb)r(orn)f(pro)r(cesses)450 3371 y(are)33 b(unlik)n(ely)i(to)f(liv)n(e)g(long)g(enough)f(to)i (justify)g(the)g(cost)f(of)g(remote)g(execution.)57 b(In)35 b(fact,)450 3471 y(our)26 b(measuremen)n(ts)f(sho)n(w)h(that)h(o)n(v)n (er)e(70\045)h(of)g(pro)r(cesses)f(ha)n(v)n(e)h(lifetimes)h(smaller)f (than)g(the)450 3571 y(smallest)h(non-preemptiv)n(e)g(migration)f(cost) h(\(see)h(T)-7 b(able)27 b(3\).)533 3670 y(Th)n(us)g(a)g(newb)r(orn)g (migration)f(p)r(olicy)h(is)g(only)g(justi\014ed)h(if)g(the)g(system)f (has)g(prior)f(kno)n(wl-)450 3770 y(edge)i(ab)r(out)g(pro)r(cesses)e (and)i(can)g(selectiv)n(ely)f(migrate)g(pro)r(cesses)g(lik)n(ely)g(to)h (b)r(e)h(CPU)f(hogs.)450 3869 y(W)-7 b(e)30 b(ha)n(v)n(e)e(found,)i (though,)g(that)g(the)g(abilit)n(y)f(of)g(the)h(system)f(to)h(predict)f (pro)r(cess)f(lifetimes)450 3969 y(b)n(y)f(name)h(is)f(limited)i (\(Section)e(5.4\).)533 4069 y(Can)i(w)n(e)h(do)f(b)r(etter?)43 b(The)30 b(distribution)g(of)f(lifetimes)i(implies)f(that)f(w)n(e)h (exp)r(ect)g(and)f(old)450 4168 y(pro)r(cess)k(to)i(run)f(longer)f (than)i(a)f(y)n(oung)f(pro)r(cess;)k(th)n(us,)f(it)f(is)g(preferable)e (to)i(migrate)e(old)450 4268 y(pro)r(cesses.)533 4368 y(There)d(are)f(t)n(w)n(o)h(p)r(oten)n(tial)g(problems)g(with)h(this)f (approac)n(h.)43 b(First,)31 b(since)g(the)f(v)-5 b(ast)30 b(ma-)450 4467 y(jorit)n(y)35 b(of)g(pro)r(cesses)e(are)i(short,)h (there)f(migh)n(t)g(not)g(b)r(e)h(enough)f(old)g(pro)r(cesses)e(to)i (ha)n(v)n(e)f(a)450 4567 y(signi\014can)n(t)i(load)h(balancing)f (e\013ect.)66 b(In)37 b(fact,)j(although)c(there)h(are)f(few)h (long-liv)n(ed)f(pro-)450 4666 y(cesses,)41 b(they)e(accoun)n(t)f(for)h (a)f(large)g(part)g(of)h(the)h(total)f(CPU)f(load.)71 b(According)38 b(to)h(our)450 4766 y(measuremen)n(ts,)26 b(t)n(ypically)f(few)n(er)h(than)h(4\045)f(of)h(pro)r(cesses)d(liv)n(e) i(longer)g(than)g(2)g(seconds,)g(y)n(et)450 4866 y(these)36 b(pro)r(cesses)e(mak)n(e)h(up)i(more)e(than)h(60\045)f(of)h(the)g (total)g(CPU)f(load.)61 b(This)36 b(is)g(due)g(to)450 4965 y(the)28 b(long)e(tail)h(of)h(the)f(pro)r(cess)f(lifetime)j (distribution.)36 b(F)-7 b(urthermore,)27 b(w)n(e)g(will)g(see)g(that)g (the)450 5065 y(abilit)n(y)32 b(to)g(migrate)f(ev)n(en)h(a)g(few)g (large)f(jobs)h(can)g(ha)n(v)n(e)f(a)h(large)e(e\013ect)j(on)f(system)g (p)r(erfor-)p eop %%Page: 12 12 12 11 bop 450 250 a Fq(12)142 b Fp(\001)158 b Fq(M.)26 b(Ha)n(rchol-Balter)f(and)f(A.)j(B.)f(Do)n(wney)450 465 y Ft(mance,)d(since)f(a)g(single)g(long)g(pro)r(cess)f(on)h(a)g(busy)g (host)g(imp)r(oses)g(slo)n(wdo)n(wns)f(on)h(man)n(y)g(short)450 565 y(pro)r(cesses.)533 665 y(A)27 b(second)f(problem)h(with)g (migrating)e(old)i(pro)r(cesses)e(is)i(that)g(the)g(migration)f(cost)g (for)g(an)450 765 y(activ)n(e)34 b(pro)r(cess)g(is)h(m)n(uc)n(h)g (greater)f(than)h(the)g(cost)g(of)g(remote)g(execution.)59 b(If)35 b(preemptiv)n(e)450 864 y(migration)f(is)h(done)g(carelessly)-7 b(,)35 b(this)h(additional)e(cost)h(migh)n(t)g(o)n(v)n(erwhelm)e(the)j (b)r(ene\014t)g(of)450 964 y(migrating)26 b(pro)r(cesses)h(with)h (longer)e(exp)r(ected)i(liv)n(es.)450 1138 y Fx(3.1)41 b(Our)28 b(Migration)e(P)n(olicy)450 1271 y Ft(F)-7 b(or)34 b(this)h(reason,)f(w)n(e)h(prop)r(ose)e(a)h(strategy)f(that)i(guaran)n (tees)d(that)j(ev)n(ery)f(migration)f(im-)450 1371 y(pro)n(v)n(es)g (the)i(exp)r(ected)f(p)r(erformance)g(of)g(the)h(migran)n(t)f(pro)r (cess)f(and)i(the)f(other)g(pro)r(cesses)450 1470 y(at)i(the)h(source)d (host.)63 b(This)36 b(strategy)f(migrates)g(a)g(pro)r(cess)g Fo(only)k(if)f(it)g(impr)l(oves)h(the)e(ex-)450 1570 y(p)l(e)l(cte)l(d)g(slowdown)h(of)f(the)g(pr)l(o)l(c)l(ess)p Ft(,)g(where)d(slo)n(wdo)n(wn)g(is)g(de\014ned)i(as)e(in)h(Section)g (1.2.)58 b(Of)450 1669 y(course,)33 b(pro)r(cesses)f(on)h(the)h(target) e(host)h(are)f(slo)n(w)n(ed)g(b)n(y)h(an)g(arriving)e(migran)n(t,)j (but)f(on)g(a)450 1769 y(mo)r(derately-loaded)d(system)h(there)g(are)f (almost)h(alw)n(a)n(ys)f(idle)h(hosts;)i(th)n(us)f(the)g(n)n(um)n(b)r (er)f(of)450 1869 y(pro)r(cesses)e(at)i(the)h(target)e(host)g(is)h (usually)f(zero.)46 b(In)31 b(an)n(y)g(case,)g(the)g(n)n(um)n(b)r(er)g (of)f(pro)r(cesses)450 1968 y(at)d(the)h(target)f(is)h(alw)n(a)n(ys)d (less)i(than)h(the)g(n)n(um)n(b)r(er)f(at)h(the)g(source.)533 2068 y(If)g(there)f(is)g(no)h(pro)r(cess)e(on)h(the)h(host)f(that)h (satis\014es)e(the)i(ab)r(o)n(v)n(e)e(migration)h(criterion,)f(no)450 2168 y(migration)35 b(is)g(done.)62 b(If)36 b(migration)e(costs)i(are)e (high,)k(few)e(pro)r(cesses)f(will)h(b)r(e)g(eligible)f(for)450 2268 y(migration;)c(in)g(the)g(extreme)f(there)g(will)h(b)r(e)g(no)f (migration)g(at)g(all.)45 b(But)31 b(in)g(no)f(case)g(is)g(the)450 2367 y(p)r(erformance)j(of)i(the)g(system)f(w)n(orse)f(\(in)i(exp)r (ectation\))g(than)f(the)h(p)r(erformance)e(without)450 2467 y(migration.)533 2567 y(Using)e(the)g(distribution)h(of)f(pro)r (cess)f(lifetimes,)i(w)n(e)f(calculate)f(the)i(exp)r(ected)f(slo)n(wdo) n(wn)450 2666 y(imp)r(osed)36 b(on)g(a)g(migran)n(t)f(pro)r(cess,)i (and)g(use)f(this)g(result)g(to)g(deriv)n(e)f(a)h(minim)n(um)h(age)e (for)450 2766 y(migration)25 b(based)h(on)g(the)h(cost)f(of)g (migration.)35 b(Denoting)27 b(the)f(age)g(of)g(the)h(migran)n(t)e(pro) r(cess)450 2866 y(b)n(y)j Fm(a)p Ft(;)h(the)g(cost)e(of)i(migration)e (b)n(y)h Fm(c)p Ft(;)h(the)f(\(ev)n(en)n(tual)g(total\))h(lifetime)g (of)f(the)h(migran)n(t)e(b)n(y)h Fm(L)p Ft(,)450 2965 y(the)k(n)n(um)n(b)r(er)f(of)h(pro)r(cesses)e(at)h(the)h(source)e(host) h(b)n(y)h Fm(n)p Ft(;)h(and)e(the)h(n)n(um)n(b)r(er)g(of)f(pro)r (cesses)f(at)450 3065 y(the)e(target)f(host)g(\(including)h(the)g (migran)n(t\))f(b)n(y)g Fm(m)p Ft(,)h(w)n(e)f(ha)n(v)n(e:)1093 3322 y Fn(E)14 b Fl(f)o Ft(slo)n(wdo)n(wn)27 b(of)g(migran)n(t)o Fl(g)987 3496 y Ft(=)1093 3383 y Fd(Z)1176 3404 y Fc(1)1140 3572 y Fk(t)p Fg(=)p Fk(a)1270 3496 y Fn(Pr)1388 3379 y Fd(\032)1488 3445 y Ft(Lifetime)h(of)1471 3545 y(migran)n(t)f(is)g(t) 1919 3379 y Fd(\033)2000 3496 y Fl(\001)2041 3379 y Fd(\032)2124 3445 y Ft(Slo)n(wdo)n(wn)g(giv)n(en)2206 3545 y(lifetime)i(is)e(t)2722 3379 y Fd(\033)2798 3496 y Fm(dt)987 3727 y Ft(=)1093 3614 y Fd(Z)1176 3634 y Fc(1)1140 3802 y Fk(t)p Fg(=)p Fk(a)1270 3727 y Fn(Pr)14 b Fl(f)p Fm(t)23 b Fl(\024)f Fm(L)h(<)f(t)d Ft(+)f Fm(dt)p Fl(j)p Fm(L)23 b Fl(\025)f Fm(a)p Fl(g)c(\001)2288 3670 y Fm(na)g Ft(+)g Fm(c)g Ft(+)g Fm(m)p Ft(\()p Fm(t)h Fl(\000)f Fm(a)p Ft(\))p 2288 3707 646 4 v 2595 3783 a Fm(t)987 3954 y Ft(=)1093 3841 y Fd(Z)1176 3861 y Fc(1)1140 4029 y Fk(t)p Fg(=)p Fk(a)1291 3898 y Fm(a)p 1280 3935 68 4 v 1280 4011 a(t)1310 3987 y Fg(2)1375 3954 y Fl(\001)1427 3898 y Fm(na)g Ft(+)g Fm(c)g Ft(+)g Fm(m)p Ft(\()p Fm(t)h Fl(\000)f Fm(a)p Ft(\))p 1427 3935 646 4 v 1734 4011 a Fm(t)2082 3954 y(dt)987 4172 y Ft(=)1103 4116 y(1)p 1103 4153 42 4 v 1103 4229 a(2)1169 4080 y Fd(\020)1232 4116 y Fm(c)p 1228 4153 44 4 v 1228 4229 a(a)1301 4172 y Ft(+)g Fm(m)g Ft(+)g Fm(n)1608 4080 y Fd(\021)533 4353 y Ft(If)24 b(there)f(are)f Fm(n)h Ft(pro)r(cesses)f(at)h(a)g(hea)n(vily)g(loaded)f(host,)i(then)g (a)f(pro)r(cess)f(should)h(b)r(e)h(eligible)450 4452 y(for)i(migration)f(only)h(if)g(its)h(exp)r(ected)f(slo)n(wdo)n(wn)f (after)h(migration)f(is)h(less)g(than)g Fm(n)h Ft(\(whic)n(h)f(is)450 4552 y(the)i(slo)n(wdo)n(wn)e(it)i(exp)r(ects)g(in)g(the)g(absence)e (of)i(migration\).)533 4652 y(Th)n(us,)f(w)n(e)h(require)1178 4619 y Fg(1)p 1178 4633 34 4 v 1178 4681 a(2)1221 4652 y Ft(\()1266 4619 y Fk(c)p 1263 4633 37 4 v 1263 4681 a(a)1328 4652 y Ft(+)18 b Fm(m)g Ft(+)g Fm(n)p Ft(\))23 b Fm(<)g(n)p Ft(,)28 b(whic)n(h)f(implies)p 1120 4750 1648 4 v 1120 4938 4 188 v 1176 4874 a(Minim)n(um)i(migration)d(age)c (=)2174 4832 y(Migration)k(cost)p 2174 4855 529 4 v 2326 4906 a Fm(n)18 b Fl(\000)g Fm(m)p 2765 4938 4 188 v 1120 4941 1648 4 v 533 5065 a Ft(W)-7 b(e)37 b(can)e(extend)i(this)f (analysis)f(to)h(the)h(case)e(of)i(heterogeneous)d(pro)r(cessor)g(sp)r (eeds)i(b)n(y)p eop %%Page: 13 13 13 12 bop 783 250 a Fq(Exploiting)24 b(Pro)r(cess)j(Lifetime)e (Distributions)e(fo)n(r)j(Dynamic)f(Load)g(Balancing)157 b Fp(\001)141 b Fq(13)450 465 y Ft(applying)27 b(a)g(scale)g(factor)g (to)g Fm(n)h Ft(or)e Fm(m)p Ft(.)533 566 y(This)20 b(analysis)f (assumes)h(that)h(curren)n(t)e(load)h(predicts)g(future)h(load;)h(that) e(is,)i(that)f(the)g(load)450 666 y(at)i(the)g(source)f(and)h(target)f (hosts)h(will)g(b)r(e)h(constan)n(t)e(during)h(the)g(migration.)34 b(In)23 b(an)g(attempt)450 765 y(to)33 b(ev)-5 b(aluate)33 b(this)g(assumption,)h(and)f(p)r(ossibly)f(impro)n(v)n(e)g(it,)j(w)n(e) d(considered)h(a)f(n)n(um)n(b)r(er)h(of)450 865 y(alternativ)n(e)h (load)h(predictors,)h(including)g(\(1\))f(taking)g(a)g(load)g(a)n(v)n (erage)d(\(o)n(v)n(er)i(an)h(in)n(terv)-5 b(al)450 965 y(of)36 b(time\),)j(\(2\))e(summing)f(the)g(ages)f(of)h(the)h(pro)r (cesses)e(running)g(on)h(the)h(host,)h(and)e(a)g(\(3\))450 1064 y(calculating)31 b(a)g(prediction)g(of)g(surviv)n(ors)e(and)i (future)h(arriv)-5 b(als)30 b(based)h(on)g(the)h(distribution)450 1164 y(mo)r(del)24 b(prop)r(osed)e(here.)35 b(W)-7 b(e)24 b(found)g(that)g(curren)n(t)f(\(instan)n(taneous\))g(load)g(is)g(the)h (b)r(est)g(single)450 1264 y(predictor,)e(and)g(that)g(using)g(sev)n (eral)e(predictiv)n(e)i(v)-5 b(ariables)20 b(in)j(com)n(bination)e(did) h(not)g(greatly)450 1363 y(impro)n(v)n(e)30 b(the)i(accuracy)e(of)h (prediction.)49 b(These)31 b(results)g(are)f(in)i(accord)e(with)i(Zhou) f([Zhou)450 1463 y(1987])26 b(and)h(Kunz)h([Kunz)f(1991].)450 1651 y Fx(3.2)41 b(Prio)n(r)27 b(Preemptive)h(P)n(olicies)450 1785 y Ft(Only)18 b(a)g(few)h(preemptiv)n(e)g(strategies)e(ha)n(v)n(e)g (b)r(een)i(implemen)n(ted)h(in)e(real)g(systems)g(or)g(prop)r(osed)450 1884 y(in)24 b(prior)f(studies.)36 b(The)24 b(three)f(that)h(w)n(e)g (ha)n(v)n(e)f(found)h(are,)g(lik)n(e)f(ours,)h(based)f(on)h(the)g (principle)450 1984 y(that)k(a)f(pro)r(cess)f(should)i(b)r(e)g (migrated)f(if)h(it)g(is)f(old)h(enough.)533 2085 y(In)g(man)n(y)f (cases,)f(the)i(de\014nition)g(of)g Fo(old)i(enough)e Ft(dep)r(ends)g(on)g(a)f(\\v)n(o)r(o)r(do)r(o")e(constan)n(t)3301 2054 y Fg(1)3337 2085 y Ft(:)37 b(a)450 2184 y(free)27 b(parameter)e(whose)h(v)-5 b(alue)27 b(is)g(c)n(hosen)e(without)j (explanation,)e(and)h(that)g(w)n(ould)f(need)h(to)450 2284 y(b)r(e)h(re-tuned)f(for)g(a)h(di\013eren)n(t)f(system)h(or)e (another)h(w)n(orkload.)533 2384 y(Under)h(Leland)f(and)g(Ott's)h(p)r (olicy)-7 b(,)28 b(a)f(pro)r(cess)f Fm(p)i Ft(is)f(eligible)g(for)h (migration)e(if)1203 2572 y(age\()p Fm(p)p Ft(\))50 b Fm(>)h Ft(ages)26 b(of)i Fm(k)i Ft(y)n(ounger)c(jobs)h(at)h(host)533 2743 y(where)33 b Fm(k)k Ft(is)d(a)f(free)g(parameter)g(called)g (MINCRIT)h([Leland)g(and)f(Ott)h(1986].)54 b(Krueger)450 2843 y(and)24 b(Livn)n(y's)g(p)r(olicy)-7 b(,)25 b(lik)n(e)e(ours,)h (tak)n(es)g(the)g(job's)h(migration)e(cost)h(in)n(to)g(accoun)n(t.)34 b(A)25 b(pro)r(cess)450 2943 y Fm(p)i Ft(is)h(eligible)f(for)g (migration)g(if)1356 3130 y(age\()p Fm(p)p Ft(\))50 b Fm(>)22 b Ft(0)p Fm(:)p Ft(1)c Fl(\003)g Ft(migration)26 b(cost\()p Fm(p)p Ft(\))450 3301 y(but)34 b(they)f(do)g(not)g(explain)g (ho)n(w)g(they)g(c)n(hose)f(the)i(v)-5 b(alue)33 b(0)p Fm(:)p Ft(1)f([Krueger)g(and)h(Livn)n(y)g(1988].)450 3401 y(The)27 b(MOSIX)g(p)r(olicy)f(is)h(similar)f([Barak)f(et)i(al.)f (1993];)g(a)g(pro)r(cess)g(is)g(eligible)h(for)f(migration)450 3501 y(if)1344 3672 y(age\()p Fm(p)p Ft(\))50 b Fm(>)23 b Ft(1)p Fm(:)p Ft(0)17 b Fl(\003)h Ft(migration)27 b(cost\()p Fm(p)p Ft(\))p Fm(:)533 3843 y Ft(The)e(c)n(hoice)f(of)h(the)g(constan) n(t)g(\(1)p Fm(:)p Ft(0\))f(in)i(the)f(MOSIX)g(p)r(olicy)g(ensures)f (that)h(the)g(slo)n(wdo)n(wn)450 3943 y(of)38 b(a)f(migran)n(t)g(pro)r (cess)f(is)i(nev)n(er)f(more)g(than)h(2,)i(since)d(in)h(the)g(w)n(orst) f(case)g(the)h(migran)n(t)450 4042 y(completes)27 b(immediately)h(up)r (on)g(arriv)-5 b(al)26 b(at)h(the)h(target.)533 4143 y(Despite)i(this)f(justi\014cation,)h(the)g(c)n(hoice)e(of)i(the)f (maxim)n(um)g(slo)n(wdo)n(wn)f(\(2\))i(is)f(arbitrary)-7 b(.)450 4243 y(W)g(e)24 b(exp)r(ect)g(the)g(MOSIX)f(p)r(olicy)g(to)h(b) r(e)g(to)r(o)f(restrictiv)n(e,)g(for)g(t)n(w)n(o)g(reasons.)33 b(First,)25 b(it)e(ignores)450 4342 y(the)32 b(slo)n(wdo)n(wn)e(that)i (w)n(ould)f(b)r(e)h(imp)r(osed)g(at)g(the)g(source)e(host)i(in)g(the)g (absence)f(of)g(migra-)450 4442 y(tion)j(\(presumably)f(there)h(is)g (more)f(than)h(one)f(pro)r(cess)g(there,)i(or)e(the)i(system)e(w)n (ould)h(not)450 4542 y(b)r(e)f(attempting)h(to)f(migrate)f(pro)r (cesses)f(a)n(w)n(a)n(y\).)51 b(Second,)35 b(it)e(is)g(based)f(on)h (the)g(w)n(orst-case)450 4641 y(slo)n(wdo)n(wn)g(rather)h(than)h(the)g (exp)r(ected)g(slo)n(wdo)n(wn.)57 b(In)35 b(Section)f(5.5,)i(w)n(e)f (sho)n(w)e(that)i(the)450 4741 y(b)r(est)25 b(c)n(hoice)f(for)h(this)g (parameter,)f(for)g(our)g(w)n(orkload,)g(is)h(usually)f(near)g(0.4,)h (but)g(it)g(dep)r(ends)450 4841 y(on)i(load.)p 450 4985 391 4 v 450 5041 a Ff(1)485 5065 y Fw(This)c(term)f(w)n(as)i(coined)h (b)n(y)f(Professor)e(John)j(Ousterhout)g(at)f(U.C.)e(Berk)n(eley)-6 b(.)p eop %%Page: 14 14 14 13 bop 450 250 a Fq(14)142 b Fp(\001)158 b Fq(M.)26 b(Ha)n(rchol-Balter)f(and)f(A.)j(B.)f(Do)n(wney)450 465 y Fx(4.)41 b(MODEL)27 b(OF)h(MIGRA)-7 b(TION)27 b(COSTS)450 598 y Ft(Migration)i(cost)g(has)g(suc)n(h)h(a)f(large)g(e\013ect)h(on)g (the)g(p)r(erformance)f(of)h(preemptiv)n(e)f(load)g(bal-)450 698 y(ancing;)d(this)h(section)g(presen)n(ts)e(the)j(mo)r(del)e(of)h (migration)f(costs)g(w)n(e)g(use)h(in)f(our)g(sim)n(ulation)450 798 y(studies.)533 897 y(W)-7 b(e)25 b(mo)r(del)h(the)f(cost)g(of)g (migrating)f(an)g(activ)n(e)h(pro)r(cess)e(as)i(the)g(sum)g(of)g(a)g Fo(\014xe)l(d)i(migr)l(ation)450 997 y(c)l(ost)34 b Ft(for)g(migrating) g(the)g(pro)r(cess's)f(system)i(state)f(and)g(a)g Fo(memory)j(tr)l (ansfer)f(c)l(ost)e Ft(that)h(is)450 1097 y(prop)r(ortional)26 b(to)h(the)h(amoun)n(t)f(of)h(the)g(pro)r(cess's)e(memory)h(that)h(m)n (ust)g(b)r(e)g(transferred.)533 1196 y(W)-7 b(e)30 b(mo)r(del)g Fo(r)l(emote)h(exe)l(cution)g(c)l(ost)f Ft(as)f(a)g(\014xed)h(cost;)g (it)g(is)f(the)h(same)f(for)g(all)g(pro)r(cesses.)450 1296 y(The)d(cost)g(of)g(remote)f(execution)h(includes)g(sending)g(the) g(command)g(and)g(argumen)n(ts)f(to)g(the)450 1395 y(remote)e(host,)h (logging)f(in)h(or)e(otherwise)h(authen)n(ticating)h(the)g(pro)r(cess,) f(and)h(creating)e(a)i(new)450 1495 y(shell)k(and)f(en)n(vironmen)n(t)g (on)g(the)h(remote)f(host.)533 1595 y(Throughout)f(this)i(pap)r(er,)g (w)n(e)f(use)g(the)h(follo)n(wing)f(notation:)450 1745 y(|)p Fm(r)r Ft(:)38 b(the)28 b(cost)f(of)g(remote)g(execution,)h(in)g (seconds)450 1863 y(|)p Fm(f)9 b Ft(:)37 b(the)28 b(\014xed)f(cost)g (of)h(preemptiv)n(e)f(migration,)g(in)g(seconds)450 1980 y(|)p Fm(b)p Ft(:)37 b(the)28 b(memory)e(transfer)h(bandwidth,)h(in)g (MB)g(p)r(er)f(second)450 2097 y(|)p Fm(m)p Ft(:)37 b(the)28 b(memory)f(size)g(of)g(migran)n(t)g(pro)r(cesses,)f(in)i(MB)450 2247 y(and)f(th)n(us:)1357 2397 y(cost)g(of)g(remote)g(execution)41 b(=)g Fm(r)1197 2522 y Ft(cost)27 b(of)h(preemptiv)n(e)f(migration)40 b(=)h Fm(f)27 b Ft(+)19 b Fm(m=b)450 2672 y Ft(where)27 b(the)h(quotien)n(t)g Fm(m=b)e Ft(is)i(the)g(memory)e(transfer)h(cost.) 450 2839 y Fx(4.1)41 b(Memo)n(ry)27 b(transfer)h(costs)450 2972 y Ft(The)37 b(amoun)n(t)f(of)h(a)f(pro)r(cess's)f(memory)h(that)h (m)n(ust)g(b)r(e)g(transferred)e(during)h(preemptiv)n(e)450 3071 y(migration)20 b(dep)r(ends)i(on)f(prop)r(erties)f(of)i(the)f (distributed)h(system.)35 b(Douglis)20 b(and)i(Ousterhout)450 3171 y([Douglis)34 b(and)f(Ousterhout)h(1991])e(ha)n(v)n(e)g(an)i (excellen)n(t)g(discussion)f(of)h(this)g(issue,)h(and)f(w)n(e)450 3271 y(b)r(orro)n(w)26 b(from)h(them)h(here.)533 3370 y(A)n(t)i(the)g(most,)g(it)g(migh)n(t)f(b)r(e)h(necessary)e(to)i (transfer)e(a)h(pro)r(cess's)g(en)n(tire)g(memory)-7 b(.)42 b(On)29 b(a)450 3470 y(system)e(lik)n(e)g(Sprite,)g(whic)n(h)g (in)n(tegrates)f(virtual)h(memory)f(with)i(a)f(distributed)h(\014le)f (system,)450 3570 y(it)h(is)g(only)f(necessary)f(to)h(write)h(dirt)n(y) f(pages)f(to)i(the)g(\014le)g(system)f(b)r(efore)g(migration.)36 b(When)450 3669 y(the)28 b(pro)r(cess)f(is)h(restarted)e(at)i(the)g (target)f(host,)h(it)g(will)g(retriev)n(e)e(these)i(pages.)37 b(In)28 b(this)g(case)450 3769 y(the)g(cost)f(of)h(migration)e(is)i (prop)r(ortional)e(to)h(the)h(size)g(of)f(the)h(residen)n(t)f(set)h (rather)f(than)g(the)450 3868 y(size)g(of)h(memory)-7 b(.)533 3968 y(In)25 b(systems)f(that)i(use)e(precop)n(ying,)g(suc)n(h) h(as)f(V)h([Theimer)g(et)g(al.)g(1985],)e(pages)h(are)g(trans-)450 4068 y(ferred)k(while)h(the)g(program)e(con)n(tin)n(ues)g(to)i(run)g (at)f(the)h(source)f(host.)39 b(When)30 b(the)f(job)f(stops)450 4167 y(execution)g(at)g(the)h(source,)e(it)i(will)f(ha)n(v)n(e)f(to)h (transfer)g(again)f(an)n(y)g(pages)g(that)i(ha)n(v)n(e)e(b)r(ecome)450 4267 y(dirt)n(y)j(during)g(the)h(precop)n(y)-7 b(.)45 b(Although)30 b(the)h(n)n(um)n(b)r(er)f(of)h(pages)e(transferred)g (migh)n(t)i(b)r(e)g(in-)450 4367 y(creased,)24 b(the)i(dela)n(y)e(imp)r (osed)h(on)g(the)h(migran)n(t)e(pro)r(cess)g(is)h(greatly)f(decreased.) 35 b(Additional)450 4466 y(tec)n(hniques)27 b(can)h(reduce)f(the)h (cost)f(of)g(transferring)f(memory)h(ev)n(en)g(more)g([Za)n(y)n(as)e (1987].)450 4633 y Fx(4.2)41 b(Migration)26 b(costs)g(in)i(real)g (systems)450 4766 y Ft(The)36 b(sp)r(eci\014c)g(parameters)e(of)h (migration)g(cost)g(dep)r(end)i(not)f(only)f(on)g(the)h(nature)g(of)f (the)450 4866 y(system)27 b(\(as)g(discussed)g(ab)r(o)n(v)n(e\))g(but)h (also)e(on)h(the)h(sp)r(eed)g(of)f(the)h(net)n(w)n(ork.)35 b(T)-7 b(ables)27 b(3)g(and)55 b(4)450 4965 y(sho)n(w)24 b(rep)r(orted)f(costs)h(from)g(a)h(v)-5 b(ariet)n(y)23 b(of)i(real)e(systems.)36 b(Later)23 b(w)n(e)i(will)f(use)h(a)f (trace-driv)n(en)450 5065 y(sim)n(ulator)33 b(to)g(ev)-5 b(aluate)34 b(the)g(e\013ect)h(of)e(these)h(parameters)f(on)g(system)h (p)r(erformance.)54 b(W)-7 b(e)p eop %%Page: 15 15 15 14 bop 783 250 a Fq(Exploiting)24 b(Pro)r(cess)j(Lifetime)e (Distributions)e(fo)n(r)j(Dynamic)f(Load)g(Balancing)157 b Fp(\001)141 b Fq(15)p 595 436 2700 4 v 593 519 4 84 v 644 494 a Fw(System)p 1751 519 V 936 w(Hardw)n(are)p 2712 519 V 663 w(Cost)24 b(of)g(rexec,)g Fi(r)p 3293 519 V 595 522 2700 4 v 595 539 V 593 622 4 84 v 644 597 a Fw(Sprite)p 1751 622 V 974 w(SP)-6 b(AR)n(Cstation1)p 2712 622 V 480 w(0.33)24 b(sec)p 3293 622 V 593 705 V 644 680 a([Douglis)f(and)h(Ousterhout)h(1991])p 1751 705 V 214 w(10Mb/sec)g(Ethernet)p 2712 705 V 3293 705 V 595 708 2700 4 v 593 791 4 84 v 644 766 a(GLUNIX)p 1751 791 V 875 w(HP)f(w)n(orkstations)p 2712 791 V 448 w(0.25)g(to)g(0.5)g(sec)p 3293 791 V 593 874 V 644 849 a([V)-6 b(ahdat)25 b(et)f(al.)f(1994])h([V)-6 b(ahdat)25 b(1995])p 1751 874 V 100 w(A)-6 b(TM)23 b(net)n(w)n(ork)p 2712 874 V 3293 874 V 595 877 2700 4 v 593 960 4 84 v 644 935 a(MIST)p 1751 960 V 978 w(HP9000/720)p 2712 960 V 580 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a Fw(Sprite)p 1698 1967 V 1051 w(SP)-6 b(AR)n(Cstation1)p 2465 1967 V 286 w(0.33)24 b(sec)p 2839 1967 V 135 w(2.00)g(sec/MB)p 3423 1967 V 463 2050 V 514 2026 a([Douglis)f(and)h(Ousterhout)h(1991])p 1698 2050 V 291 w(10Mb/sec)g(Ethernet)p 2465 2050 V 2839 2050 V 3423 2050 V 465 2054 2960 4 v 463 2137 4 84 v 514 2112 a(MOSIX)p 1698 2137 V 998 w(In)n(tel)g(P)n(en)n(tium)e(90MHz)p 2465 2137 V 100 w(0.006)h(sec)p 2839 2137 V 100 w(0.44)g(sec/MB)p 3423 2137 V 463 2220 V 514 2195 a([Barak)g(et)g(al.)f(1993])h([Bra)n(v) n(erman)f(1995])p 1698 2220 V 100 w(and)h(486)h(66MHz)p 2465 2220 V 2839 2220 V 3423 2220 V 465 2223 2960 4 v 463 2306 4 84 v 514 2281 a(MIST)p 1698 2306 V 1055 w(HP9000/720s)p 2465 2306 V 358 w(0.24)f(sec)p 2839 2306 V 135 w(0.99)g(sec/MB)p 3423 2306 V 463 2389 V 514 2364 a([Prout)n(y)g(1996])p 1698 2389 V 819 w(10Mb/sec)h(Ethernet)p 2465 2389 V 2839 2389 V 3423 2389 V 465 2393 2960 4 v 450 2596 a(T)-6 b(able)28 b(4.)71 b(V)-6 b(alues)28 b(for)f(preemptiv)n(e)h(migration)f (costs)i(from)d(v)l(arious)h(systems.)44 b(Man)n(y)28 b(of)g(these)h(n)n(um)n(b)r(ers)450 2679 y(w)n(ere)d(obtained)i(from)c (p)r(ersonal)j(comm)n(unication)e(with)h(the)h(authors.)40 b(The)26 b(memory)f(transfer)g(cost)i(is)f(the)450 2762 y(pro)r(duct)f(of)e(the)i(in)n(v)n(erse)e(bandwidth,)i(1)p Fi(=b)p Fw(,)f(and)g(the)g(amoun)n(t)g(of)g(memory)d(that)k(m)n(ust)e (b)r(e)h(transferred,)f Fi(m)p Fw(.)450 2992 y Ft(will)35 b(mak)n(e)f(the)h(p)r(essimistic)g(simpli\014cation)g(that)g(a)g (migran)n(t's)e(en)n(tire)h(memory)h(m)n(ust)f(b)r(e)450 3091 y(transferred,)26 b(although,)h(as)g(p)r(oin)n(ted)h(out)g(ab)r(o) n(v)n(e,)e(this)i(is)f(not)h(necessarily)e(the)i(case.)450 3335 y Fx(5.)41 b(TRA)n(CE-DRIVEN)26 b(SIMULA)-7 b(TION)450 3469 y Ft(In)35 b(this)g(section)g(w)n(e)f(presen)n(t)g(the)i(results)e (of)h(a)f(trace-driv)n(en)f(sim)n(ulation)h(of)h(pro)r(cess)f(mi-)450 3569 y(gration.)g(W)-7 b(e)25 b(compare)f(t)n(w)n(o)f(migration)h (strategies:)34 b(our)23 b(prop)r(osed)h(age-based)e(preemptiv)n(e)450 3669 y(migration)h(strategy)h(\(Section)g(3.1\))h(and)f(a)g (non-preemptiv)n(e)g(strategy)f(that)i(migrates)e(new-)450 3768 y(b)r(orn)35 b(pro)r(cesses)f(according)g(to)h(the)h(pro)r(cess)e (name)h(\(similar)g(to)h(strategies)e(prop)r(osed)g(b)n(y)450 3868 y([W)-7 b(ang)33 b(et)g(al.)g(1993])e(and)i([Sv)n(ensson)f (1990]\).)51 b(With)34 b(the)g(in)n(ten)n(tion)f(of)g(\014nding)g(a)f (conser-)450 3968 y(v)-5 b(ativ)n(e)37 b(estimate)h(of)g(the)h(b)r (ene\014t)f(of)g(preemptiv)n(e)g(migration,)h(w)n(e)f(giv)n(e)f(the)h (name-based)450 4067 y(strategy)31 b(the)h(b)r(ene\014t)h(of)g(sev)n (eral)d(unrealistic)i(adv)-5 b(an)n(tages;)32 b(for)g(example,)h(the)f (name-lists)450 4167 y(are)27 b(deriv)n(ed)f(from)i(the)g(same)f(trace) f(data)i(used)f(b)n(y)g(the)h(sim)n(ulator.)533 4268 y(Section)35 b(5.1)f(describ)r(es)g(the)i(sim)n(ulator)d(and)i(the)h(t) n(w)n(o)e(strategies)f(in)i(more)g(detail.)58 b(W)-7 b(e)450 4368 y(use)40 b(the)h(sim)n(ulator)e(to)h(run)g(three)g(exp)r (erimen)n(ts.)74 b(First,)43 b(in)e(Section)f(5.2,)i(w)n(e)e(ev)-5 b(aluate)450 4467 y(the)38 b(sensitivit)n(y)f(of)h(eac)n(h)f(strategy)f (to)i(the)g(migration)e(costs)h Fm(r)r Ft(,)k Fm(f)9 b Ft(,)40 b Fm(b)p Ft(,)g(and)e Fm(m)f Ft(discussed)450 4567 y(in)30 b(Section)g(4.)43 b(Next,)31 b(in)f(Section)g(5.3,)f(w)n (e)h(c)n(ho)r(ose)e(v)-5 b(alues)30 b(for)f(these)h(parameters)e(that)i (are)450 4666 y(represen)n(tativ)n(e)18 b(of)i(curren)n(t)f(systems)g (and)h(compare)e(the)i(p)r(erformance)f(of)h(the)g(t)n(w)n(o)f (strategies)450 4766 y(in)37 b(detail.)64 b(In)37 b(Section)f(5.4)g(w)n (e)g(discuss)h(wh)n(y)f(the)h(preemptiv)n(e)f(p)r(olicy)h(outp)r (erforms)e(the)450 4866 y(non-preemptiv)n(e)g(p)r(olicy)-7 b(.)62 b(Lastly)-7 b(,)37 b(in)f(Section)g(5.5,)h(w)n(e)f(ev)-5 b(aluate)35 b(the)i(analytic)e(criterion)450 4965 y(for)f(migration)f (age)g(prop)r(osed)h(in)g(Section)g(3.1,)i(compared)d(to)h(criteria)f (used)h(in)h(previous)450 5065 y(studies.)p eop %%Page: 16 16 16 15 bop 450 250 a Fq(16)142 b Fp(\001)158 b Fq(M.)26 b(Ha)n(rchol-Balter)f(and)f(A.)j(B.)f(Do)n(wney)450 465 y Fx(5.1)41 b(The)27 b(simulato)n(r)450 599 y Ft(W)-7 b(e)19 b(ha)n(v)n(e)e(implemen)n(ted)i(a)f(trace-driv)n(en)e(sim)n (ulation)i(of)h(a)e(net)n(w)n(ork)g(of)i(six)f(iden)n(tical)g(w)n (orkstations.)3619 569 y Fg(2)450 699 y Ft(W)-7 b(e)28 b(selected)g(six)f(da)n(ytime)h(in)n(terv)-5 b(als)26 b(from)i(the)g(traces)f(on)g(mac)n(hine)g(p)r(o)h(\(see)g(Section)f (2.1\),)450 798 y(eac)n(h)g(from)h(9:00)e(a.m.)38 b(to)28 b(5:00)f(p.m.)38 b(F)-7 b(rom)28 b(the)g(six)g(traces)f(w)n(e)h (extracted)f(the)h(start)g(times)450 898 y(and)i(CPU)f(durations)g(of)h (the)h(pro)r(cesses.)42 b(W)-7 b(e)30 b(then)h(sim)n(ulated)e(a)h(net)n (w)n(ork)e(where)i(eac)n(h)f(of)450 998 y(six)i(hosts)h(executes)f (\(concurren)n(tly)g(with)h(the)g(others\))f(the)i(pro)r(cess)d(arriv) -5 b(als)30 b(from)i(one)f(of)450 1097 y(the)d(da)n(ytime)f(traces.)533 1198 y(Although)34 b(the)h(w)n(orkloads)c(on)j(the)g(six)g(hosts)g(are) f(homogeneous)f(in)j(terms)e(of)h(the)h(job)450 1297 y(mix)40 b(and)g(distribution)g(of)g(lifetimes,)k(there)c(is)f (considerable)g(v)-5 b(ariation)39 b(in)h(the)g(lev)n(el)g(of)450 1397 y(activit)n(y)27 b(during)f(the)i(eigh)n(t-hour)e(trace.)36 b(F)-7 b(or)26 b(most)h(of)g(the)h(traces,)e(ev)n(ery)g(arriving)f(pro) r(cess)450 1497 y(\014nds)35 b(at)g(least)f(one)g(idle)h(host)g(in)g (the)g(system,)h(but)f(in)g(the)h(t)n(w)n(o)e(busiest)g(traces,)i(a)e (small)450 1596 y(fraction)c(of)g(pro)r(cesses)f(\(0)p Fm(:)p Ft(1\045\))h(arriv)n(e)f(to)h(\014nd)h(all)f(hosts)g(busy)-7 b(.)45 b(In)30 b(order)f(to)i(ev)-5 b(aluate)29 b(the)450 1696 y(e\013ect)23 b(of)g(c)n(hanges)e(in)i(system)f(load,)h(w)n(e)f (divided)h(the)g(eigh)n(t-hour)e(trace)h(in)n(to)g(eigh)n(t)g(one-hour) 450 1796 y(in)n(terv)-5 b(als.)51 b(W)-7 b(e)33 b(refer)e(to)i(these)f (as)g Fo(runs)g Ft(0)g(through)g(7,)h(where)f(the)h(runs)f(are)g (sorted)f(from)450 1895 y(lo)n(w)n(est)e(to)i(highest)f(load.)45 b(Run)30 b(0)g(has)g(a)g(total)g(of)h(15000)d(pro)r(cesses)h(submitted) i(to)f(the)h(six)450 1995 y(sim)n(ulated)24 b(hosts;)h(Run)f(7)g(has)f (30000)f(pro)r(cesses.)34 b(The)24 b(a)n(v)n(erage)d(duration)j(of)g (pro)r(cesses)e(\(for)450 2094 y(all)k(runs\))f(is)h(0.4)f(seconds.)36 b(Th)n(us)25 b(the)i(total)e(utilization)h(of)g(the)g(system,)g Fm(\032)p Ft(,)h(is)e(b)r(et)n(w)n(een)h(0.27)450 2194 y(and)h(0.54.)533 2295 y(The)j(birth)g(pro)r(cess)f(of)h(jobs)f(at)h (our)f(hosts)h(is)g(burstier)f(than)h(a)f(P)n(oisson)f(pro)r(cess.)43 b(F)-7 b(or)29 b(a)450 2394 y(giv)n(en)i(run)g(and)g(a)g(giv)n(en)f (host,)i(the)g(serial)e(correlation)g(in)h(in)n(terarriv)-5 b(al)30 b(times)h(is)g(t)n(ypically)450 2494 y(b)r(et)n(w)n(een)j(.08)g (and)g(.24,)i(whic)n(h)e(is)g(signi\014can)n(tly)g(higher)g(than)g(one) g(w)n(ould)g(exp)r(ect)h(from)f(a)450 2593 y(P)n(oisson)j(pro)r(cess)g (\(uncorrelated)g(in)n(terarriv)-5 b(al)37 b(times)i(yield)f(a)g (serial)g(correlation)e(of)j(0.0;)450 2693 y(p)r(erfect)28 b(correlation)e(is)h(1.0\).)533 2794 y(Although)32 b(the)f(start)g (times)h(and)f(durations)g(of)h(the)f(pro)r(cesses)f(come)h(from)h (trace)e(data,)450 2893 y(the)36 b(memory)g(size)g(of)g(eac)n(h)f(pro)r (cess,)i(whic)n(h)f(determines)g(its)g(migration)f(cost,)j(is)e(c)n (hosen)450 2993 y(randomly)24 b(from)h(a)g(measured)f(distribution)i (\(see)f(Section)g(5.2\).)36 b(This)25 b(simpli\014cation)g(oblit-)450 3093 y(erates)g(an)n(y)g(correlations)f(b)r(et)n(w)n(een)i(memory)g (size)g(and)g(other)f(pro)r(cess)g(c)n(haracteristics,)f(but)450 3192 y(it)i(allo)n(ws)e(us)h(to)g(con)n(trol)f(the)i(mean)f(memory)g (size)g(as)g(a)g(parameter)f(and)h(examine)g(its)g(e\013ect)450 3292 y(on)i(system)h(p)r(erformance.)533 3392 y(In)c(our)f(system)g(mo) r(del,)i(w)n(e)e(assume)g(that)h(pro)r(cesses)e(are)g(alw)n(a)n(ys)g (ready)h(to)g(run;)i(i.e.)36 b(they)450 3492 y(are)21 b(nev)n(er)g(blo)r(c)n(k)n(ed)h(on)g(I/O.)f(During)h(a)g(giv)n(en)f (time)i(in)n(terv)-5 b(al,)23 b(w)n(e)e(divide)i(CPU)f(time)h(equally) 450 3592 y(among)k(the)g(pro)r(cesses)g(on)g(the)h(host)f(\(pro)r (cessor)f(sharing\).)533 3692 y(In)g(real)e(systems,)i(part)f(of)g(the) h(migration)e(time)i(is)f(sp)r(en)n(t)h(on)f(the)h(source)e(host)i(pac) n(k)-5 b(aging)450 3792 y(the)32 b(transferred)d(pages,)i(part)g(in)g (transit)g(in)h(the)f(net)n(w)n(ork,)g(and)g(part)f(on)h(the)h(target)e (host)450 3891 y(unpac)n(king)g(the)i(data.)48 b(The)31 b(size)g(of)g(these)g(parts)g(and)g(whether)g(they)h(can)f(b)r(e)h(o)n (v)n(erlapp)r(ed)450 3991 y(dep)r(end)k(on)f(details)g(of)g(the)h (system.)60 b(In)36 b(our)e(sim)n(ulation)h(w)n(e)g(c)n(harge)e(the)j (en)n(tire)f(cost)g(of)450 4091 y(migration)29 b(to)i(the)f(source)g (host.)45 b(This)30 b(simpli\014cation)g(is)h(conserv)-5 b(ativ)n(e)28 b(in)j(the)g(sense)f(that)450 4190 y(it)e(mak)n(es)f (preemptiv)n(e)g(migration)f(less)h(e\013ectiv)n(e.)533 4349 y(5.1.1)41 b Fo(Str)l(ate)l(gies.)h Ft(W)-7 b(e)20 b(compare)e(the)i(preemptiv)n(e)f(migration)g(strategy)f(prop)r(osed)g (in)i(Sec-)450 4449 y(tion)i(3.1)g(with)g(a)g(non-preemptiv)n(e)f (migration)g(strategy)-7 b(,)22 b(where)g(the)h(non-preemptiv)n(e)e (strat-)450 4549 y(egy)26 b(is)g(giv)n(en)g(unfair)g(adv)-5 b(an)n(tages.)35 b(F)-7 b(or)26 b(purp)r(oses)f(of)i(comparison,)e(w)n (e)h(ha)n(v)n(e)f(tried)h(to)h(mak)n(e)450 4648 y(the)k(p)r(olicies)g (as)f(simple)h(and)g(as)f(similar)g(as)h(p)r(ossible.)46 b(F)-7 b(or)30 b(b)r(oth)i(t)n(yp)r(es)f(of)g(migration,)f(w)n(e)450 4748 y(consider)g(p)r(erforming)h(a)g(migration)f(only)h(when)h(a)e (new)i(pro)r(cess)e(is)h(b)r(orn,)h(ev)n(en)f(though)g(a)p 450 4902 391 4 v 450 4958 a Ff(2)485 4982 y Fw(The)139 b(trace-driv)n(en)h(sim)n(ulator)d(and)j(the)g(trace)f(data)i(are)e(a)n (v)l(ailable)g(at)450 5065 y(h)n(ttp://h)n(ttp.cs.b)r(erk)n(eley)-6 b(.edu/)p Fs(\030)p Fw(harc)n(hol/loadbalancing.h)n(tml.)p eop %%Page: 17 17 17 16 bop 783 250 a Fq(Exploiting)24 b(Pro)r(cess)j(Lifetime)e (Distributions)e(fo)n(r)j(Dynamic)f(Load)g(Balancing)157 b Fp(\001)141 b Fq(17)450 465 y Ft(preemptiv)n(e)34 b(strategy)g(migh)n (t)g(b)r(ene\014t)i(b)n(y)e(initiating)h(migrations)e(at)i(other)f (times.)58 b(Also,)450 565 y(for)31 b(b)r(oth)i(strategies,)e(a)g(host) h(is)g(considered)e(hea)n(vily-loaded)g(an)n(y)h(time)i(it)f(con)n (tains)f(more)450 665 y(than)36 b(one)f(pro)r(cess;)k(in)d(other)f(w)n (ords,)i(an)n(y)e(time)h(it)g(w)n(ould)g(b)r(e)g(sensible)f(to)h (consider)f(mi-)450 764 y(gration.)41 b(Finally)-7 b(,)30 b(w)n(e)f(use)h(the)g(same)f(lo)r(cation)g(p)r(olicy)g(in)h(b)r(oth)g (cases:)39 b(the)30 b(host)f(with)h(the)450 864 y(lo)n(w)n(est)f (instan)n(taneous)f(load)h(is)h(c)n(hosen)f(as)g(the)h(target)f(host)g (\(ties)h(are)f(brok)n(en)f(b)n(y)i(random)450 964 y(selection\).)533 1063 y(Th)n(us)i(the)h(only)f(di\013erence)h(b)r(et)n(w)n(een)f(the)h (t)n(w)n(o)f(migration)f(p)r(olicies)i(is)f(whic)n(h)g(pro)r(cesses)450 1163 y(are)27 b(considered)f(eligible)i(for)f(migration:)533 1312 y Fo(Name-b)l(ase)l(d)j(non-pr)l(e)l(emptive)h(migr)l(ation.)42 b Ft(A)25 b(pro)r(cess)e(is)h(eligible)f(for)h(migration)f(only)g(if) 450 1412 y(its)31 b(name)f(is)h(on)f(a)h(list)g(of)f(pro)r(cesses)f (that)i(tend)h(to)e(b)r(e)h(long-liv)n(ed.)45 b(If)31 b(an)g(eligible)f(pro)r(cess)450 1512 y(is)h(b)r(orn)g(at)f(a)h(hea)n (vily-loaded)e(host,)j(the)f(pro)r(cess)f(is)h(executed)g(remotely)f (on)h(the)g(selected)450 1611 y(host.)37 b(Pro)r(cesses)25 b(cannot)i(b)r(e)h(migrated)f(once)g(they)h(ha)n(v)n(e)e(b)r(egun)i (execution.)533 1711 y(The)k(p)r(erformance)e(of)i(this)g(strategy)e (dep)r(ends)i(on)g(the)g(list)g(of)f(eligible)h(pro)r(cess)e(names.)450 1810 y(W)-7 b(e)24 b(deriv)n(ed)g(this)g(list)g(b)n(y)g(sorting)f(the)h (pro)r(cesses)e(from)i(the)g(traces)f(according)f(to)i(name)g(and)450 1910 y(duration)g(and)h(selecting)f(the)h(15)f(common)g(names)g(with)h (the)g(longest)f Fo(me)l(an)j(dur)l(ations)p Ft(.)36 b(W)-7 b(e)450 2010 y(c)n(hose)20 b(a)h(threshold)f(on)h(mean)g (duration)f(that)i(is)e(empirically)h(optimal)g(\(for)f(this)i(set)f (of)g(runs\).)450 2109 y(Adding)30 b(more)e(names)h(to)g(the)h(list)f (detracts)g(from)g(the)g(p)r(erformance)f(of)i(the)f(system,)h(as)e(it) 450 2209 y(allo)n(ws)k(more)g(short-liv)n(ed)g(pro)r(cesses)g(to)h(b)r (e)g(migrated.)53 b(Remo)n(ving)32 b(names)h(from)g(the)h(list)450 2309 y(detracts)e(from)h(p)r(erformance)f(as)h(it)g(b)r(ecomes)g(imp)r (ossible)g(to)g(migrate)f(enough)g(pro)r(cesses)450 2408 y(to)c(balance)e(the)i(load)f(e\013ectiv)n(ely)-7 b(.)37 b(Since)28 b(w)n(e)f(used)h(the)g(trace)f(data)g(itself)h(to)f (construct)g(the)450 2508 y(list,)h(our)f(results)g(ma)n(y)g(o)n(v)n (erestimate)e(the)j(p)r(erformance)f(b)r(ene\014ts)h(of)g(this)f (strategy)-7 b(.)533 2624 y Fo(A)l(ge-b)l(ase)l(d)30 b(pr)l(e)l(emptive)h(migr)l(ation.)43 b Ft(A)26 b(pro)r(cess)f(is)h (eligible)f(for)h(migration)f(only)g(if)i(it)f(has)450 2724 y(aged)d(for)h(some)f(fraction)g(of)h(its)h(migration)d(cost.)36 b(Based)23 b(on)h(the)g(deriv)-5 b(ation)23 b(in)i(Section)f(3.1,)450 2823 y(this)33 b(fraction)g(is)1088 2791 y Fg(1)p 1029 2805 152 4 v 1029 2852 a Fk(n)p Fc(\000)p Fk(m)1191 2823 y Ft(,)h(where)f Fm(n)g Ft(\(resp)r(ectiv)n(ely)g Fm(m)p Ft(\))g(is)g(the)h(n)n(um)n(b)r(er)f(of)g(pro)r(cesses)e(at)i(the)450 2923 y(source)j(\(target\))i(host.)66 b(When)39 b(a)e(new)h(pro)r(cess) e(is)i(b)r(orn)f(at)g(a)h(hea)n(vily-loaded)d(host,)40 b(all)450 3023 y(pro)r(cesses)26 b(that)i(satisfy)f(the)h(migration)f (criterion)f(are)h(migrated)g(a)n(w)n(a)n(y)-7 b(.)533 3122 y(This)26 b(strategy)f(understates)g(the)i(p)r(erformance)e(b)r (ene\014ts)i(of)f(preemptiv)n(e)f(migration,)h(b)r(e-)450 3222 y(cause)c(it)i(do)r(es)f(not)g(allo)n(w)f(the)i(system)f(to)g (initiate)h(migrations)d(except)j(when)f(a)g(new)g(pro)r(cess)450 3321 y(arriv)n(es.)533 3471 y(As)37 b(describ)r(ed)f(in)g(Section)h (3.1,)h(w)n(e)e(also)f(mo)r(deled)i(other)e(lo)r(cation)h(p)r(olicies)g (based)g(on)450 3571 y(more)31 b(complicated)h(predictors)f(of)h (future)h(loads,)g(but)f(none)g(of)h(these)f(predictors)f(yielded)450 3670 y(signi\014can)n(tly)c(b)r(etter)h(p)r(erformance)e(than)i(the)g (instan)n(taneous)e(load)h(w)n(e)g(use)h(here.)533 3770 y(W)-7 b(e)36 b(also)e(considered)h(the)h(e\013ect)g(of)g(allo)n(wing)e (preemptiv)n(e)h(migration)f(at)i(times)f(other)450 3869 y(than)g(when)f(a)h(new)f(pro)r(cess)g(arriv)n(es.)55 b(Ideally)-7 b(,)36 b(one)e(w)n(ould)g(lik)n(e)h(to)f(initiate)h(a)f (migration)450 3969 y(whenev)n(er)28 b(a)g(pro)r(cess)g(b)r(ecomes)h (eligible)f(\(since)h(the)g(eligibilit)n(y)g(criterion)f(guaran)n(tees) f(that)450 4069 y(the)g(p)r(erformance)e(of)h(the)g(migran)n(t)g(will)g (impro)n(v)n(e)f(in)h(exp)r(ectation\).)37 b(One)26 b(of)g(the)g (strategies)450 4168 y(w)n(e)35 b(considered)f(p)r(erforms)g(p)r(erio)r (dic)i(c)n(hec)n(ks)e(of)h(eac)n(h)f(pro)r(cess)g(on)h(a)g(hea)n (vily-loaded)e(host)450 4268 y(to)28 b(see)g(if)h(an)n(y)f(satisfy)g (the)h(criterion.)38 b(The)28 b(p)r(erformance)f(of)i(this)f(strategy)g (is)g(signi\014can)n(tly)450 4368 y(b)r(etter)g(than)g(that)g(of)f(the) h(simpler)f(p)r(olicy)h(\(migrating)f(only)g(at)g(pro)r(cess)g(arriv)-5 b(al)26 b(times\).)533 4517 y(5.1.2)41 b Fo(Metrics.)i Ft(W)-7 b(e)37 b(ev)-5 b(aluate)36 b(the)h(e\013ectiv)n(eness)e(of)i (eac)n(h)e(strategy)h(according)e(to)i(the)450 4617 y(follo)n(wing)27 b(p)r(erformance)f(metrics:)533 4766 y Fo(Me)l(an)k(slowdown.)44 b Ft(Slo)n(wdo)n(wn)21 b(is)i(the)g(ratio)f(of)h(w)n(all-clo)r(c)n(k)e (execution)i(time)g(to)g(CPU)f(time)450 4866 y(\(th)n(us,)j(it)f(is)f (alw)n(a)n(ys)f(greater)g(than)i(one\).)35 b(The)24 b(a)n(v)n(erage)c (slo)n(wdo)n(wn)i(of)i(all)f(jobs)h(is)f(a)g(common)450 4965 y(metric)j(of)g(system)f(p)r(erformance.)36 b(When)26 b(w)n(e)g(compute)f(the)i(ratio)e(of)g(mean)h(slo)n(wdo)n(wns)e(\(as) 450 5065 y(from)35 b(di\013eren)n(t)f(strategies\))g(w)n(e)h(will)g (use)f(normalized)g(slo)n(wdo)n(wn,)h(whic)n(h)g(is)g(the)g(ratio)f(of) p eop %%Page: 18 18 18 17 bop 450 250 a Fq(18)142 b Fp(\001)158 b Fq(M.)26 b(Ha)n(rchol-Balter)f(and)f(A.)j(B.)f(Do)n(wney)1194 382 y 11840716 11840716 13024788 18945146 27299430 33219788 startTexFig 1194 382 a %%BeginDocument: har3.ps % This file contains the standard Postscript prolog used when % generating Postscript from canvas widgets. % % Header:/user6/ouster/wish/library/RCS/prolog.ps,v1.693/04/0114:03:52ousterExpHeader: /user6/ouster/wish/library/RCS/prolog.ps,v 1.6 93/04/01 14:03:52 ouster Exp Header:/user6/ouster/wish/library/RCS/prolog.ps,v1.693/04/0114:03:52ousterExp SPRITE (Berkeley); 50 dict begin % The definitions below just define all of the variables used in % any of the procedures here. This is needed for obscure reasons % explained on p. 716 of the Postscript manual (Section H.2.7, % "Initializing Variables," in the section on Encapsulated Postscript). /baseline 0 def /stipimage 0 def /height 0 def /justify 0 def /maxwidth 0 def /spacing 0 def /stipple 0 def /strings 0 def /xoffset 0 def /yoffset 0 def /tmpstip null def /encoding {ISOLatin1Encoding} def % Override setfont to automatically encode the font in the style defined by % by 'encoding' (ISO Latin1 by default). systemdict /encodefont known { /realsetfont /setfont load def /setfont { encoding encodefont realsetfont } def } if % desiredSize EvenPixels closestSize % % The procedure below is used for stippling. Given the optimal size % of a dot in a stipple pattern in the current user coordinate system, % compute the closest size that is an exact multiple of the device's % pixel size. This allows stipple patterns to be displayed without % aliasing effects. /EvenPixels { % Compute exact number of device pixels per stipple dot. dup 0 matrix currentmatrix dtransform dup mul exch dup mul add sqrt % Round to an integer, make sure the number is at least 1, and compute % user coord distance corresponding to this. dup round dup 1 lt {pop 1} if exch div mul } bind def % width height string filled StippleFill -- % % Given a path and other graphics information already set up, this % procedure will fill the current path in a stippled fashion. "String" % contains a proper image description of the stipple pattern and % "width" and "height" give its dimensions. If "filled" is true then % it means that the area to be stippled is gotten by filling the % current path (e.g. the interior of a polygon); if it's false, the % area is gotten by stroking the current path (e.g. a wide line). % Each stipple dot is assumed to be about one unit across in the % current user coordinate system. /StippleFill { % Turn the path into a clip region that we can then cover with % lots of images corresponding to the stipple pattern. Warning: % some Postscript interpreters get errors during strokepath for % dashed lines. If this happens, turn off dashes and try again. 1 index /tmpstip exch def %% Works around NeWSprint bug gsave {eoclip} {{strokepath} stopped {grestore gsave [] 0 setdash strokepath} if clip} ifelse % Change the scaling so that one user unit in user coordinates % corresponds to the size of one stipple dot. 1 EvenPixels dup scale % Compute the bounding box occupied by the path (which is now % the clipping region), and round the lower coordinates down % to the nearest starting point for the stipple pattern. pathbbox 4 2 roll 5 index div cvi 5 index mul 4 1 roll 6 index div cvi 6 index mul 3 2 roll % Stack now: width height string y1 y2 x1 x2 % Below is a doubly-nested for loop to iterate across this area % in units of the stipple pattern size, going up columns then % across rows, blasting out a stipple-pattern-sized rectangle at % each position 6 index exch { 2 index 5 index 3 index { % Stack now: width height string y1 y2 x y gsave 1 index exch translate 5 index 5 index true matrix tmpstip imagemask grestore } for pop } for pop pop pop pop pop grestore newpath } bind def % -- AdjustColor -- % Given a color value already set for output by the caller, adjusts % that value to a grayscale or mono value if requested by the CL % variable. /AdjustColor { CL 2 lt { currentgray CL 0 eq { .5 lt {0} {1} ifelse } if setgray } if } bind def % x y strings spacing xoffset yoffset justify stipple stipimage DrawText -- % This procedure does all of the real work of drawing text. The % color and font must already have been set by the caller, and the % following arguments must be on the stack: % % x, y - Coordinates at which to draw text. % strings - An array of strings, one for each line of the text item, % in order from top to bottom. % spacing - Spacing between lines. % xoffset - Horizontal offset for text bbox relative to x and y: 0 for % nw/w/sw anchor, -0.5 for n/center/s, and -1.0 for ne/e/se. % yoffset - Vertical offset for text bbox relative to x and y: 0 for % nw/n/ne anchor, +0.5 for w/center/e, and +1.0 for sw/s/se. % justify - 0 for left justification, 0.5 for center, 1 for right justify. % stipple - Boolean value indicating whether or not text is to be % drawn in stippled fashion. % stipimage - Image for stippling, if stipple is True. % % Also, when this procedure is invoked, the color and font must already % have been set for the text. /DrawText { /stipimage exch def /stipple exch def /justify exch def /yoffset exch def /xoffset exch def /spacing exch def /strings exch def % First scan through all of the text to find the widest line. /maxwidth 0 def strings { stringwidth pop dup maxwidth gt {/maxwidth exch def} {pop} ifelse newpath } forall % Compute the baseline offset and the actual font height. 0 0 moveto (TXygqPZ) false charpath pathbbox dup /baseline exch def exch pop exch sub /height exch def pop newpath % Translate coordinates first so that the origin is at the upper-left % corner of the text's bounding box. Remember that x and y for % positioning are still on the stack. translate maxwidth xoffset mul strings length 1 sub spacing mul height add yoffset mul translate % Now use the baseline and justification information to translate so % that the origin is at the baseline and positioning point for the % first line of text. justify maxwidth mul baseline neg translate % Iterate over each of the lines to output it. For each line, % compute its width again so it can be properly justified, then % display it. strings { dup stringwidth pop justify neg mul 0 moveto show 0 spacing neg translate } forall } bind def /CL 1 def save 306.0 396.0 translate 0.4311 0.4311 scale -250 -250 translate 0 501 moveto 501 501 lineto 501 0 lineto 0 0 lineto closepath clip newpath gsave 80 441 moveto 400 0 rlineto 0 -380 rlineto -400 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 280 481 [ (Distribution of slowdowns) ] 21 -0.5 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 495 6 [ (Slowdown) ] 21 -1 1 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 0 501 [ (Fraction) (of procs) ] 21 0 0 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 44 61 [ (0) ] 21 -0.5 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 44 137 [ (0.1) ] 21 -0.5 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 44 213 [ (0.2) ] 21 -0.5 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 44 289 [ (0.3) ] 21 -0.5 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 44 365 [ (0.4) ] 21 -0.5 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 44 441 [ (0.5) ] 21 -0.5 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 80 40.9999999999999 [ (1) ] 21 -0.5 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 120 40.9999999999999 [ (2) ] 21 -0.5 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 160 40.9999999999999 [ (3) ] 21 -0.5 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 200 40.9999999999999 [ (4) ] 21 -0.5 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 240 40.9999999999999 [ (5) ] 21 -0.5 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 280 40.9999999999999 [ (6) ] 21 -0.5 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 320 40.9999999999999 [ (7) ] 21 -0.5 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 360 40.9999999999999 [ (8) ] 21 -0.5 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 400 40.9999999999999 [ (9) ] 21 -0.5 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 440 40.9999999999999 [ (10) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 80 61 moveto 75 61 lineto 1 setlinewidth 0 setlinecap 1 setlinejoin 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 80 99 moveto 75 99 lineto 1 setlinewidth 0 setlinecap 1 setlinejoin 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 80 137 moveto 75 137 lineto 1 setlinewidth 0 setlinecap 1 setlinejoin 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 80 175 moveto 75 175 lineto 1 setlinewidth 0 setlinecap 1 setlinejoin 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 80 213 moveto 75 213 lineto 1 setlinewidth 0 setlinecap 1 setlinejoin 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 80 251 moveto 75 251 lineto 1 setlinewidth 0 setlinecap 1 setlinejoin 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 80 289 moveto 75 289 lineto 1 setlinewidth 0 setlinecap 1 setlinejoin 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 80 327 moveto 75 327 lineto 1 setlinewidth 0 setlinecap 1 setlinejoin 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 80 365 moveto 75 365 lineto 1 setlinewidth 0 setlinecap 1 setlinejoin 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 80 403 moveto 75 403 lineto 1 setlinewidth 0 setlinecap 1 setlinejoin 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 80 441 moveto 75 441 lineto 1 setlinewidth 0 setlinecap 1 setlinejoin 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 80 386.888 moveto 36.364 0 rlineto 0 -325.888 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388 mt 5690 430 L 5584 4825 mt (64) s 1465 4612 mt 1507 4612 L 5690 4612 mt 5648 4612 L 1164 4683 mt (0.1) s 1465 2500 mt 1507 2500 L 5690 2500 mt 5648 2500 L 1324 2571 mt (1) s 1465 1492 mt 1507 1492 L 5690 1492 mt 5648 1492 L 1324 1563 mt (3) s 1465 388 mt 1507 388 L 5690 388 mt 5648 388 L 1217 459 mt (10) s 1465 4612 mt 5690 4612 L 1465 388 mt 5690 388 L 1465 4612 mt 1465 388 L 5690 4612 mt 5690 388 L 1465 388 mt 1465 388 L 5690 388 mt 5690 388 L gs 1465 388 4226 4225 MR c np -704 -621 -333 -1036 2502 4612 3 MP stroke -597 -208 -107 -37 -704 -632 -418 -1443 3291 4612 5 MP stroke -704 -118 -704 -323 -384 -325 -321 -449 -317 -1663 3895 4612 6 MP stroke -704 -151 -278 -89 -426 -97 -705 -275 -492 -636 -212 -1153 -71 -959 4353 4612 8 MP stroke 48 w -704 -66 -704 -126 -705 -171 -497 -356 -207 -180 -476 -828 -148 -2112 4906 4612 8 MP stroke 6 w -704 -32 -704 -57 -705 -41 -704 -239 -695 -663 -9 -14 -309 -994 -117 -2112 5412 4612 9 MP stroke 11 105 137 1008 556 903 547 201 4439 388 5 MP 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/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 /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 fill } 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 { 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00000000000000000000000000000000000000000000000000 % 00000000000000000000000000000000000000000000000000 % 0000000e0000100001c000070000040000e0000380001c0000 % 0000000a000030000140000500000c00008000020000040000 % 0000000a00001000004000030000140000a000038000080000 % 0000000a000010000180000500001c0000a000028000080000 % 0000000e0000100001c000070000040000e000038000080000 % 00000000000000000000000000000000000000000000000000 % 00000000000000000000000000000000000000000000000000 % 00000000000000000000000000000000000000000000000000 % 00000000000000000000000000000000000000000000000000 % 00000000000000000000000000000000000000000000040000 % 0000000000000000000000000000000000000074e3a9f73300 % 0000000000000000000000000000000000000054a2a9555200 % 0000000000000000000000000000000000000054a2a9554200 % 000000000000000000000000000000000000005ca2b9577200 /InitDictCount countdictstack def gsave save mark newpath /showpage {} def % This file contains the standard Postscript prolog used when % generating Postscript from canvas widgets. % % Header:/user6/ouster/wish/library/RCS/prolog.ps,v1.693/04/0114:03:52ousterExpHeader: /user6/ouster/wish/library/RCS/prolog.ps,v 1.6 93/04/01 14:03:52 ouster Exp Header:/user6/ouster/wish/library/RCS/prolog.ps,v1.693/04/0114:03:52ousterExp SPRITE (Berkeley); 50 dict begin % The definitions below just define all of the variables used in % any of the procedures here. This is needed for obscure reasons % explained on p. 716 of the Postscript manual (Section H.2.7, % "Initializing Variables," in the section on Encapsulated Postscript). /baseline 0 def /stipimage 0 def /height 0 def /justify 0 def /maxwidth 0 def /spacing 0 def /stipple 0 def /strings 0 def /xoffset 0 def /yoffset 0 def /tmpstip null def /encoding {ISOLatin1Encoding} def % Override setfont to automatically encode the font in the style defined by % by 'encoding' (ISO Latin1 by default). systemdict /encodefont known { /realsetfont /setfont load def /setfont { encoding encodefont realsetfont } def } if % desiredSize EvenPixels closestSize % % The procedure below is used for stippling. Given the optimal size % of a dot in a stipple pattern in the current user coordinate system, % compute the closest size that is an exact multiple of the device's % pixel size. This allows stipple patterns to be displayed without % aliasing effects. /EvenPixels { % Compute exact number of device pixels per stipple dot. dup 0 matrix currentmatrix dtransform dup mul exch dup mul add sqrt % Round to an integer, make sure the number is at least 1, and compute % user coord distance corresponding to this. dup round dup 1 lt {pop 1} if exch div mul } bind def % width height string filled StippleFill -- % % Given a path and other graphics information already set up, this % procedure will fill the current path in a stippled fashion. "String" % contains a proper image description of the stipple pattern and % "width" and "height" give its dimensions. If "filled" is true then % it means that the area to be stippled is gotten by filling the % current path (e.g. the interior of a polygon); if it's false, the % area is gotten by stroking the current path (e.g. a wide line). % Each stipple dot is assumed to be about one unit across in the % current user coordinate system. /StippleFill { % Turn the path into a clip region that we can then cover with % lots of images corresponding to the stipple pattern. Warning: % some Postscript interpreters get errors during strokepath for % dashed lines. If this happens, turn off dashes and try again. 1 index /tmpstip exch def %% Works around NeWSprint bug gsave {eoclip} {{strokepath} stopped {grestore gsave [] 0 setdash strokepath} if clip} ifelse % Change the scaling so that one user unit in user coordinates % corresponds to the size of one stipple dot. 1 EvenPixels dup scale % Compute the bounding box occupied by the path (which is now % the clipping region), and round the lower coordinates down % to the nearest starting point for the stipple pattern. pathbbox 4 2 roll 5 index div cvi 5 index mul 4 1 roll 6 index div cvi 6 index mul 3 2 roll % Stack now: width height string y1 y2 x1 x2 % Below is a doubly-nested for loop to iterate across this area % in units of the stipple pattern size, going up columns then % across rows, blasting out a stipple-pattern-sized rectangle at % each position 6 index exch { 2 index 5 index 3 index { % Stack now: width height string y1 y2 x y gsave 1 index exch translate 5 index 5 index true matrix tmpstip imagemask grestore } for pop } for pop pop pop pop pop grestore newpath } bind def % -- AdjustColor -- % Given a color value already set for output by the caller, adjusts % that value to a grayscale or mono value if requested by the CL % variable. /AdjustColor { CL 2 lt { currentgray CL 0 eq { .5 lt {0} {1} ifelse } if setgray } if } bind def % x y strings spacing xoffset yoffset justify stipple stipimage DrawText -- % This procedure does all of the real work of drawing text. The % color and font must already have been set by the caller, and the % following arguments must be on the stack: % % x, y - Coordinates at which to draw text. % strings - An array of strings, one for each line of the text item, % in order from top to bottom. % spacing - Spacing between lines. % xoffset - Horizontal offset for text bbox relative to x and y: 0 for % nw/w/sw anchor, -0.5 for n/center/s, and -1.0 for ne/e/se. % yoffset - Vertical offset for text bbox relative to x and y: 0 for % nw/n/ne anchor, +0.5 for w/center/e, and +1.0 for sw/s/se. % justify - 0 for left justification, 0.5 for center, 1 for right justify. % stipple - Boolean value indicating whether or not text is to be % drawn in stippled fashion. % stipimage - Image for stippling, if stipple is True. % % Also, when this procedure is invoked, the color and font must already % have been set for the text. /DrawText { /stipimage exch def /stipple exch def /justify exch def /yoffset exch def /xoffset exch def /spacing exch def /strings exch def % First scan through all of the text to find the widest line. /maxwidth 0 def strings { stringwidth pop dup maxwidth gt {/maxwidth exch def} {pop} ifelse newpath } forall % Compute the baseline offset and the actual font height. 0 0 moveto (TXygqPZ) false charpath pathbbox dup /baseline exch def exch pop exch sub /height exch def pop newpath % Translate coordinates first so that the origin is at the upper-left % corner of the text's bounding box. Remember that x and y for % positioning are still on the stack. translate maxwidth xoffset mul strings length 1 sub spacing mul height add yoffset mul translate % Now use the baseline and justification information to translate so % that the origin is at the baseline and positioning point for the % first line of text. justify maxwidth mul baseline neg translate % Iterate over each of the lines to output it. For each line, % compute its width again so it can be properly justified, then % display it. strings { dup stringwidth pop justify neg mul 0 moveto show 0 spacing neg translate } forall } bind def /CL 1 def save 306.0 396.0 translate 0.432 0.432 scale -250 -250 translate 0 500 moveto 500 500 lineto 500 0 lineto 0 0 lineto closepath clip newpath gsave 80 470 moveto 400 0 rlineto 0 -420 rlineto -400 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 280 485 [ (Mean slowdown) ] 21 -0.5 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 105 35.0000000000001 [ (0) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 85 262.212 moveto 13 0 rlineto 0 -212.212 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 85 262.212 moveto 13 0 rlineto 0 -212.212 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 98 213.31 moveto 13 0 rlineto 0 -163.31 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 98 213.31 moveto 13 0 rlineto 0 -163.31 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 111 133.832 moveto 13 0 rlineto 0 -83.832 rlineto -13 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 111 133.832 moveto 13 0 rlineto 0 -83.832 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 155 35.0000000000001 [ (1) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 135 240.33 moveto 13 0 rlineto 0 -190.33 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 135 240.33 moveto 13 0 rlineto 0 -190.33 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 148 221.136 moveto 13 0 rlineto 0 -171.136 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 148 221.136 moveto 13 0 rlineto 0 -171.136 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 161 139.656 moveto 13 0 rlineto 0 -89.6559999999999 rlineto -13 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 161 139.656 moveto 13 0 rlineto 0 -89.6559999999999 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 205 35.0000000000001 [ (2) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 185 216.698 moveto 13 0 rlineto 0 -166.698 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 185 216.698 moveto 13 0 rlineto 0 -166.698 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 198 186.22 moveto 13 0 rlineto 0 -136.22 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 198 186.22 moveto 13 0 rlineto 0 -136.22 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 211 140.076 moveto 13 0 rlineto 0 -90.076 rlineto -13 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 211 140.076 moveto 13 0 rlineto 0 -90.076 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 255 35.0000000000001 [ (3) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 235 198.652 moveto 13 0 rlineto 0 -148.652 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 235 198.652 moveto 13 0 rlineto 0 -148.652 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 248 174.334 moveto 13 0 rlineto 0 -124.334 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 248 174.334 moveto 13 0 rlineto 0 -124.334 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 261 131.284 moveto 13 0 rlineto 0 -81.284 rlineto -13 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 261 131.284 moveto 13 0 rlineto 0 -81.284 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 305 35.0000000000001 [ (4) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 285 251.768 moveto 12.9999999999999 0 rlineto 0 -201.768 rlineto -12.9999999999999 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 285 251.768 moveto 12.9999999999999 0 rlineto 0 -201.768 rlineto -12.9999999999999 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 298 208.634 moveto 13.0000000000001 0 rlineto 0 -158.634 rlineto -13.0000000000001 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 298 208.634 moveto 13.0000000000001 0 rlineto 0 -158.634 rlineto -13.0000000000001 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 311 141.112 moveto 12.9999999999999 0 rlineto 0 -91.112 rlineto -12.9999999999999 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 311 141.112 moveto 12.9999999999999 0 rlineto 0 -91.112 rlineto -12.9999999999999 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 355 35.0000000000001 [ (5) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 335 336.398 moveto 13 0 rlineto 0 -286.398 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 335 336.398 moveto 13 0 rlineto 0 -286.398 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 348 221.738 moveto 13 0 rlineto 0 -171.738 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 348 221.738 moveto 13 0 rlineto 0 -171.738 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 361 154.44 moveto 13.0000000000001 0 rlineto 0 -104.44 rlineto -13.0000000000001 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 361 154.44 moveto 13.0000000000001 0 rlineto 0 -104.44 rlineto -13.0000000000001 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 405 35.0000000000001 [ (6) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 385 332.184 moveto 13 0 rlineto 0 -282.184 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 385 332.184 moveto 13 0 rlineto 0 -282.184 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 398 237.642 moveto 13 0 rlineto 0 -187.642 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 398 237.642 moveto 13 0 rlineto 0 -187.642 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 411 167.04 moveto 13 0 rlineto 0 -117.04 rlineto -13 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 411 167.04 moveto 13 0 rlineto 0 -117.04 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 455 35.0000000000001 [ (7) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 435 222.732 moveto 12.9999999999999 0 rlineto 0 -172.732 rlineto -12.9999999999999 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 435 222.732 moveto 12.9999999999999 0 rlineto 0 -172.732 rlineto -12.9999999999999 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 448 191.764 moveto 13 0 rlineto 0 -141.764 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 448 191.764 moveto 13 0 rlineto 0 -141.764 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 461 160.614 moveto 12.9999999999999 0 rlineto 0 -110.614 rlineto -12.9999999999999 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 461 160.614 moveto 12.9999999999999 0 rlineto 0 -110.614 rlineto -12.9999999999999 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 480 14 [ (run number) ] 21 -1 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 60 50 [ (1.0) ] 21 -1 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 60 190 [ (2.0) ] 21 -1 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 60 330 [ (3.0) ] 21 -1 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 60 470 [ (4.0) ] 21 -1 0.5 0 () false DrawText grestore gsave 460 466 moveto 14.9999999999999 0 rlineto 0 -15 rlineto -14.9999999999999 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 460 466 moveto 14.9999999999999 0 rlineto 0 -15 rlineto -14.9999999999999 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 455 466 [ (no migration) ] 21 -1 0 0 () false DrawText grestore gsave 460 448 moveto 14.9999999999999 0 rlineto 0 -15 rlineto -14.9999999999999 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 460 448 moveto 14.9999999999999 0 rlineto 0 -15 rlineto -14.9999999999999 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 455 448 [ (non-preemptive, name-based migration) ] 21 -1 0 0 () false DrawText grestore gsave 460 430 moveto 14.9999999999999 0 rlineto 0 -15 rlineto -14.9999999999999 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 460 430 moveto 14.9999999999999 0 rlineto 0 -15 rlineto -14.9999999999999 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 455 430 [ (preemptive, age-based migration) ] 21 -1 0 0 () false DrawText grestore restore showpage end countdictstack InitDictCount sub { end } repeat cleartomark restore grestore %%EndDocument endTexFig 1194 1618 a 11840716 7578087 14011514 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Header:/user6/ouster/wish/library/RCS/prolog.ps,v1.693/04/0114:03:52ousterExp SPRITE (Berkeley); 50 dict begin % The definitions below just define all of the variables used in % any of the procedures here. This is needed for obscure reasons % explained on p. 716 of the Postscript manual (Section H.2.7, % "Initializing Variables," in the section on Encapsulated Postscript). /baseline 0 def /stipimage 0 def /height 0 def /justify 0 def /maxwidth 0 def /spacing 0 def /stipple 0 def /strings 0 def /xoffset 0 def /yoffset 0 def /tmpstip null def /encoding {ISOLatin1Encoding} def % Override setfont to automatically encode the font in the style defined by % by 'encoding' (ISO Latin1 by default). systemdict /encodefont known { /realsetfont /setfont load def /setfont { encoding encodefont realsetfont } def } if % desiredSize EvenPixels closestSize % % The procedure below is used for stippling. Given the optimal size % of a dot in a stipple pattern in the current user coordinate system, % compute the closest size that is an exact multiple of the device's % pixel size. This allows stipple patterns to be displayed without % aliasing effects. /EvenPixels { % Compute exact number of device pixels per stipple dot. dup 0 matrix currentmatrix dtransform dup mul exch dup mul add sqrt % Round to an integer, make sure the number is at least 1, and compute % user coord distance corresponding to this. dup round dup 1 lt {pop 1} if exch div mul } bind def % width height string filled StippleFill -- % % Given a path and other graphics information already set up, this % procedure will fill the current path in a stippled fashion. "String" % contains a proper image description of the stipple pattern and % "width" and "height" give its dimensions. If "filled" is true then % it means that the area to be stippled is gotten by filling the % current path (e.g. the interior of a polygon); if it's false, the % area is gotten by stroking the current path (e.g. a wide line). % Each stipple dot is assumed to be about one unit across in the % current user coordinate system. /StippleFill { % Turn the path into a clip region that we can then cover with % lots of images corresponding to the stipple pattern. Warning: % some Postscript interpreters get errors during strokepath for % dashed lines. If this happens, turn off dashes and try again. 1 index /tmpstip exch def %% Works around NeWSprint bug gsave {eoclip} {{strokepath} stopped {grestore gsave [] 0 setdash strokepath} if clip} ifelse % Change the scaling so that one user unit in user coordinates % corresponds to the size of one stipple dot. 1 EvenPixels dup scale % Compute the bounding box occupied by the path (which is now % the clipping region), and round the lower coordinates down % to the nearest starting point for the stipple pattern. pathbbox 4 2 roll 5 index div cvi 5 index mul 4 1 roll 6 index div cvi 6 index mul 3 2 roll % Stack now: width height string y1 y2 x1 x2 % Below is a doubly-nested for loop to iterate across this area % in units of the stipple pattern size, going up columns then % across rows, blasting out a stipple-pattern-sized rectangle at % each position 6 index exch { 2 index 5 index 3 index { % Stack now: width height string y1 y2 x y gsave 1 index exch translate 5 index 5 index true matrix tmpstip imagemask grestore } for pop } for pop pop pop pop pop grestore newpath } bind def % -- AdjustColor -- % Given a color value already set for output by the caller, adjusts % that value to a grayscale or mono value if requested by the CL % variable. /AdjustColor { CL 2 lt { currentgray CL 0 eq { .5 lt {0} {1} ifelse } if setgray } if } bind def % x y strings spacing xoffset yoffset justify stipple stipimage DrawText -- % This procedure does all of the real work of drawing text. The % color and font must already have been set by the caller, and the % following arguments must be on the stack: % % x, y - Coordinates at which to draw text. % strings - An array of strings, one for each line of the text item, % in order from top to bottom. % spacing - Spacing between lines. % xoffset - Horizontal offset for text bbox relative to x and y: 0 for % nw/w/sw anchor, -0.5 for n/center/s, and -1.0 for ne/e/se. % yoffset - Vertical offset for text bbox relative to x and y: 0 for % nw/n/ne anchor, +0.5 for w/center/e, and +1.0 for sw/s/se. % justify - 0 for left justification, 0.5 for center, 1 for right justify. % stipple - Boolean value indicating whether or not text is to be % drawn in stippled fashion. % stipimage - Image for stippling, if stipple is True. % % Also, when this procedure is invoked, the color and font must already % have been set for the text. /DrawText { /stipimage exch def /stipple exch def /justify exch def /yoffset exch def /xoffset exch def /spacing exch def /strings exch def % First scan through all of the text to find the widest line. /maxwidth 0 def strings { stringwidth pop dup maxwidth gt {/maxwidth exch def} {pop} ifelse newpath } forall % Compute the baseline offset and the actual font height. 0 0 moveto (TXygqPZ) false charpath pathbbox dup /baseline exch def exch pop exch sub /height exch def pop newpath % Translate coordinates first so that the origin is at the upper-left % corner of the text's bounding box. Remember that x and y for % positioning are still on the stack. translate maxwidth xoffset mul strings length 1 sub spacing mul height add yoffset mul translate % Now use the baseline and justification information to translate so % that the origin is at the baseline and positioning point for the % first line of text. justify maxwidth mul baseline neg translate % Iterate over each of the lines to output it. For each line, % compute its width again so it can be properly justified, then % display it. strings { dup stringwidth pop justify neg mul 0 moveto show 0 spacing neg translate } forall } bind def /CL 1 def save 306.0 396.0 translate 0.432 0.432 scale -250 -250 translate 0 500 moveto 500 500 lineto 500 0 lineto 0 0 lineto closepath clip newpath gsave 80 470 moveto 400 0 rlineto 0 -420 rlineto -400 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 280 485 [ (Standard deviation of slowdown) ] 21 -0.5 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 105 35.0000000000001 [ (0) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 85 257.858 moveto 13 0 rlineto 0 -207.858 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 85 257.858 moveto 13 0 rlineto 0 -207.858 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 98 258.887 moveto 13 0 rlineto 0 -208.887 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 98 258.887 moveto 13 0 rlineto 0 -208.887 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 111 138.358 moveto 13 0 rlineto 0 -88.358 rlineto -13 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 111 138.358 moveto 13 0 rlineto 0 -88.358 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 155 35.0000000000001 [ (1) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 135 237.351 moveto 13 0 rlineto 0 -187.351 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 135 237.351 moveto 13 0 rlineto 0 -187.351 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 148 315.272 moveto 13 0 rlineto 0 -265.272 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 148 315.272 moveto 13 0 rlineto 0 -265.272 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 161 144.584 moveto 13 0 rlineto 0 -94.584 rlineto -13 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 161 144.584 moveto 13 0 rlineto 0 -94.584 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 205 35.0000000000001 [ (2) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 185 215.553 moveto 13 0 rlineto 0 -165.553 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 185 215.553 moveto 13 0 rlineto 0 -165.553 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 198 200.581 moveto 13 0 rlineto 0 -150.581 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 198 200.581 moveto 13 0 rlineto 0 -150.581 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 211 142.368 moveto 13 0 rlineto 0 -92.368 rlineto -13 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 211 142.368 moveto 13 0 rlineto 0 -92.368 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 255 35.0000000000001 [ (3) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 235 201.988 moveto 13 0 rlineto 0 -151.988 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 235 201.988 moveto 13 0 rlineto 0 -151.988 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 248 210.419 moveto 13 0 rlineto 0 -160.419 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 248 210.419 moveto 13 0 rlineto 0 -160.419 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 261 138.788 moveto 13 0 rlineto 0 -88.788 rlineto -13 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 261 138.788 moveto 13 0 rlineto 0 -88.788 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 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Header:/user6/ouster/wish/library/RCS/prolog.ps,v1.693/04/0114:03:52ousterExpHeader: /user6/ouster/wish/library/RCS/prolog.ps,v 1.6 93/04/01 14:03:52 ouster Exp Header:/user6/ouster/wish/library/RCS/prolog.ps,v1.693/04/0114:03:52ousterExp SPRITE (Berkeley); 50 dict begin % The definitions below just define all of the variables used in % any of the procedures here. This is needed for obscure reasons % explained on p. 716 of the Postscript manual (Section H.2.7, % "Initializing Variables," in the section on Encapsulated Postscript). /baseline 0 def /stipimage 0 def /height 0 def /justify 0 def /maxwidth 0 def /spacing 0 def /stipple 0 def /strings 0 def /xoffset 0 def /yoffset 0 def /tmpstip null def /encoding {ISOLatin1Encoding} def % Override setfont to automatically encode the font in the style defined by % by 'encoding' (ISO Latin1 by default). systemdict /encodefont known { /realsetfont /setfont load def /setfont { encoding encodefont realsetfont } def } if % desiredSize EvenPixels closestSize % % The procedure below is used for stippling. Given the optimal size % of a dot in a stipple pattern in the current user coordinate system, % compute the closest size that is an exact multiple of the device's % pixel size. This allows stipple patterns to be displayed without % aliasing effects. /EvenPixels { % Compute exact number of device pixels per stipple dot. dup 0 matrix currentmatrix dtransform dup mul exch dup mul add sqrt % Round to an integer, make sure the number is at least 1, and compute % user coord distance corresponding to this. dup round dup 1 lt {pop 1} if exch div mul } bind def % width height string filled StippleFill -- % % Given a path and other graphics information already set up, this % procedure will fill the current path in a stippled fashion. "String" % contains a proper image description of the stipple pattern and % "width" and "height" give its dimensions. If "filled" is true then % it means that the area to be stippled is gotten by filling the % current path (e.g. the interior of a polygon); if it's false, the % area is gotten by stroking the current path (e.g. a wide line). % Each stipple dot is assumed to be about one unit across in the % current user coordinate system. /StippleFill { % Turn the path into a clip region that we can then cover with % lots of images corresponding to the stipple pattern. Warning: % some Postscript interpreters get errors during strokepath for % dashed lines. If this happens, turn off dashes and try again. 1 index /tmpstip exch def %% Works around NeWSprint bug gsave {eoclip} {{strokepath} stopped {grestore gsave [] 0 setdash strokepath} if clip} ifelse % Change the scaling so that one user unit in user coordinates % corresponds to the size of one stipple dot. 1 EvenPixels dup scale % Compute the bounding box occupied by the path (which is now % the clipping region), and round the lower coordinates down % to the nearest starting point for the stipple pattern. pathbbox 4 2 roll 5 index div cvi 5 index mul 4 1 roll 6 index div cvi 6 index mul 3 2 roll % Stack now: width height string y1 y2 x1 x2 % Below is a doubly-nested for loop to iterate across this area % in units of the stipple pattern size, going up columns then % across rows, blasting out a stipple-pattern-sized rectangle at % each position 6 index exch { 2 index 5 index 3 index { % Stack now: width height string y1 y2 x y gsave 1 index exch translate 5 index 5 index true matrix tmpstip imagemask grestore } for pop } for pop pop pop pop pop grestore newpath } bind def % -- AdjustColor -- % Given a color value already set for output by the caller, adjusts % that value to a grayscale or mono value if requested by the CL % variable. /AdjustColor { CL 2 lt { currentgray CL 0 eq { .5 lt {0} {1} ifelse } if setgray } if } bind def % x y strings spacing xoffset yoffset justify stipple stipimage DrawText -- % This procedure does all of the real work of drawing text. The % color and font must already have been set by the caller, and the % following arguments must be on the stack: % % x, y - Coordinates at which to draw text. % strings - An array of strings, one for each line of the text item, % in order from top to bottom. % spacing - Spacing between lines. % xoffset - Horizontal offset for text bbox relative to x and y: 0 for % nw/w/sw anchor, -0.5 for n/center/s, and -1.0 for ne/e/se. % yoffset - Vertical offset for text bbox relative to x and y: 0 for % nw/n/ne anchor, +0.5 for w/center/e, and +1.0 for sw/s/se. % justify - 0 for left justification, 0.5 for center, 1 for right justify. % stipple - Boolean value indicating whether or not text is to be % drawn in stippled fashion. % stipimage - Image for stippling, if stipple is True. % % Also, when this procedure is invoked, the color and font must already % have been set for the text. /DrawText { /stipimage exch def /stipple exch def /justify exch def /yoffset exch def /xoffset exch def /spacing exch def /strings exch def % First scan through all of the text to find the widest line. /maxwidth 0 def strings { stringwidth pop dup maxwidth gt {/maxwidth exch def} {pop} ifelse newpath } forall % Compute the baseline offset and the actual font height. 0 0 moveto (TXygqPZ) false charpath pathbbox dup /baseline exch def exch pop exch sub /height exch def pop newpath % Translate coordinates first so that the origin is at the upper-left % corner of the text's bounding box. Remember that x and y for % positioning are still on the stack. translate maxwidth xoffset mul strings length 1 sub spacing mul height add yoffset mul translate % Now use the baseline and justification information to translate so % that the origin is at the baseline and positioning point for the % first line of text. justify maxwidth mul baseline neg translate % Iterate over each of the lines to output it. For each line, % compute its width again so it can be properly justified, then % display it. strings { dup stringwidth pop justify neg mul 0 moveto show 0 spacing neg translate } forall } bind def /CL 1 def save 306.0 396.0 translate 0.432 0.432 scale -250 -250 translate 0 500 moveto 500 500 lineto 500 0 lineto 0 0 lineto closepath clip newpath gsave 80 470 moveto 400 0 rlineto 0 -420 rlineto -400 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 280 485 [ (Processes slowed by a factor of 3 or more) ] 21 -0.5 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 105 35.0000000000001 [ (0) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 85 379.106 moveto 13 0 rlineto 0 -329.106 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 85 379.106 moveto 13 0 rlineto 0 -329.106 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 98 301.546 moveto 13 0 rlineto 0 -251.546 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 98 301.546 moveto 13 0 rlineto 0 -251.546 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 111 131.281 moveto 13 0 rlineto 0 -81.281 rlineto -13 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 111 131.281 moveto 13 0 rlineto 0 -81.281 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 155 35.0000000000001 [ (1) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 135 342.091 moveto 13 0 rlineto 0 -292.091 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 135 342.091 moveto 13 0 rlineto 0 -292.091 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 148 297.972 moveto 13 0 rlineto 0 -247.972 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 148 297.972 moveto 13 0 rlineto 0 -247.972 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 161 140.727 moveto 13 0 rlineto 0 -90.727 rlineto -13 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 161 140.727 moveto 13 0 rlineto 0 -90.727 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 205 35.0000000000001 [ (2) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 185 352.179 moveto 13 0 rlineto 0 -302.179 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 185 352.179 moveto 13 0 rlineto 0 -302.179 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 198 299.45 moveto 13 0 rlineto 0 -249.45 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 198 299.45 moveto 13 0 rlineto 0 -249.45 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 211 181.684 moveto 13 0 rlineto 0 -131.684 rlineto -13 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 211 181.684 moveto 13 0 rlineto 0 -131.684 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 255 35.0000000000001 [ (3) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 235 263.018 moveto 13 0 rlineto 0 -213.018 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 235 263.018 moveto 13 0 rlineto 0 -213.018 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 248 209.646 moveto 13 0 rlineto 0 -159.646 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 248 209.646 moveto 13 0 rlineto 0 -159.646 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 261 123.059 moveto 13 0 rlineto 0 -73.059 rlineto -13 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 261 123.059 moveto 13 0 rlineto 0 -73.059 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 305 35.0000000000001 [ (4) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 285 367.442 moveto 12.9999999999999 0 rlineto 0 -317.442 rlineto -12.9999999999999 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 285 367.442 moveto 12.9999999999999 0 rlineto 0 -317.442 rlineto -12.9999999999999 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 298 300.668 moveto 13.0000000000001 0 rlineto 0 -250.668 rlineto -13.0000000000001 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 298 300.668 moveto 13.0000000000001 0 rlineto 0 -250.668 rlineto -13.0000000000001 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 311 156.588 moveto 12.9999999999999 0 rlineto 0 -106.588 rlineto -12.9999999999999 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 311 156.588 moveto 12.9999999999999 0 rlineto 0 -106.588 rlineto -12.9999999999999 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 355 35.0000000000001 [ (5) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 335 463.707 moveto 13 0 rlineto 0 -413.707 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 335 463.707 moveto 13 0 rlineto 0 -413.707 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 348 345.582 moveto 13 0 rlineto 0 -295.582 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 348 345.582 moveto 13 0 rlineto 0 -295.582 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 361 176.815 moveto 13.0000000000001 0 rlineto 0 -126.815 rlineto -13.0000000000001 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 361 176.815 moveto 13.0000000000001 0 rlineto 0 -126.815 rlineto -13.0000000000001 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 405 35.0000000000001 [ (6) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 385 445.419 moveto 13 0 rlineto 0 -395.419 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 385 445.419 moveto 13 0 rlineto 0 -395.419 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 398 357.296 moveto 13 0 rlineto 0 -307.296 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 398 357.296 moveto 13 0 rlineto 0 -307.296 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 411 207.34 moveto 13 0 rlineto 0 -157.34 rlineto -13 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 411 207.34 moveto 13 0 rlineto 0 -157.34 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 455 35.0000000000001 [ (7) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 435 309.715 moveto 12.9999999999999 0 rlineto 0 -259.715 rlineto -12.9999999999999 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 435 309.715 moveto 12.9999999999999 0 rlineto 0 -259.715 rlineto -12.9999999999999 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 448 266.32 moveto 13 0 rlineto 0 -216.32 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 448 266.32 moveto 13 0 rlineto 0 -216.32 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 461 187.953 moveto 12.9999999999999 0 rlineto 0 -137.953 rlineto -12.9999999999999 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 461 187.953 moveto 12.9999999999999 0 rlineto 0 -137.953 rlineto -12.9999999999999 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 480 14 [ (run number) ] 21 -1 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 60 50 [ (0%) ] 21 -1 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 60 170 [ (10%) ] 21 -1 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 60 290 [ (20%) ] 21 -1 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 60 410 [ (30%) ] 21 -1 0.5 0 () false DrawText grestore gsave 460 466 moveto 14.9999999999999 0 rlineto 0 -15 rlineto -14.9999999999999 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 460 466 moveto 14.9999999999999 0 rlineto 0 -15 rlineto -14.9999999999999 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 455 466 [ (no migration) ] 21 -1 0 0 () false DrawText grestore gsave 460 448 moveto 14.9999999999999 0 rlineto 0 -15 rlineto -14.9999999999999 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 460 448 moveto 14.9999999999999 0 rlineto 0 -15 rlineto -14.9999999999999 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 455 448 [ (non-preemptive, name-based migration) ] 21 -1 0 0 () false DrawText grestore gsave 460 430 moveto 14.9999999999999 0 rlineto 0 -15 rlineto -14.9999999999999 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 460 430 moveto 14.9999999999999 0 rlineto 0 -15 rlineto -14.9999999999999 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 455 430 [ (preemptive, age-based migration) ] 21 -1 0 0 () false DrawText grestore restore showpage end countdictstack InitDictCount sub { end } repeat cleartomark restore grestore %%EndDocument endTexFig 1194 3555 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0000000050000180000a000028000060000400001000002000 % 000000005000008000020000180000a0000500001c00004000 % 0000000050000080000c0000280000e0000500001400004000 % 0000000070000080000e000038000020000700001c00004000 % 00000000000000000000000000000000000000000000000000 % 00000000000000000000000000000000000000000000000000 % 00000000000000000000000000000000000000000000000000 % 00000000000000000000000000000000000000000000000000 % 00000000000000000000000000000000000000000000002000 % 0000000000000000000000000000000000000003a71d4fb998 % 0000000000000000000000000000000000000002a5154aaa90 % 0000000000000000000000000000000000000002a5154aaa10 % 0000000000000000000000000000000000000002e515cabb90 /InitDictCount countdictstack def gsave save mark newpath /showpage {} def % This file contains the standard Postscript prolog used when % generating Postscript from canvas widgets. % % Header:/user6/ouster/wish/library/RCS/prolog.ps,v1.693/04/0114:03:52ousterExpHeader: /user6/ouster/wish/library/RCS/prolog.ps,v 1.6 93/04/01 14:03:52 ouster Exp Header:/user6/ouster/wish/library/RCS/prolog.ps,v1.693/04/0114:03:52ousterExp SPRITE (Berkeley); 50 dict begin % The definitions below just define all of the variables used in % any of the procedures here. This is needed for obscure reasons % explained on p. 716 of the Postscript manual (Section H.2.7, % "Initializing Variables," in the section on Encapsulated Postscript). /baseline 0 def /stipimage 0 def /height 0 def /justify 0 def /maxwidth 0 def /spacing 0 def /stipple 0 def /strings 0 def /xoffset 0 def /yoffset 0 def /tmpstip null def /encoding {ISOLatin1Encoding} def % Override setfont to automatically encode the font in the style defined by % by 'encoding' (ISO Latin1 by default). systemdict /encodefont known { /realsetfont /setfont load def /setfont { encoding encodefont realsetfont } def } if % desiredSize EvenPixels closestSize % % The procedure below is used for stippling. Given the optimal size % of a dot in a stipple pattern in the current user coordinate system, % compute the closest size that is an exact multiple of the device's % pixel size. This allows stipple patterns to be displayed without % aliasing effects. /EvenPixels { % Compute exact number of device pixels per stipple dot. dup 0 matrix currentmatrix dtransform dup mul exch dup mul add sqrt % Round to an integer, make sure the number is at least 1, and compute % user coord distance corresponding to this. dup round dup 1 lt {pop 1} if exch div mul } bind def % width height string filled StippleFill -- % % Given a path and other graphics information already set up, this % procedure will fill the current path in a stippled fashion. "String" % contains a proper image description of the stipple pattern and % "width" and "height" give its dimensions. If "filled" is true then % it means that the area to be stippled is gotten by filling the % current path (e.g. the interior of a polygon); if it's false, the % area is gotten by stroking the current path (e.g. a wide line). % Each stipple dot is assumed to be about one unit across in the % current user coordinate system. /StippleFill { % Turn the path into a clip region that we can then cover with % lots of images corresponding to the stipple pattern. Warning: % some Postscript interpreters get errors during strokepath for % dashed lines. If this happens, turn off dashes and try again. 1 index /tmpstip exch def %% Works around NeWSprint bug gsave {eoclip} {{strokepath} stopped {grestore gsave [] 0 setdash strokepath} if clip} ifelse % Change the scaling so that one user unit in user coordinates % corresponds to the size of one stipple dot. 1 EvenPixels dup scale % Compute the bounding box occupied by the path (which is now % the clipping region), and round the lower coordinates down % to the nearest starting point for the stipple pattern. pathbbox 4 2 roll 5 index div cvi 5 index mul 4 1 roll 6 index div cvi 6 index mul 3 2 roll % Stack now: width height string y1 y2 x1 x2 % Below is a doubly-nested for loop to iterate across this area % in units of the stipple pattern size, going up columns then % across rows, blasting out a stipple-pattern-sized rectangle at % each position 6 index exch { 2 index 5 index 3 index { % Stack now: width height string y1 y2 x y gsave 1 index exch translate 5 index 5 index true matrix tmpstip imagemask grestore } for pop } for pop pop pop pop pop grestore newpath } bind def % -- AdjustColor -- % Given a color value already set for output by the caller, adjusts % that value to a grayscale or mono value if requested by the CL % variable. /AdjustColor { CL 2 lt { currentgray CL 0 eq { .5 lt {0} {1} ifelse } if setgray } if } bind def % x y strings spacing xoffset yoffset justify stipple stipimage DrawText -- % This procedure does all of the real work of drawing text. The % color and font must already have been set by the caller, and the % following arguments must be on the stack: % % x, y - Coordinates at which to draw text. % strings - An array of strings, one for each line of the text item, % in order from top to bottom. % spacing - Spacing between lines. % xoffset - Horizontal offset for text bbox relative to x and y: 0 for % nw/w/sw anchor, -0.5 for n/center/s, and -1.0 for ne/e/se. % yoffset - Vertical offset for text bbox relative to x and y: 0 for % nw/n/ne anchor, +0.5 for w/center/e, and +1.0 for sw/s/se. % justify - 0 for left justification, 0.5 for center, 1 for right justify. % stipple - Boolean value indicating whether or not text is to be % drawn in stippled fashion. % stipimage - Image for stippling, if stipple is True. % % Also, when this procedure is invoked, the color and font must already % have been set for the text. /DrawText { /stipimage exch def /stipple exch def /justify exch def /yoffset exch def /xoffset exch def /spacing exch def /strings exch def % First scan through all of the text to find the widest line. /maxwidth 0 def strings { stringwidth pop dup maxwidth gt {/maxwidth exch def} {pop} ifelse newpath } forall % Compute the baseline offset and the actual font height. 0 0 moveto (TXygqPZ) false charpath pathbbox dup /baseline exch def exch pop exch sub /height exch def pop newpath % Translate coordinates first so that the origin is at the upper-left % corner of the text's bounding box. Remember that x and y for % positioning are still on the stack. translate maxwidth xoffset mul strings length 1 sub spacing mul height add yoffset mul translate % Now use the baseline and justification information to translate so % that the origin is at the baseline and positioning point for the % first line of text. justify maxwidth mul baseline neg translate % Iterate over each of the lines to output it. For each line, % compute its width again so it can be properly justified, then % display it. strings { dup stringwidth pop justify neg mul 0 moveto show 0 spacing neg translate } forall } bind def /CL 1 def save 306.0 396.0 translate 0.432 0.432 scale -250 -250 translate 0 500 moveto 500 500 lineto 500 0 lineto 0 0 lineto closepath clip newpath gsave 80 470 moveto 400 0 rlineto 0 -420 rlineto -400 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 280 485 [ (Processes slowed by a factor of 5 or more) ] 21 -0.5 0.5 0 () false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 105 35.0000000000001 [ (0) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 85 271.092 moveto 13 0 rlineto 0 -221.092 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 85 271.092 moveto 13 0 rlineto 0 -221.092 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 98 151.645 moveto 13 0 rlineto 0 -101.645 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 98 151.645 moveto 13 0 rlineto 0 -101.645 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 111 60.497 moveto 13 0 rlineto 0 -10.497 rlineto -13 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 111 60.497 moveto 13 0 rlineto 0 -10.497 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 155 35.0000000000001 [ (1) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 135 273.398 moveto 13 0 rlineto 0 -223.398 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 135 273.398 moveto 13 0 rlineto 0 -223.398 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 148 179.492 moveto 13 0 rlineto 0 -129.492 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 148 179.492 moveto 13 0 rlineto 0 -129.492 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 161 67.213 moveto 13 0 rlineto 0 -17.213 rlineto -13 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 161 67.213 moveto 13 0 rlineto 0 -17.213 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 205 35.0000000000001 [ (2) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 185 187.387 moveto 13 0 rlineto 0 -137.387 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 185 187.387 moveto 13 0 rlineto 0 -137.387 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 198 108.26 moveto 13 0 rlineto 0 -58.2599999999999 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 198 108.26 moveto 13 0 rlineto 0 -58.2599999999999 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 211 62.273 moveto 13 0 rlineto 0 -12.273 rlineto -13 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 211 62.273 moveto 13 0 rlineto 0 -12.273 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 255 35.0000000000001 [ (3) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 235 161.046 moveto 13 0 rlineto 0 -111.046 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 235 161.046 moveto 13 0 rlineto 0 -111.046 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 248 91.407 moveto 13 0 rlineto 0 -41.407 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 248 91.407 moveto 13 0 rlineto 0 -41.407 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 261 61.644 moveto 13 0 rlineto 0 -11.644 rlineto -13 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 261 61.644 moveto 13 0 rlineto 0 -11.644 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 305 35.0000000000001 [ (4) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 285 240.295 moveto 12.9999999999999 0 rlineto 0 -190.295 rlineto -12.9999999999999 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 285 240.295 moveto 12.9999999999999 0 rlineto 0 -190.295 rlineto -12.9999999999999 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 298 137.408 moveto 13.0000000000001 0 rlineto 0 -87.408 rlineto -13.0000000000001 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 298 137.408 moveto 13.0000000000001 0 rlineto 0 -87.408 rlineto -13.0000000000001 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 311 65.36 moveto 12.9999999999999 0 rlineto 0 -15.36 rlineto -12.9999999999999 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 311 65.36 moveto 12.9999999999999 0 rlineto 0 -15.36 rlineto -12.9999999999999 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 355 35.0000000000001 [ (5) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 335 418.735 moveto 13 0 rlineto 0 -368.735 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 335 418.735 moveto 13 0 rlineto 0 -368.735 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 348 175.806 moveto 13 0 rlineto 0 -125.806 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 348 175.806 moveto 13 0 rlineto 0 -125.806 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 361 74.005 moveto 13.0000000000001 0 rlineto 0 -24.005 rlineto -13.0000000000001 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 361 74.005 moveto 13.0000000000001 0 rlineto 0 -24.005 rlineto -13.0000000000001 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 405 35.0000000000001 [ (6) ] 21 -0.5 0.5 0 () false DrawText grestore gsave 385 418.699 moveto 13 0 rlineto 0 -368.699 rlineto -13 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 385 418.699 moveto 13 0 rlineto 0 -368.699 rlineto -13 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 398 213.41 moveto 13 0 rlineto 0 -163.41 rlineto -13 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 398 213.41 moveto 13 0 rlineto 0 -163.41 rlineto -13 0 rlineto closepath 1 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b(jobs)g(later)g(in)h(their)g(liv)n(es.)533 1643 y Fo(Migr)l(ating)j(short-live)l(d)g(jobs.)43 b Ft(This)c(t)n(yp)r(e)g(of)g(error)e(imp)r(oses)h(large)g(slo)n(wdo)n (wns)f(on)h(the)450 1742 y(migrated)27 b(pro)r(cess,)f(w)n(astes)h(net) n(w)n(ork)f(resources,)f(and)j(fails)f(to)h(e\013ect)g(signi\014can)n (t)f(load)f(bal-)450 1842 y(ancing.)45 b(Under)30 b(non-preemptiv)n(e)g (migration,)g(this)h(error)d(o)r(ccurs)i(when)g(a)g(pro)r(cess)g(whose) 450 1941 y(name)f(is)h(on)g(the)g(eligible)f(list)h(turns)g(out)f(to)h (b)r(e)g(short-liv)n(ed.)42 b(Our)29 b(preemptiv)n(e)g(migration)450 2041 y(strategy)c(all)h(but)h(eliminates)f(this)g(t)n(yp)r(e)h(of)f (error)e(b)n(y)i(guaran)n(teeing)e(that)i(the)h(p)r(erformance)450 2141 y(of)h(a)f(migran)n(t)f(impro)n(v)n(es)g(in)i(exp)r(ectation.)533 2275 y(Ev)n(en)18 b(o)r(ccasional)g(mistak)n(es)g(of)h(the)g(\014rst)g (kind)h(can)e(ha)n(v)n(e)g(a)h(large)f(impact)h(on)g(p)r(erformance,) 450 2375 y(b)r(ecause)k(one)h(long)f(job)g(on)h(a)f(busy)h(mac)n(hine)f (will)h(imp)r(ede)g(man)n(y)f(small)h(jobs.)35 b(This)24 b(e\013ect)g(is)450 2475 y(aggra)n(v)-5 b(ated)27 b(b)n(y)h(the)i (serial)e(correlation)f(b)r(et)n(w)n(een)i(arriv)-5 b(al)28 b(times)i(\(see)f(Section)g(5.1\),)g(whic)n(h)450 2574 y(suggests)d(that)i(a)f(busy)h(host)f(is)h(lik)n(ely)f(to)g(receiv)n(e) g(man)n(y)g(future)h(arriv)-5 b(als.)533 2674 y(Th)n(us,)20 b(an)f(imp)r(ortan)n(t)f(feature)h(of)g(a)f(migration)g(p)r(olicy)g(is) h(its)g(abilit)n(y)f(to)h(iden)n(tify)g(long-liv)n(ed)450 2773 y(jobs)27 b(for)g(migration.)36 b(T)-7 b(o)27 b(ev)-5 b(aluate)28 b(this)g(abilit)n(y)-7 b(,)27 b(w)n(e)g(consider)g(the)h(a) n(v)n(erage)c(lifetime)29 b(of)e(the)450 2873 y(pro)r(cesses)20 b(c)n(hosen)h(for)g(migration)f(under)i(eac)n(h)f(p)r(olicy)-7 b(.)35 b(Under)21 b(non-preemptiv)n(e)g(migration,)450 2973 y(the)27 b(a)n(v)n(erage)c(lifetime)k(of)f(migran)n(t)g(pro)r (cesses)e(w)n(as)i(2)p Fm(:)p Ft(0)f(seconds)g(\(the)i(mean)f(lifetime) h(for)f(all)450 3072 y(pro)r(cesses)c(is)i(0)p Fm(:)p Ft(4)f(seconds\),)i(and)e(the)i(median)f(lifetime)g(of)g(migran)n(ts)f (w)n(as)g(0)p Fm(:)p Ft(9)g(seconds.)35 b(The)450 3172 y(non-preemptiv)n(e)26 b(p)r(olicy)h(migrated)g(ab)r(out)g(1\045)g(of)h (all)f(jobs,)g(whic)n(h)g(accoun)n(ted)f(for)h(5)p Fm(:)p Ft(7\045)g(of)450 3272 y(the)h(total)f(CPU.)533 3371 y(The)h(preemptiv)n(e)f(migration)f(p)r(olicy)i(w)n(as)f(b)r(etter)h (able)f(to)g(iden)n(tify)i(long)d(jobs;)i(the)g(a)n(v)n(er-)450 3471 y(age)f(lifetime)i(of)e(migran)n(t)g(pro)r(cesses)g(under)g (preemptiv)n(e)h(migration)e(w)n(as)h(4)p Fm(:)p Ft(9)g(seconds;)g(the) 450 3571 y(median)j(lifetime)h(of)e(migran)n(ts)g(w)n(as)g(2)p Fm(:)p Ft(0)g(seconds.)43 b(The)30 b(preemptiv)n(e)f(p)r(olicy)h (migrated)f(4\045)450 3670 y(of)d(all)g(jobs,)h(but)g(since)f(these)h (migran)n(ts)e(w)n(ere)g(long-liv)n(ed,)g(they)i(accoun)n(ted)f(for)f (55\045)h(of)g(the)450 3770 y(total)h(CPU.)533 3869 y(Th)n(us)g(the)g (primary)f(reason)f(for)h(the)i(success)e(of)g(preemptiv)n(e)h (migration)f(is)g(its)h(abilit)n(y)g(to)450 3969 y(iden)n(tify)h(long)f (jobs)g(accurately)g(and)g(to)h(migrate)e(those)h(jobs)h(a)n(w)n(a)n(y) d(from)j(busy)f(hosts.)533 4069 y(The)36 b(second)g(t)n(yp)r(e)h(of)f (error)e(did)j(not)g(ha)n(v)n(e)e(as)g(great)h(an)g(impact)g(on)g(the)h (mean)f(slo)n(w-)450 4168 y(do)n(wn)26 b(for)f(all)h(pro)r(cesses,)f (but)i(it)g(did)f(imp)r(ose)h(large)d(slo)n(wdo)n(wns)h(on)h(some)f (small)h(pro)r(cesses.)450 4268 y(These)h(outliers)g(are)f(re\015ected) i(in)f(the)h(standard)f(deviation)g(of)g(slo)n(wdo)n(wns)f(|)h(b)r (ecause)g(the)450 4368 y(non-preemptiv)n(e)k(p)r(olicy)g(sometimes)h (migrates)e(v)n(ery)h(short)g(jobs,)i(it)f(can)f(mak)n(e)g(the)h(stan-) 450 4467 y(dard)g(deviation)h(of)g(slo)n(wdo)n(wns)e(w)n(orse)g(than)i (with)g(no)g(migration)f(\(see)h(Figure)f(5b\).)53 b(The)450 4567 y(age-based)36 b(preemptiv)n(e)i(migration)f(criterion)h (eliminates)g(most)g(errors)e(of)i(this)h(t)n(yp)r(e)f(b)n(y)450 4666 y(guaran)n(teeing)25 b(that)j(the)g(p)r(erformance)f(of)g(the)h (migran)n(t)f(will)h(impro)n(v)n(e)e(in)i(exp)r(ectation.)533 4766 y(There)f(is,)h(ho)n(w)n(ev)n(er,)e(one)i(t)n(yp)r(e)g(of)g (migration)e(error)g(that)i(is)g(more)f(problematic)g(for)h(pre-)450 4866 y(emptiv)n(e)k(migration)f(than)i(for)f(non-preemptiv)n(e)f (migration:)45 b(stale)32 b(load)f(information.)51 b(A)450 4965 y(target)33 b(host)g(ma)n(y)g(ha)n(v)n(e)f(a)h(lo)n(w)g(load)g (when)g(a)h(migration)e(is)h(initiated,)j(but)e(its)g(load)f(ma)n(y)450 5065 y(ha)n(v)n(e)22 b(increased)f(b)n(y)i(the)g(time)g(the)h(migran)n (t)e(arriv)n(es.)33 b(This)22 b(is)h(more)f(lik)n(ely)h(for)f(a)g (preemptiv)n(e)p eop %%Page: 24 24 24 23 bop 450 250 a Fq(24)142 b Fp(\001)158 b Fq(M.)26 b(Ha)n(rchol-Balter)f(and)f(A.)j(B.)f(Do)n(wney)450 465 y Ft(migration)h(b)r(ecause)h(the)g(migration)g(time)g(is)g(longer.)38 b(In)28 b(our)g(sim)n(ulations,)f(w)n(e)h(found)h(that)450 565 y(these)d(errors)d(do)j(o)r(ccur,)f(although)g(infrequen)n(tly)h (enough)f(that)h(they)g(do)g(not)f(ha)n(v)n(e)g(a)g(sev)n(ere)450 665 y(impact)j(on)f(p)r(erformance.)533 765 y(Sp)r(eci\014cally)-7 b(,)25 b(w)n(e)f(coun)n(ted)g(the)h(n)n(um)n(b)r(er)f(of)h(migran)n(t)e (pro)r(cesses)g(that)i(arriv)n(ed)d(at)j(a)f(target)450 865 y(host)j(and)g(found)h(that)f(the)h(load)f(w)n(as)f(higher)h(than)g (it)h(had)f(b)r(een)h(at)f(the)h(source)e(host)h(when)450 965 y(migration)g(b)r(egan.)38 b(F)-7 b(or)28 b(most)g(runs,)g(this)g (o)r(ccurred)f(less)h(than)g(0)p Fm(:)p Ft(5\045)f(of)i(the)f(time)h (\(for)f(t)n(w)n(o)450 1064 y(runs)22 b(with)g(high)g(loads)g(it)g(w)n (as)f(0)p Fm(:)p Ft(7\045\).)35 b(Somewhat)22 b(more)f(often,)j(3\045)e (of)g(the)g(time,)i(a)e(migran)n(t)450 1164 y(pro)r(cess)28 b(arriv)n(ed)f(at)i(a)g(target)f(host)h(and)g(found)g(that)g(the)h (load)e(at)h(the)g(target)g(w)n(as)f(greater)450 1263 y(than)f(the)g Fo(curr)l(ent)f Ft(load)g(at)h(the)g(source.)36 b(These)26 b(results)h(suggest)f(that)h(the)g(p)r(erformance)f(of)450 1363 y(a)j(preemptiv)n(e)g(migration)g(strategy)f(migh)n(t)i(b)r(e)g (impro)n(v)n(ed)e(b)n(y)h(a)g(reserv)-5 b(ation)28 b(system)i(as)f(in) 450 1463 y(MOSIX.)533 1563 y(One)36 b(other)f(p)r(oten)n(tial)h (problem)g(with)g(preemptiv)n(e)g(migration)f(is)h(the)g(v)n(olume)g (of)g(net-)450 1663 y(w)n(ork)30 b(tra\016c)i(that)g(results)f(from)g (large)g(memory)g(transfers.)48 b(In)32 b(our)f(sim)n(ulations,)h(w)n (e)f(did)450 1762 y(not)25 b(mo)r(del)h(net)n(w)n(ork)e(congestion,)h (on)g(the)h(assumption)f(that)h(the)f(tra\016c)g(generated)g(b)n(y)g (mi-)450 1862 y(gration)33 b(w)n(ould)h(not)g(b)r(e)g(excessiv)n(e.)56 b(This)34 b(assumption)f(seems)h(to)g(b)r(e)h(reasonable:)48 b(under)450 1962 y(our)32 b(preemptiv)n(e)h(migration)e(strategy)h(few) n(er)g(than)h(4\045)g(of)g(pro)r(cesses)e(are)h(migrated)g(once)450 2061 y(and)24 b(few)n(er)f(than)h Fm(:)p Ft(25\045)f(of)h(pro)r(cesses) e(are)h(migrated)g(more)g(than)h(once.)35 b(F)-7 b(urthermore,)24 b(there)450 2161 y(is)j(seldom)h(more)e(than)i(one)f(migration)g(in)h (progress)d(at)i(a)h(time.)533 2261 y(In)23 b(summary)-7 b(,)23 b(the)h(adv)-5 b(an)n(tage)21 b(of)i(preemptiv)n(e)g(migration)e (|)i(its)h(abilit)n(y)e(to)h(iden)n(tify)h(long)450 2361 y(jobs)k(and)h(mo)n(v)n(e)e(them)i(a)n(w)n(a)n(y)e(from)h(busy)h(hosts) f(|)g(o)n(v)n(ercomes)e(its)j(disadv)-5 b(an)n(tages)27 b(\(longer)450 2461 y(migration)f(times)i(and)g(stale)f(load)g (information\).)533 2620 y(5.4.1)41 b Fo(E\013e)l(ct)28 b(of)i(migr)l(ation)f(on)f(short)h(and)g(long)g(jobs.)43 b Ft(W)-7 b(e)26 b(ha)n(v)n(e)f(claimed)h(that)h(iden)n(tify-)450 2720 y(ing)22 b(long)g(jobs)g(and)g(migrating)f(them)i(a)n(w)n(a)n(y)d (from)i(busy)g(hosts)g(helps)h(not)f(only)g(the)g(long)g(jobs)450 2819 y(\(whic)n(h)33 b(run)f(on)g(more)f(ligh)n(tly-loaded)g(hosts\))h (but)h(also)e(the)i(short)f(jobs)g(that)g(run)g(on)g(the)450 2919 y(source)26 b(host.)36 b(T)-7 b(o)27 b(test)h(this)f(claim,)h(w)n (e)e(divided)i(the)f(pro)r(cesses)f(in)n(to)h(three)g(lifetime)h (groups)450 3019 y(and)e(measured)g(the)h(p)r(erformance)f(b)r (ene\014t)h(for)f(eac)n(h)g(group)g(due)g(to)h(migration.)35 b(The)27 b(n)n(um-)450 3118 y(b)r(er)k(of)f(jobs)h(in)f(short)g(group)g (is)g(roughly)g(ten)h(times)f(the)h(n)n(um)n(b)r(er)g(in)g(the)g (medium)g(group,)450 3218 y(whic)n(h)f(in)h(turn)f(is)g(roughly)f(ten)i (times)f(the)h(n)n(um)n(b)r(er)f(in)g(the)h(long)e(group.)44 b(Figure)29 b(6)h(sho)n(ws)450 3317 y(that)c(migration)f(reduces)g(the) i(mean)f(slo)n(wdo)n(wn)e(of)i(all)g(three)g(groups:)34 b(for)26 b(non-preemptiv)n(e)450 3417 y(migration)f(the)i(impro)n(v)n (emen)n(t)e(is)h(the)g(same)g(for)g(all)g(groups;)f(under)h(preemptiv)n (e)g(migration)450 3517 y(the)i(long)f(jobs)g(enjo)n(y)g(a)h(sligh)n (tly)f(greater)e(b)r(ene\014t.)533 3617 y(This)i(breakdo)n(wn)e(b)n(y)i (lifetime)h(group)e(is)h(useful)g(for)g(ev)-5 b(aluating)26 b(v)-5 b(arious)26 b(metrics)h(of)g(sys-)450 3717 y(tem)k(p)r (erformance.)46 b(The)31 b(metric)g(w)n(e)g(are)e(using)i(here,)g(slo)n (wdo)n(wn,)g(giv)n(es)e(equal)i(w)n(eigh)n(t)f(to)450 3816 y(all)25 b(jobs;)h(as)f(a)h(result,)f(the)h(mean)g(slo)n(wdo)n(wn) e(metric)h(is)h(dominated)f(b)n(y)h(the)g(most)f(p)r(opulous)450 3916 y(group,)f(short)g(jobs.)36 b(Another)25 b(common)f(metric,)h (residence)g(time,)h(e\013ectiv)n(ely)e(w)n(eigh)n(ts)g(jobs)450 4016 y(according)h(to)j(their)f(lifetimes.)37 b(Th)n(us)27 b(the)h(mean)f(residence)f(time)i(metric)f(re\015ects,)g(primar-)450 4115 y(ily)-7 b(,)31 b(the)f(p)r(erformance)f(b)r(ene\014t)i(for)f (long)f(jobs.)44 b(Under)30 b(the)g(mean)g(residence)f(time)i(metric,) 450 4215 y(then,)d(preemptiv)n(e)f(migration)g(app)r(ears)f(ev)n(en)h (more)g(e\013ectiv)n(e.)450 4400 y Fx(5.5)41 b(Evaluation)26 b(of)h(analytic)h(migration)e(criterion)450 4534 y Ft(As)g(deriv)n(ed)f (in)h(Section)g(3.1,)g(the)g(minim)n(um)g(age)f(for)h(a)f(migran)n(t)g (pro)r(cess)g(according)f(to)i(our)450 4633 y Fo(analytic)31 b(criterion)e Ft(is)1439 4796 y(Minim)n(um)1366 4896 y(migration)d(age)1908 4847 y(=)2005 4791 y(Migration)h(cost)p 2005 4828 529 4 v 2158 4904 a Fm(n)18 b Fl(\000)g Fm(m)450 5065 y Ft(where)j Fm(n)g Ft(is)g(the)g(load)g(at)g(the)g(source)f(host) h(and)g Fm(m)g Ft(is)g(the)g(load)g(at)g(the)g(target)g(host)f (\(including)p eop %%Page: 25 25 25 24 bop 783 250 a Fq(Exploiting)24 b(Pro)r(cess)j(Lifetime)e (Distributions)e(fo)n(r)j(Dynamic)f(Load)g(Balancing)157 b Fp(\001)141 b Fq(25)1194 660 y 11840716 11840716 5920358 11840716 34403860 40324218 startTexFig 1194 660 a %%BeginDocument: har6.ps 50 dict begin % This is a standard prolog for Postscript generated by Tk's canvas % widget. % @(#) prolog.ps 1.2 94/12/09 10:53:18 % The definitions below just define all of the variables used in % any of the procedures here. This is needed for obscure reasons % explained on p. 716 of the Postscript manual (Section H.2.7, % "Initializing Variables," in the section on Encapsulated Postscript). /baseline 0 def /stipimage 0 def /height 0 def /justify 0 def /lineLength 0 def /spacing 0 def /stipple 0 def /strings 0 def /xoffset 0 def /yoffset 0 def /tmpstip null def % Define the array ISOLatin1Encoding (which specifies how characters are % encoded for ISO-8859-1 fonts), if it isn't already present (Postscript % level 2 is supposed to define it, but level 1 doesn't). systemdict /ISOLatin1Encoding known not { /ISOLatin1Encoding [ /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /minus /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /less /equal /greater /question /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /braceleft /bar /braceright /asciitilde /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /space /dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent /dieresis /space /ring /cedilla /space /hungarumlaut /ogonek /caron /space /exclamdown /cent /sterling /currency /yen /brokenbar /section /dieresis /copyright /ordfeminine /guillemotleft /logicalnot /hyphen /registered /macron /degree /plusminus /twosuperior /threesuperior /acute /mu /paragraph /periodcentered /cedillar /onesuperior /ordmasculine /guillemotright /onequarter /onehalf /threequarters /questiondown /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla /Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis /Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply /Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls /agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla /egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis /eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide /oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis ] def } if % Override the setfont procedure with a new procedure that re-encodes % the font to use the ISO Latin-1 style. The body of this procedure % comes from Section 5.6.1 of the Postscript book. /realsetfont /setfont load def /setfont { dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end % I'm not sure why it's necessary to use "definefont" on this new % font, but it seems to be important; just use the name "Temporary" % for the font. /Temporary exch definefont realsetfont } bind def % StrokeClip % % This procedure converts the current path into a clip area under % the assumption of stroking. It's a bit tricky because some Postscript % interpreters get errors during strokepath for dashed lines. If % this happens then turn off dashes and try again. /StrokeClip { {strokepath} stopped { (This Postscript printer gets limitcheck overflows when) = (stippling dashed lines; lines will be printed solid instead.) = [] 0 setdash strokepath} if clip } bind def % desiredSize EvenPixels closestSize % % The procedure below is used for stippling. Given the optimal size % of a dot in a stipple pattern in the current user coordinate system, % compute the closest size that is an exact multiple of the device's % pixel size. This allows stipple patterns to be displayed without % aliasing effects. /EvenPixels { % Compute exact number of device pixels per stipple dot. dup 0 matrix currentmatrix dtransform dup mul exch dup mul add sqrt % Round to an integer, make sure the number is at least 1, and compute % user coord distance corresponding to this. dup round dup 1 lt {pop 1} if exch div mul } bind def % width height string StippleFill -- % % Given a path already set up and a clipping region generated from % it, this procedure will fill the clipping region with a stipple % pattern. "String" contains a proper image description of the % stipple pattern and "width" and "height" give its dimensions. Each % stipple dot is assumed to be about one unit across in the current % user coordinate system. This procedure trashes the graphics state. /StippleFill { % The following code is needed to work around a NeWSprint bug. /tmpstip 1 index def % Change the scaling so that one user unit in user coordinates % corresponds to the size of one stipple dot. 1 EvenPixels dup scale % Compute the bounding box occupied by the path (which is now % the clipping region), and round the lower coordinates down % to the nearest starting point for the stipple pattern. Be % careful about negative numbers, since the rounding works % differently on them. pathbbox 4 2 roll 5 index div dup 0 lt {1 sub} if cvi 5 index mul 4 1 roll 6 index div dup 0 lt {1 sub} if cvi 6 index mul 3 2 roll % Stack now: width height string y1 y2 x1 x2 % Below is a doubly-nested for loop to iterate across this area % in units of the stipple pattern size, going up columns then % across rows, blasting out a stipple-pattern-sized rectangle at % each position 6 index exch { 2 index 5 index 3 index { % Stack now: width height string y1 y2 x y gsave 1 index exch translate 5 index 5 index true matrix tmpstip imagemask grestore } for pop } for pop pop pop pop pop } bind def % -- AdjustColor -- % Given a color value already set for output by the caller, adjusts % that value to a grayscale or mono value if requested by the CL % variable. /AdjustColor { CL 2 lt { currentgray CL 0 eq { .5 lt {0} {1} ifelse } if setgray } if } bind def % x y strings lineLength spacing xoffset yoffset justify stipple DrawText -- % This procedure does all of the real work of drawing text. The % color and font must already have been set by the caller, and the % following arguments must be on the stack: % % x, y - Coordinates at which to draw text. % strings - An array of strings, one for each line of the text item, % in order from top to bottom. % lineLength - Minimum line length: needed to justify text properly. % spacing - Spacing between lines. % xoffset - Horizontal offset for text bbox relative to x and y: 0 for % nw/w/sw anchor, -0.5 for n/center/s, and -1.0 for ne/e/se. % yoffset - Vertical offset for text bbox relative to x and y: 0 for % nw/n/ne anchor, +0.5 for w/center/e, and +1.0 for sw/s/se. % justify - 0 for left justification, 0.5 for center, 1 for right justify. % stipple - Boolean value indicating whether or not text is to be % drawn in stippled fashion. If text is stippled, % procedure StippleText must have been defined to call % StippleFill in the right way. % % Also, when this procedure is invoked, the color and font must already % have been set for the text. /DrawText { /stipple exch def /justify exch def /yoffset exch def /xoffset exch def /spacing exch def /lineLength exch def /strings exch def % First scan through all of the text to find the widest line (if it's % longer than the "lineLength" argument). strings { stringwidth pop dup lineLength gt {/lineLength exch def} {pop} ifelse newpath } forall % Compute the baseline offset and the actual font height. 0 0 moveto (TXygqPZ) false charpath pathbbox dup /baseline exch def exch pop exch sub /height exch def pop newpath % Translate coordinates first so that the origin is at the upper-left % corner of the text's bounding box. Remember that x and y for % positioning are still on the stack. translate lineLength xoffset mul strings length 1 sub spacing mul height add yoffset mul translate % Now use the baseline and justification information to translate so % that the origin is at the baseline and positioning point for the % first line of text. justify lineLength mul baseline neg translate % Iterate over each of the lines to output it. For each line, % compute its width again so it can be properly justified, then % display it. strings { dup stringwidth pop justify neg mul 0 moveto stipple { % The text is stippled, so turn it into a path and print % by calling StippledText, which in turn calls StippleFill. % Unfortunately, many Postscript interpreters will get % overflow errors if we try to do the whole string at % once, so do it a character at a time. gsave /char (X) def { char 0 3 -1 roll put currentpoint gsave char true charpath clip StippleText grestore char stringwidth translate moveto } forall grestore } {show} ifelse 0 spacing neg translate } forall } bind def /CL 1 def save 306.0 396.0 translate 0.8521 0.8521 scale -253 -253 translate 0 507 moveto 507 507 lineto 507 0 lineto 0 0 lineto closepath clip newpath gsave 80 447 moveto 400 0 rlineto 0 -380 rlineto -400 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 280 487 [ (Mean slowdown by age group) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave 452 438 moveto 17.0000000000001 0 rlineto 0 -17 rlineto -17.0000000000001 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 452 438 moveto 17.0000000000001 0 rlineto 0 -17 rlineto -17.0000000000001 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 440 430 [ (no migration) ] 0 20 -1 0.5 0 false DrawText grestore gsave 452 417 moveto 17.0000000000001 0 rlineto 0 -17 rlineto -17.0000000000001 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 452 417 moveto 17.0000000000001 0 rlineto 0 -17 rlineto -17.0000000000001 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 440 409 [ (non-preemptive migration) ] 0 20 -1 0.5 0 false DrawText grestore gsave 452 396 moveto 17.0000000000001 0 rlineto 0 -17 rlineto -17.0000000000001 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 452 396 moveto 17.0000000000001 0 rlineto 0 -17 rlineto -17.0000000000001 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 440 388 [ (preemptive migration) ] 0 20 -1 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 495 12 [ (Duration) ] 0 20 -1 1 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 45 67 [ (1.0) ] 0 20 -1 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 45 162 [ (1.5) ] 0 20 -1 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 45 257 [ (2.0) ] 0 20 -1 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 45 352 [ (2.5) ] 0 20 -1 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 45 447 [ (3.0) ] 0 20 -1 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 146.667 46.9999999999999 [ (dur < .5s) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 280 46.9999999999999 [ (.5s < dur < 5s) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave /Helvetica findfont 18 scalefont setfont 0.000 0.000 0.000 setrgbcolor AdjustColor 413.333 46.9999999999999 [ (dur > 5s.) ] 0 20 -0.5 0.5 0 false DrawText grestore gsave 89.5238 371.409 moveto 38.0952 0 rlineto 0 -304.409 rlineto -38.0952 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 89.5238 371.409 moveto 38.0952 0 rlineto 0 -304.409 rlineto -38.0952 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 127.619 297.515 moveto 38.095 0 rlineto 0 -230.515 rlineto -38.095 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 127.619 297.515 moveto 38.095 0 rlineto 0 -230.515 rlineto -38.095 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 165.714 204.98 moveto 38.095 0 rlineto 0 -137.98 rlineto -38.095 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 165.714 204.98 moveto 38.095 0 rlineto 0 -137.98 rlineto -38.095 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 222.857 367.202 moveto 38.095 0 rlineto 0 -300.202 rlineto -38.095 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 222.857 367.202 moveto 38.095 0 rlineto 0 -300.202 rlineto -38.095 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 260.952 253.955 moveto 38.095 0 rlineto 0 -186.955 rlineto -38.095 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 260.952 253.955 moveto 38.095 0 rlineto 0 -186.955 rlineto -38.095 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 299.047 185.131 moveto 38.095 0 rlineto 0 -118.131 rlineto -38.095 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 299.047 185.131 moveto 38.095 0 rlineto 0 -118.131 rlineto -38.095 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 356.19 370.536 moveto 38.095 0 rlineto 0 -303.536 rlineto -38.095 0 rlineto closepath 0.898 0.898 0.898 setrgbcolor AdjustColor fill 356.19 370.536 moveto 38.095 0 rlineto 0 -303.536 rlineto -38.095 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 394.285 243.575 moveto 38.095 0 rlineto 0 -176.575 rlineto -38.095 0 rlineto closepath 0.702 0.702 0.702 setrgbcolor AdjustColor fill 394.285 243.575 moveto 38.095 0 rlineto 0 -176.575 rlineto -38.095 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke grestore gsave 432.38 129.4 moveto 38.0950000000001 0 rlineto 0 -62.4 rlineto -38.0950000000001 0 rlineto closepath 0.498 0.498 0.498 setrgbcolor AdjustColor fill 432.38 129.4 moveto 38.0950000000001 0 rlineto 0 -62.4 rlineto -38.0950000000001 0 rlineto closepath 1 setlinewidth 0 setlinejoin 2 setlinecap 0.000 0.000 0.000 setrgbcolor AdjustColor stroke 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Header:/user6/ouster/wish/library/RCS/prolog.ps,v1.693/04/0114:03:52ousterExp SPRITE (Berkeley); 50 dict begin % The definitions below just define all of the variables used in % any of the procedures here. This is needed for obscure reasons % explained on p. 716 of the Postscript manual (Section H.2.7, % "Initializing Variables," in the section on Encapsulated Postscript). /baseline 0 def /stipimage 0 def /height 0 def /justify 0 def /maxwidth 0 def /spacing 0 def /stipple 0 def /strings 0 def /xoffset 0 def /yoffset 0 def /tmpstip null def /encoding {ISOLatin1Encoding} def % Override setfont to automatically encode the font in the style defined by % by 'encoding' (ISO Latin1 by default). systemdict /encodefont known { /realsetfont /setfont load def /setfont { encoding encodefont realsetfont } def } if % desiredSize EvenPixels closestSize % % The procedure below is used for stippling. Given the optimal size % of a dot in a stipple pattern in the current user coordinate system, % compute the closest size that is an exact multiple of the device's % pixel size. This allows stipple patterns to be displayed without % aliasing effects. /EvenPixels { % Compute exact number of device pixels per stipple dot. dup 0 matrix currentmatrix dtransform dup mul exch dup mul add sqrt % Round to an integer, make sure the number is at least 1, and compute % user coord distance corresponding to this. dup round dup 1 lt {pop 1} if exch div mul } bind def % width height string filled StippleFill -- % % Given a path and other graphics information already set up, this % procedure will fill the current path in a stippled fashion. "String" % contains a proper image description of the stipple pattern and % "width" and "height" give its dimensions. If "filled" is true then % it means that the area to be stippled is gotten by filling the % current path (e.g. the interior of a polygon); if it's false, the % area is gotten by stroking the current path (e.g. a wide line). % Each stipple dot is assumed to be about one unit across in the % current user coordinate system. /StippleFill { % Turn the path into a clip region that we can then cover with % lots of images corresponding to the stipple pattern. Warning: % some Postscript interpreters get errors during strokepath for % dashed lines. If this happens, turn off dashes and try again. 1 index /tmpstip exch def %% Works around NeWSprint bug gsave {eoclip} {{strokepath} stopped {grestore gsave [] 0 setdash strokepath} if clip} ifelse % Change the scaling so that one user unit in user coordinates % corresponds to the size of one stipple dot. 1 EvenPixels dup scale % Compute the bounding box occupied by the path (which is now % the clipping region), and round the lower coordinates down % to the nearest starting point for the stipple pattern. pathbbox 4 2 roll 5 index div cvi 5 index mul 4 1 roll 6 index div cvi 6 index mul 3 2 roll % Stack now: width height string y1 y2 x1 x2 % Below is a doubly-nested for loop to iterate across this area % in units of the stipple pattern size, going up columns then % across rows, blasting out a stipple-pattern-sized rectangle at % each position 6 index exch { 2 index 5 index 3 index { % Stack now: width height string y1 y2 x y gsave 1 index exch translate 5 index 5 index true matrix tmpstip imagemask grestore } for pop } for pop pop pop pop pop grestore newpath } bind def % -- AdjustColor -- % Given a color value already set for output by the caller, adjusts % that value to a grayscale or mono value if requested by the CL % variable. /AdjustColor { CL 2 lt { currentgray CL 0 eq { .5 lt {0} {1} ifelse } if setgray } if } bind def % x y strings spacing xoffset yoffset justify stipple stipimage DrawText -- % This procedure does all of the real work of drawing text. The % color and font must already have been set by the caller, and the % following arguments must be on the stack: % % x, y - Coordinates at which to draw text. % strings - An array of strings, one for each line of the text item, % in order from top to bottom. % spacing - Spacing between lines. % xoffset - Horizontal offset for text bbox relative to x and y: 0 for % nw/w/sw anchor, -0.5 for n/center/s, and -1.0 for ne/e/se. % yoffset - Vertical offset for text bbox relative to x and y: 0 for % nw/n/ne anchor, +0.5 for w/center/e, and +1.0 for sw/s/se. % justify - 0 for left justification, 0.5 for center, 1 for right justify. % stipple - Boolean value indicating whether or not text is to be % drawn in stippled fashion. % stipimage - Image for stippling, if stipple is True. % % Also, when this procedure is invoked, the color and font must already % have been set for the text. /DrawText { /stipimage exch def /stipple exch def /justify exch def /yoffset exch def /xoffset exch def /spacing exch def /strings exch def % First scan through all of the text to find the widest line. /maxwidth 0 def strings { stringwidth pop dup maxwidth gt {/maxwidth exch def} {pop} ifelse newpath } forall % Compute the baseline offset and the actual font height. 0 0 moveto (TXygqPZ) false charpath pathbbox dup /baseline exch def exch pop exch sub /height exch def pop newpath % Translate coordinates first so that the origin is at the upper-left % corner of the text's bounding box. Remember that x and y for % positioning are still on the stack. translate maxwidth xoffset mul strings length 1 sub spacing mul height add yoffset mul translate % Now use the baseline and justification information to translate so % that the origin is at the baseline and positioning point for the % first line of text. justify maxwidth mul baseline neg translate % Iterate over each of the lines to output it. 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Ft(Our)21 b(mo)r(del)i(do)r(es)e(not)i(consider)e(the)h(e\013ect)h (of)f(increased)f(net)n(w)n(ork)450 1276 y(tra\016c)g(as)g(a)h(result)f (of)h(pro)r(cess)e(migration.)34 b(W)-7 b(e)22 b(observ)n(e,)f(ho)n(w)n (ev)n(er,)g(that)h(for)f(the)i(load)e(lev)n(els)450 1375 y(w)n(e)27 b(sim)n(ulated,)h(migrations)f(are)g(o)r(ccasional)f(\(one)h (ev)n(ery)g(few)h(seconds\),)f(and)h(that)g(there)g(is)450 1475 y(seldom)f(more)g(than)h(one)f(migration)f(in)i(progress)d(at)j(a) f(time.)450 1644 y Fx(7.)41 b(FUTURE)27 b(W)n(ORK)450 1777 y Ft(In)d(our)f(w)n(orkload)f(mo)r(del)i(w)n(e)f(ha)n(v)n(e)g (assumed)g(that)h(all)g(pro)r(cesses)e(are)h(CPU-b)r(ound.)36 b(Of)23 b(pri-)450 1877 y(mary)17 b(in)n(terest)h(in)h(future)g(w)n (ork)e(is)h(including)h(in)n(teractiv)n(e,)g(I/O-b)r(ound,)g(and)f (non-migratable)450 1976 y(jobs)27 b(in)n(to)h(our)f(w)n(orkload.)533 2076 y(In)c(a)f(w)n(orkload)e(that)j(includes)f(in)n(teractiv)n(e)g (jobs,)h(I/O-b)r(ound)f(jobs,)h(and)f(daemons,)h(there)450 2176 y(will)31 b(b)r(e)h(some)f(jobs)g(that)g(should)g(not)g(or)f (cannot)h(b)r(e)h(migrated.)46 b(An)32 b(I/O-b)r(ound)e(job,)i(for)450 2275 y(example,)g(will)h(not)e(necessarily)f(run)i(faster)f(on)h(a)f (more)g(ligh)n(tly-loaded)g(host,)h(and)g(migh)n(t)450 2375 y(run)38 b(slo)n(w)n(er)e(if)i(it)h(is)e(migrated)g(a)n(w)n(a)n(y) f(from)i(the)g(disk)g(or)f(other)g(I/O)g(device)h(it)g(uses.)68 b(A)450 2475 y(migrated)35 b(in)n(teractiv)n(e)f(job)h(migh)n(t)h(b)r (ene\014t)g(b)n(y)f(running)g(on)g(a)g(more)g(ligh)n(tly-loaded)f(host) 450 2574 y(if)c(it)f(uses)g(signi\014can)n(t)f(CPU)h(time,)h(but)g (will)g(su\013er)f(p)r(erformance)f(p)r(enalties)h(for)g(all)f(future) 450 2674 y(in)n(teractions.)60 b(Finally)-7 b(,)38 b(some)d(jobs)h (\(e.g.)61 b(man)n(y)35 b(daemons\))g(cannot)h(b)r(e)g(migrated)f(a)n (w)n(a)n(y)450 2773 y(from)27 b(their)h(hosts.)533 2873 y(The)34 b(p)r(olicy)f(w)n(e)g(prop)r(osed)f(for)h(preemptiv)n(e)g (migration)f(can)i(b)r(e)f(extended)h(to)f(deal)g(ap-)450 2973 y(propriately)e(with)i(in)n(teractiv)n(e)e(and)i(I/O)e(b)r(ound)i (jobs)g(b)n(y)f(including)g(in)h(the)g(de\014nition)g(of)450 3072 y(migration)i(cost)g(the)h(additional)g(costs)f(that)h(will)g(b)r (e)g(imp)r(osed)g(on)g(these)g(jobs)f(after)h(mi-)450 3172 y(gration,)30 b(including)h(net)n(w)n(ork)f(dela)n(ys,)h(access)e (to)i(non-lo)r(cal)f(data,)h(etc.)47 b(The)31 b(estimates)g(of)450 3272 y(these)d(costs)f(migh)n(t)h(b)r(e)g(based)f(on)h(the)g(recen)n(t) f(b)r(eha)n(vior)g(of)h(the)g(job;)g(e.g.)37 b(the)28 b(n)n(um)n(b)r(er)g(and)450 3371 y(frequency)33 b(of)g(I/O)g(requests)f (and)h(in)n(teractions.)53 b(Jobs)32 b(that)i(are)e(explicitly)i (forbidden)f(to)450 3471 y(migrate)27 b(could)g(b)r(e)h(assigned)e(an)i (in\014nite)g(migration)f(cost.)533 3571 y(The)j(presence)f(of)g(a)g (set)h(of)g(jobs)f(that)h(are)e(either)i(exp)r(ensiv)n(e)f(or)g(imp)r (ossible)g(to)h(migrate)450 3670 y(migh)n(t)d(reduce)g(the)g(abilit)n (y)g(of)g(the)h(migration)e(p)r(olicy)h(to)g(mo)n(v)n(e)f(w)n(ork)g (around)g(the)h(net)n(w)n(ork)450 3770 y(and)i(balance)f(loads)g (e\013ectiv)n(ely)-7 b(.)41 b(Ho)n(w)n(ev)n(er,)28 b(w)n(e)g(observ)n (e)g(that)h(the)h(ma)5 b(jorit)n(y)27 b(of)i(long-liv)n(ed)450 3869 y(jobs)39 b(are,)i(in)f(fact,)i(CPU-b)r(ound,)g(and)d(it)h(is)f (these)g(long-liv)n(ed)f(jobs)h(that)h(consume)e(the)450 3969 y(ma)5 b(jorit)n(y)21 b(of)i(CPU)f(time.)36 b(Th)n(us,)24 b(ev)n(en)e(if)h(the)g(migration)e(p)r(olicy)i(w)n(ere)f(only)g(able)g (to)h(migrate)450 4069 y(a)32 b(subset)g(of)h(the)f(jobs)h(in)f(the)h (system,)h(it)e(could)h(still)f(ha)n(v)n(e)f(a)h(signi\014can)n(t)g (load-balancing)450 4168 y(e\013ect.)533 4268 y(Another)24 b(w)n(a)n(y)f(in)i(whic)n(h)f(the)h(prop)r(osed)f(migration)f(p)r (olicy)h(should)g(b)r(e)h(altered)f(in)h(a)f(more)450 4368 y(general)19 b(en)n(vironmen)n(t)h(is)g(that)h Fm(n)g Ft(\(the)g(n)n(um)n(b)r(er)g(of)f(jobs)h(at)f(the)h(source\))f(and)g Fm(m)h Ft(\(the)g(n)n(um)n(b)r(er)450 4467 y(of)30 b(jobs)g(at)f(the)i (target)e(host\))h(should)f(distinguish)h(b)r(et)n(w)n(een)g(CPU-b)r (ound)g(jobs)g(and)f(other)450 4567 y(t)n(yp)r(es)d(of)f(jobs,)h(since) f(only)h(CPU-b)r(ound)f(jobs)g(a\013ect)h(CPU)f(con)n(ten)n(tion,)h (and)f(therefore)g(are)450 4666 y(signi\014can)n(t)i(in)h(CPU)f(load)g (balancing.)533 4766 y(Another)20 b(imp)r(ortan)n(t)g(consideration)e (in)j(load)e(balancing)g(is)h(the)g(e\013ect)h(of)f(lo)r(cal)f(sc)n (heduling)450 4866 y(at)24 b(the)h(hosts.)35 b(Most)24 b(prior)f(studies)i(of)f(load)g(balancing)f(ha)n(v)n(e)g(assumed,)i(as) e(w)n(e)h(do,)h(that)f(the)450 4965 y(lo)r(cal)35 b(sc)n(heduling)f(is) i(round-robin)d(\(or)i(pro)r(cessor-sharing\).)56 b(A)36 b(few)g(assume)e(\014rst-come-)450 5065 y(\014rst-serv)n(e)g(\(F)n (CFS\))j(sc)n(heduling,)h(but)f(few)n(er)e(still)i(ha)n(v)n(e)e (studied)h(the)h(e\013ect)f(of)g(feedbac)n(k)p eop %%Page: 28 28 28 27 bop 450 250 a Fq(28)142 b Fp(\001)158 b Fq(M.)26 b(Ha)n(rchol-Balter)f(and)f(A.)j(B.)f(Do)n(wney)450 465 y Ft(sc)n(heduling,)31 b(where)g(pro)r(cesses)e(that)i(ha)n(v)n(e)f (used)h(the)g(least)g(CPU)g(time)g(are)f(giv)n(en)g(priorit)n(y)450 565 y(o)n(v)n(er)f(older)h(pro)r(cesses.)45 b(W)-7 b(e)31 b(sim)n(ulated)f(feedbac)n(k)g(sc)n(heduling)g(and)h(found)g(that)g(it) g(greatly)450 665 y(reduced)21 b(mean)g(slo)n(wdo)n(wn)e(\(from)i (appro)n(ximately)e(2)p Fm(:)p Ft(5)i(to)g(b)r(et)n(w)n(een)g(1)p Fm(:)p Ft(2)f(and)h(1)p Fm(:)p Ft(7,)g(dep)r(ending)450 764 y(on)39 b(load\))g(ev)n(en)g(without)h(migration.)71 b(Th)n(us,)42 b(the)d(p)r(oten)n(tial)h(b)r(ene\014t)g(of)f(either)g(t) n(yp)r(e)h(of)450 864 y(migration)26 b(is)i(greatly)e(reduced.)533 964 y(W)-7 b(e)22 b(ev)-5 b(aluated)22 b(the)g(non-preemptiv)n(e)e (migration)h(p)r(olicy)h(from)f(Section)h(5.1.1)e(under)i(feed-)450 1064 y(bac)n(k)29 b(sc)n(heduling,)g(and)h(found)g(that)g(it)g(often)f (mak)n(es)g(things)g(w)n(orse,)g(increasing)f(the)i(mean)450 1164 y(slo)n(wdo)n(wn)22 b(in)h(5)g(of)g(the)g(8)g(runs,)h(and)f(only)g (decreasing)e(it)j(b)n(y)f(11\045)f(in)h(the)h(b)r(est)f(case)g (\(highest)450 1263 y(load\).)533 1364 y(T)-7 b(o)39 b(ev)-5 b(aluate)39 b(our)g(preemptiv)n(e)g(p)r(olicy)-7 b(,)43 b(w)n(e)c(had)h(to)f(c)n(hange)g(the)g(migration)g(criterion)450 1463 y(to)32 b(re\015ect)f(the)h(e\013ect)g(of)g(lo)r(cal)f(sc)n (heduling.)49 b(Under)31 b(pro)r(cessor)f(sharing,)h(w)n(e)h(assume)f (that)450 1563 y(the)38 b(slo)n(wdo)n(wn)e(imp)r(osed)h(on)h(a)f(pro)r (cess)f(is)h(equal)g(to)h(the)g(n)n(um)n(b)r(er)f(of)g(pro)r(cesses)f (on)h(the)450 1663 y(host.)g(Under)27 b(feedbac)n(k)g(sc)n(heduling,)g (the)h(slo)n(wdo)n(wn)e(is)i(closer)e(to)i(the)g(n)n(um)n(b)r(er)f(of)g Fo(younger)450 1762 y Ft(pro)r(cesses,)19 b(since)g(older)f(pro)r (cesses)f(ha)n(v)n(e)h(lo)n(w)n(er)g(priorit)n(y)-7 b(.)32 b(Th)n(us,)21 b(w)n(e)d(mo)r(di\014ed)i(the)f(migration)450 1862 y(criterion)27 b(in)h(Section)g(3.1)f(so)g(that)h Fm(n)g Ft(and)g Fm(m)g Ft(are)f(the)h(n)n(um)n(b)r(er)g(of)g(pro)r (cesses)e(at)i(the)g(source)450 1961 y(and)j(target)e(hosts)i(that)g (are)e(y)n(ounger)g(than)i(the)g(migran)n(t)f(pro)r(cess.)45 b(Using)31 b(this)g(criterion,)450 2061 y(preemptiv)n(e)26 b(migration)g(reduces)g(mean)h(normalized)e(slo)n(wdo)n(wn)h(b)n(y)g (12{32\045,)f(and)i(reduces)450 2161 y(the)h(n)n(um)n(b)r(er)f(of)h (sev)n(erely)e(slo)n(w)n(ed)g(pro)r(cesses)g(\(slo)n(wdo)n(wn)h (greater)e(than)j(5\))g(b)n(y)f(30{60\045.)533 2261 y(An)d(issue)f (that)h(remains)e(unresolv)n(ed)g(is)h(whether)h(feedbac)n(k)e(sc)n (heduling)h(is)h(as)e(e\013ectiv)n(e)i(in)450 2361 y(real)29 b(systems)g(as)g(it)h(w)n(as)e(in)i(our)f(sim)n(ulations.)42 b(F)-7 b(or)29 b(example,)g(deca)n(y-usage)f(sc)n(heduling)h(as)450 2460 y(used)j(in)g(UNIX)g(has)f(some)g(c)n(haracteristics)f(of)h(b)r (oth)h(round-robin)f(and)g(feedbac)n(k)g(p)r(olicies)450 2560 y([Ep)r(ema)k(1995].)60 b(Y)-7 b(oung)36 b(jobs)f(do)h(ha)n(v)n(e) e(some)h(precedence,)j(but)e(old)g(jobs)f(that)h(p)r(erform)450 2660 y(in)n(teraction)c(or)g(other)g(I/O)g(are)g(giv)n(en)g(higher)g (priorit)n(y)-7 b(,)33 b(whic)n(h)g(allo)n(ws)e(them)j(to)f(in)n (terfere)450 2759 y(with)d(short)e(jobs.)41 b(In)29 b(our)f(exp)r (erimen)n(ts)h(on)g(a)f(SP)-7 b(AR)n(C)29 b(w)n(orkstation)e(running)i (SunOS,)g(w)n(e)450 2859 y(found)21 b(that)f(a)g(long-running)f(job)h (that)g(p)r(erforms)g(p)r(erio)r(dic)g(I/O)f(can)h(obtain)g(more)f (than)i(50\045)450 2958 y(of)33 b(the)h(CPU)g(time,)h(ev)n(en)e(if)h (it)g(is)f(sharing)f(a)i(host)f(with)h(m)n(uc)n(h)f(y)n(ounger)f(pro)r (cesses.)53 b(The)450 3058 y(more)34 b(recen)n(t)g(lottery)f(sc)n (heduling)h(b)r(eha)n(v)n(es)g(more)f(lik)n(e)i(pro)r(cessor-sharing)30 b([W)-7 b(aldspurger)450 3158 y(and)34 b(W)-7 b(eihl)34 b(1994].)54 b(T)-7 b(o)34 b(understand)g(the)g(e\013ect)g(of)g(lo)r (cal)g(sc)n(heduling)f(on)h(load)f(balancing)450 3257 y(requires)26 b(a)h(pro)r(cess)g(mo)r(del)h(that)g(includes)f(in)n (teraction)g(and)g(I/O.)450 3472 y Fx(8.)41 b(CONCLUSIONS)450 3606 y Ft(|T)-7 b(o)38 b(ev)-5 b(aluate)37 b(migration)g(strategies,)i (it)g(is)f(imp)r(ortan)n(t)f(to)h(mo)r(del)g(the)h(distribution)f(of) 533 3705 y(pro)r(cess)27 b(lifetimes)j(accurately)-7 b(.)38 b(Assuming)29 b(an)f(exp)r(onen)n(tial)g(distribution)h(can)f (underes-)533 3805 y(timate)g(the)g(b)r(ene\014ts)g(of)f(preemptiv)n(e) g(migration,)f(b)r(ecause)h(it)h(ignores)e(the)i(fact)f(that)h(old)533 3905 y(jobs)e(are)e(exp)r(ected)i(to)g(b)r(e)g(long-liv)n(ed.)35 b(Ev)n(en)25 b(a)g(lifetime)i(distribution)e(that)h(matc)n(hes)f(the) 533 4004 y(measured)d(distribution)g(in)h(b)r(oth)g(mean)f(and)h(v)-5 b(ariance)21 b(ma)n(y)h(b)r(e)h(misleading)f(in)h(designing)533 4104 y(and)k(ev)-5 b(aluating)27 b(load)g(balancing)g(p)r(olicies.)450 4236 y(|Preemptiv)n(e)17 b(migration)h(outp)r(erforms)f(non-preemptiv)n (e)h(migration)f(ev)n(en)h(when)g(memory-)533 4335 y(transfer)38 b(costs)h(are)f(high,)43 b(for)c(the)g(follo)n(wing)g(reason:)59 b(non-preemptiv)n(e)38 b(name-based)533 4435 y(strategies)26 b(c)n(ho)r(ose)g(pro)r(cesses)g(for)h(migration)f(that)i(are)e(exp)r (ected)i(to)f(ha)n(v)n(e)g(long)f(liv)n(es.)36 b(If)533 4535 y(this)31 b(prediction)f(is)g(wrong,)g(and)g(a)g(pro)r(cess)g (runs)g(longer)f(than)h(exp)r(ected,)i(it)f(cannot)e(b)r(e)533 4634 y(migrated)23 b(a)n(w)n(a)n(y)-7 b(,)22 b(and)h(man)n(y)g (subsequen)n(t)g(small)g(pro)r(cesses)f(will)h(b)r(e)h(dela)n(y)n(ed.) 35 b(A)23 b(preemp-)533 4734 y(tiv)n(e)e(strategy)f(is)i(able)f(to)g (predict)g(lifetimes)h(more)f(accurately)f(\(based)h(on)g(age\))g(and,) i(more)533 4833 y(imp)r(ortan)n(tly)-7 b(,)27 b(if)h(the)g(prediction)g (is)f(wrong,)f(the)i(system)g(can)f(reco)n(v)n(er)e(b)n(y)i(migrating)f (the)533 4933 y(pro)r(cess)g(later.)450 5065 y(|Migrating)35 b(a)g(long)g(job)i(a)n(w)n(a)n(y)c(from)j(a)g(busy)f(host)h(helps)g (not)g(only)g(the)g(long)f(job,)j(but)p eop %%Page: 29 29 29 28 bop 783 250 a Fq(Exploiting)24 b(Pro)r(cess)j(Lifetime)e (Distributions)e(fo)n(r)j(Dynamic)f(Load)g(Balancing)157 b Fp(\001)141 b Fq(29)533 465 y Ft(also)25 b(the)h(man)n(y)g(short)f (jobs)h(that)g(are)f(exp)r(ected)i(to)f(arriv)n(e)e(at)i(the)g(host)g (in)g(the)h(future.)37 b(A)533 565 y(busy)32 b(host)g(is)g(exp)r(ected) h(to)f(receiv)n(e)f(man)n(y)h(arriv)-5 b(als)30 b(b)r(ecause)i(of)g (the)h(serial)e(correlation)533 665 y(\(burstiness\))d(of)f(the)h (arriv)-5 b(al)26 b(pro)r(cess.)450 795 y(|Using)c(the)h(functional)g (form)f(of)g(the)h(distribution)g(of)f(pro)r(cess)f(lifetimes,)j(w)n(e) e(ha)n(v)n(e)g(deriv)n(ed)533 894 y(a)h(criterion)f(for)g(the)i(minim)n (um)f(time)h(a)e(pro)r(cess)g(m)n(ust)h(age)f(b)r(efore)h(b)r(eing)g (migrated.)35 b(This)533 994 y(criterion)27 b(is)g(parameterless)f(and) h(robust)g(across)f(a)h(range)f(of)i(loads.)450 1124 y(|Exclusiv)n(e)f(use)i(of)g(mean)f(slo)n(wdo)n(wn)g(as)g(a)g(metric)h (of)f(system)h(p)r(erformance)f(understates)533 1224 y(the)19 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2281 y Fb(A)n(CKNO)n(WLEDGMENTS)450 2398 y Ft(W)g(e)34 b(w)n(ould)f(lik)n(e)g(to)h(thank)f(T)-7 b(om)34 b(Anderson)e(and)i(the)g(mem)n(b)r(ers)f(of)h(the)f(NO)n(W)h (group)e(for)450 2498 y(commen)n(ts)22 b(and)h(suggestions)d(on)j(our)e (exp)r(erimen)n(tal)i(setup.)35 b(W)-7 b(e)23 b(are)e(also)h(greatly)f (indebted)450 2597 y(to)j(the)g(anon)n(ymous)f(review)n(ers)f(from)i (SIGMETRICS)g(and)f(SOSP)-7 b(,)24 b(and)g(to)g(John)f(Zahorjan,)450 2697 y(whose)k(commen)n(ts)g(greatly)f(impro)n(v)n(ed)h(the)h(qualit)n (y)f(of)g(this)h(pap)r(er.)450 2908 y Fb(REFERENCES)531 3024 y Fa(Abrahams,)21 b(D.)i(M.)f(and)f(Rizzardi,)j(F.)72 b Fw(1988.)91 b Fu(The)23 b(Berkeley)f(Inter)l(active)g(Statistic)l(al) h(System)p Fw(.)d(W.)655 3107 y(W.)k(Norton)g(and)g(Co.)531 3203 y Fa(A)n(gra)-6 b(w)g(al,)21 b(R.)g(and)f(Ezzet,)j(A.)71 b Fw(1987.)89 b(Lo)r(cation)21 b(indep)r(enden)n(t)g(remote)d (execution)j(in)d(NEST.)g Fu(IEEE)655 3286 y(T)-5 b(r)l(ansactions)27 b(on)f(Softwar)l(e)g(Engine)l(ering)k(13)p Fw(,)24 b(8)f(\(August\),)i (905{912.)531 3383 y Fa(Ahmad,)d(I.,)i(Ghaf)o(oor,)d(A.,)j(and)e(Mehr)o (otra,)g(K.)71 b Fw(1991.)92 b(P)n(erformance)20 b(prediction)i(of)e (distributed)655 3466 y(load)k(balancing)h(on)f(m)n(ulticomputer)e (systems.)h(In)h Fu(Sup)l(er)l(c)l(omputing)31 b Fw(\(1991\),)26 b(pp.)d(830{839.)531 3562 y Fa(Ar)l(tsy,)34 b(Y.)f(and)g(Finkel,)i(R.) 71 b Fw(1989.)103 b(Designing)31 b(a)g(pro)r(cess)h(migration)e (facilit)n(y:)46 b(The)32 b(Charlotte)655 3645 y(exp)r(erience.)25 b Fu(IEEE)i(Computer)7 b Fw(,)24 b(47{56.)531 3741 y Fa(Barak,)39 b(A.,)h(Shai,)f(G.,)g(and)e(Wheeler,)j(R.)d(G.)70 b Fw(1993.)107 b Fu(The)36 b(MOSIX)g(Distribute)l(d)g(Op)l(er)l(ating) 655 3824 y(System:)d(L)l(o)l(ad)27 b(Balancing)f(for)g(UNIX)p Fw(.)d(Springer)h(V)-6 b(erlag,)23 b(Berlin.)531 3920 y Fa(Bonomi,)i(F.)h(and)g(Kumar,)f(A.)71 b Fw(1990.)95 b(Adaptiv)n(e)25 b(optimal)e(load)h(balancing)h(in)f(a)g (nonhomogeneous)655 4003 y(m)n(ultiserv)n(er)f(system)h(with)g(a)g(cen) 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(v)n(ersion)f(of)f(p)n(vm.)f Fu(Computing)23 b(Systems)h(8)p Fw(,)c(2)f(\(Spring\),)655 4803 y(171{216.)531 4899 y Fa(Casa)-6 b(v)g(ant,)41 b(T.)d(L.)h(and)f(Kuhl,)j(J.)d(G.)70 b Fw(1987.)108 b(Analysis)36 b(of)h(three)g(dynamic)g(distributed)g (load-)655 4982 y(balancing)e(strategies)g(with)f(v)l(arying)g(global)h (information)d(requiremen)n(ts.)h(In)i Fu(7th)h(International)655 5065 y(Confer)l(enc)l(e)26 b(on)g(Distribute)l(d)f(Computing)i(Systems) h Fw(\(Septem)n(b)r(er)d(1987\),)g(pp.)e(185{192.)p eop %%Page: 30 30 30 29 bop 450 250 a Fq(30)142 b Fp(\001)158 b Fq(M.)26 b(Ha)n(rchol-Balter)f(and)f(A.)j(B.)f(Do)n(wney)531 465 y Fa(Cho)o(wdhur)l(y,)35 b(S.)71 b Fw(1990.)103 b(The)33 b(greedy)g(load)f(sharing)h(algorithm.)d Fu(Journal)36 b(of)e(Par)l(al)t(lel)h(and)f(Dis-)655 549 y(tribute)l(d)26 b(Computing)k(9)p Fw(,)23 b(93{99.)531 644 y Fa(De)j(P)-6 b(a)o(oli,)26 b(D.)g(and)g(Goscinski,)h(A.)71 b Fw(1995.)96 b(The)25 b(rho)r(dos)f(migration)g(facilit)n(y)-6 b(.)23 b Fu(Journal)28 b(of)f(Systems)655 727 y(and)g(Softwar)l(e)5 b Fw(.)24 b(Submitted.)g(See)g(also)g(h)n (ttp://www.cm.deakin.edu.au/rho)r(dos/.)531 823 y Fa(Douglis,)19 b(F.)f(and)g(Ousterhout,)i(J.)70 b Fw(1991.)87 b(T)-6 b(ransparen)n(t)17 b(pro)r(cess)f(migration:)26 b(Design)17 b(alternativ)n(es)655 906 y(and)28 b(the)g(sprite)e(implemen)n(tation.) g Fu(Softwar)l(e)k({)f(Pr)l(actic)l(e)g(and)g(Exp)l(erienc)l(e)j(21)p Fw(,)c(8)f(\(August\),)i(757{)655 989 y(785.)531 1085 y Fa(Do)o(wney,)36 b(A.)e(B.)h(and)f(Har)o(chol-Bal)l(ter,)i(M.)70 b Fw(1995.)104 b(A)33 b(note)h(on)f(\\The)g(limited)e(p)r(erformance) 655 1168 y(b)r(ene\014ts)f(of)e(migrating)f(activ)n(e)j(pro)r(cesses)e (for)g(load)g(sharing".)g(T)-6 b(ec)n(hnical)29 b(Rep)r(ort)g (UCB/CSD-95-)655 1251 y(888)c(\(No)n(v)n(em)n(b)r(er\),)e(Univ)n(ersit) n(y)h(of)f(California,)f(Berk)n(eley)-6 b(.)531 1347 y Fa(Ea)o(ger,)30 b(D.)g(L.,)h(Lazo)o(wska,)h(E.)e(D.,)i(and)d (Zahorjan,)i(J.)71 b Fw(1986.)99 b(Adaptiv)n(e)29 b(load)g(sharing)f (in)g(ho-)655 1430 y(mogeneous)23 b(distributed)g(systems.)e Fu(IEEE)k(T)-5 b(r)l(ansactions)25 b(on)g(Softwar)l(e)g(Engine)l(ering) j(12)p Fw(,)23 b(5)f(\(Ma)n(y\),)655 1513 y(662{675.)531 1609 y Fa(Ea)o(ger,)d(D.)f(L.,)i(Lazo)o(wska,)h(E.)e(D.,)h(and)e (Zahorjan,)i(J.)70 b Fw(1988.)88 b(The)17 b(limited)e(p)r(erformance)h (b)r(ene\014ts)655 1692 y(of)h(migrating)f(activ)n(e)j(pro)r(cesses)e (for)f(load)i(sharing.)e(In)i Fu(A)n(CM)h(Sigmetrics)g(Confer)l(enc)l (e)h(on)g(Me)l(asuring)655 1775 y(and)27 b(Mo)l(deling)f(of)g(Computer) g(Systems)j Fw(\(Ma)n(y)24 b(1988\),)h(pp.)e(662{675.)531 1871 y Fa(Epema,)d(D.)71 b Fw(1995.)89 b(An)18 b(analysis)f(of)h(deca)n (y-usage)h(sc)n(heduling)g(in)f(m)n(ultipro)r(cessors.)d(In)k Fu(A)n(CM)h(Sigmet-)655 1954 y(rics)26 b(Confer)l(enc)l(e)g(on)g(Me)l (asur)l(ement)g(and)g(Mo)l(deling)h(of)f(Computer)g(Systems)j Fw(\(1995\),)c(pp.)e(74{85.)531 2050 y Fa(Ev)-6 b(ans,)23 b(D.)f(J.)g(and)g(Butt,)i(W.)f(U.)f(N.)71 b Fw(1993.)92 b(Dynamic)20 b(load)h(balancing)h(using)e(task-transfer)h(prob-)655 2133 y(abilites.)i Fu(Par)l(al)t(lel)28 b(Computing)i(19)p Fw(,)24 b(897{916.)531 2229 y Fa(Ha)627 2223 y(\023)626 2229 y(c,)f(A.)g(and)f(Jin,)h(X.)71 b Fw(1990.)92 b(Dynamic)20 b(load)i(balancing)g(in)e(a)i(distributed)f(system)g(using)g(a)g (sender-)655 2312 y(initiated)k(algorithm.)d Fu(Journal)27 b(of)f(Systems)f(Softwar)l(e)30 b(11)p Fw(,)24 b(79{94.)531 2407 y Fa(Hennessy,)h(J.)f(L.)h(and)f(P)-6 b(a)l(tterson,)25 b(D.)g(A.)70 b Fw(1990.)94 b Fu(Computer)26 b(A)n(r)l(chite)l(ctur)l(e) f(A)g(Quantitative)f(Ap-)655 2490 y(pr)l(o)l(ach)p Fw(.)i(Morgan)d (Kaufmann)g(Publishers,)g(San)h(Mateo,)g(CA.)531 2586 y Fa(Kr)o(ueger,)i(P.)h(and)f(Livny,)h(M.)71 b Fw(1988.)96 b(A)25 b(comparison)f(of)h(preemptiv)n(e)g(and)h(non-preemptiv)n(e)f (load)655 2669 y(distributing.)33 b(In)h Fu(8th)i(International)g (Confer)l(enc)l(e)f(on)g(Distribute)l(d)f(Computing)i(Systems)i Fw(\(June)655 2752 y(1988\),)25 b(pp.)e(123{130.)531 2848 y Fa(Kunz,)c(T.)71 b Fw(1991.)87 b(The)17 b(in\015uence)h(of)e (di\013eren)n(t)h(w)n(orkload)f(descriptions)h(on)g(a)f(heuristic)g (load)h(balancing)655 2931 y(sc)n(heme.)23 b Fu(IEEE)k(T)-5 b(r)l(ansactions)27 b(on)f(Softwar)l(e)g(Engine)l(ering)k(17)p Fw(,)24 b(7)f(\(July\),)i(725{730.)531 3027 y Fa(Larsen,)h(R.)g(J.)g (and)g(Marx,)f(M.)h(L.)71 b Fw(1986.)95 b Fu(A)n(n)27 b(intr)l(o)l(duction)g(to)f(mathematic)l(al)i(statistics)e(and)h(its) 655 3110 y(applic)l(ations)k Fw(\(2nd)25 b(ed.\).)f(Pren)n(tice)g (Hall,)f(Englew)n(o)r(o)r(d)h(Cli\013s,)f(N.J.)531 3206 y Fa(Leland,)29 b(W.)f(E.)g(and)f(Ott,)i(T.)f(J.)70 b Fw(1986.)98 b(Load-balancing)27 b(heuristics)f(and)h(pro)r(cess)f(b)r (eha)n(vior.)g(In)655 3289 y Fu(Pr)l(o)l(c)l(e)l(e)l(dings)i(of)e (Performanc)l(e)h('86)f(and)g(A)n(CM)g(Sigmetrics)5 b Fw(,)23 b(V)-6 b(olume)22 b(14)i(\(1986\),)i(pp.)d(54{69.)531 3385 y Fa(Lin,)d(H.-C.)g(and)f(Ra)o(gha)-6 b(vendra,)19 b(C.)71 b Fw(1993.)89 b(A)17 b(state-aggregation)j(metho)r(d)e(for)f 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Fw(\(April)23 b(1982\),)h(pp.)g (47{55.)531 4183 y Fa(Milojicic,)f(D.)g(S.)70 b Fw(1993.)92 b Fu(L)l(o)l(ad)24 b(Distribution:)31 b(Implementation)24 b(for)f(the)g(Mach)g(Micr)l(okernel)p Fw(.)d(PhD)655 4266 y(Dissertation,)k(Univ)n(ersit)n(y)f(of)h(Kaiserslautern.)531 4362 y Fa(Mir)o(chand)o(aney,)34 b(R.,)i(To)o(wsley,)h(D.,)g(and)d(St)l (ank)o(o)o(vic,)g(J.)g(A.)71 b Fw(1990.)104 b(Adaptiv)n(e)33 b(load)g(sharing)655 4445 y(in)d(heterogeneous)j(distributed)e (systems.)e Fu(Journal)34 b(of)e(Par)l(al)t(lel)h(and)g(Distribute)l(d) e(Computing)37 b(9)p Fw(,)655 4528 y(331{346.)531 4624 y Fa(Po)o(well,)24 b(M.)f(and)g(Miller,)h(B.)71 b Fw(1983.)93 b(Pro)r(cess)22 b(migrations)e(in)i(DEMOS/MP.)e(In)i Fu(6th)j(A)n(CM)e(Sym-)655 4707 y(p)l(osium)28 b(on)e(Op)l(er)l(ating)g (Systems)f(Principles)k Fw(\(No)n(v)n(em)n(b)r(er)24 b(1983\),)h(pp.)e(110{119.)531 4803 y Fa(Pr)o(outy,)i(R.)71 b Fw(1996.)95 b(P)n(ersonal)23 b(Comm)n(unication.)531 4899 y Fa(Pulid)o(as,)34 b(S.,)f(To)o(wsley,)i(D.,)f(and)d(St)l(ank)o (o)o(vic,)h(J.)g(A.)71 b Fw(1988.)102 b(Im)n(b)r(edding)30 b(gradien)n(t)h(estimators)655 4982 y(in)d(load)g(balancing)h (algorithms.)e(In)h Fu(8th)j(International)f(Confer)l(enc)l(e)g(on)h (Distribute)l(d)e(Computing)655 5065 y(Systems)g Fw(\(June)c(1988\),)g (pp.)e(482{490.)p eop %%Page: 31 31 31 30 bop 783 250 a Fq(Exploiting)24 b(Pro)r(cess)j(Lifetime)e (Distributions)e(fo)n(r)j(Dynamic)f(Load)g(Balancing)157 b Fp(\001)141 b Fq(31)531 465 y Fa(R)n(ommel,)22 b(C.)h(G.)70 b Fw(1991.)91 b(The)21 b(probabilit)n(y)g(of)f(load)h(balancing)g (success)g(in)f(a)h(homogeneous)g(net)n(w)n(ork.)655 549 y Fu(IEEE)27 b(T)-5 b(r)l(ansactions)27 b(on)f(Softwar)l(e)g (Engine)l(ering)k(17)p Fw(,)24 b(922{933.)531 640 y Fa(R)n(osin,)j(R.)f (F.)72 b Fw(1965.)95 b(Determining)24 b(a)h(computing)g(cen)n(ter)h(en) n(vironmen)n(t.)f Fu(Communic)l(ations)j(of)f(the)655 723 y(A)n(CM)34 b(8)p Fw(,)23 b(7.)531 814 y Fa(Silberscha)l(tz,)28 b(A.,)h(Peterson,)h(J.,)f(and)f(Gal)-6 b(vin,)28 b(P.)71 b Fw(1994.)97 b Fu(Op)l(er)l(ating)29 b(System)f(Conc)l(epts,)h(4th)655 897 y(Edition)p Fw(.)24 b(Addison-W)-6 b(esley)g(,)24 b(Reading,)g(MA.)531 989 y Fa(Svensson,)k(A.)71 b Fw(1990.)97 b(History)-6 b(,)25 b(an)i(in)n(telligen)n(t)f(load)g(sharing)g (\014lter.)g(In)g Fu(IEEE)j(10th)g(International)655 1072 y(Confer)l(enc)l(e)d(on)g(Distribute)l(d)f(Computing)i(Systems)h Fw(\(1990\),)e(pp.)d(546{553.)531 1163 y Fa(T)-6 b(anenba)o(um,)24 b(A.,)j(v)-6 b(an)26 b(Renesse,)h(R.,)g(v)-6 b(an)26 b(St)l(a)-6 b(veren,)25 b(H.,)i(and)g(Sharp,)e(G.)71 b Fw(1990.)96 b(Exp)r(eriences)655 1246 y(with)24 b(the)h(Amo)r(eba)e (distributed)h(op)r(erating)h(system.)d Fu(Communic)l(ations)28 b(of)e(the)f(A)n(CM)10 b Fw(,)23 b(336{346.)531 1337 y Fa(Theimer,)c(M.)f(M.,)i(Lantz,)g(K.)e(A.,)i(and)e(Cheriton,)i(D.)e (R.)71 b Fw(1985.)88 b(Preemptable)17 b(remote)f(execution)655 1420 y(facilities)33 b(for)g(the)i(V-System.)e(In)h Fu(10th)i(A)n(CM)f (Symp)l(osium)i(on)f(Op)l(er)l(ating)f(Systems)g(Principles)655 1503 y Fw(\(Decem)n(b)r(er)24 b(1985\),)h(pp.)e(2{12.)531 1595 y Fa(Thiel,)36 b(G.)70 b Fw(1991.)104 b(Lo)r(cus)33 b(op)r(erating)g(system,)h(a)f(transparen)n(t)g(system.)f Fu(Computer)i(Communic)l(a-)655 1678 y(tions)29 b(14)p Fw(,)24 b(6,)g(336{346.)531 1769 y Fa(V)-8 b(ahd)o(a)l(t,)24 b(A.)71 b Fw(1995.)95 b(P)n(ersonal)24 b(Comm)n(unication.)531 1860 y Fa(V)-8 b(ahd)o(a)l(t,)29 b(A.)g(M.,)h(Ghormley,)g(D.)f(P.,)h (and)f(Anderson,)i(T.)f(E.)71 b Fw(1994.)98 b(E\016cien)n(t,)29 b(p)r(ortable,)g(and)655 1943 y(robust)f(extension)h(of)e(op)r(erating) i(system)e(functionalit)n(y)-6 b(.)28 b(T)-6 b(ec)n(hnical)28 b(Rep)r(ort)g(UCB//CSD-94-842,)655 2026 y(Univ)n(ersit)n(y)c(of)f (California,)f(Berk)n(eley)-6 b(.)531 2118 y Fa(W)e(aldspur)o(ger,)25 b(C.)h(A.)g(and)f(Weihl,)g(W.)h(E.)71 b Fw(1994.)95 b(Lottery)25 b(sc)n(heduling:)32 b(Flexible)24 b(prop)r(ortional-)655 2201 y(share)i(resource)g(managemen)n(t.)f(In)h Fu(Pr)l(o)l(c)l(e)l(e)l (dings)j(of)f(the)f(First)h(Symp)l(osium)h(on)e(Op)l(er)l(ating)h (System)655 2284 y(Design)d(and)i(Implementation)j Fw(\(No)n(v)n(em)n (b)r(er)24 b(1994\),)h(pp.)e(1{11.)531 2375 y Fa(W)-8 b(ang,)19 b(J.,)g(Zhou,)h(S.,)f(K.Ahmed,)g(and)f(Long,)h(W.)72 b Fw(1993.)87 b(LSBA)-6 b(TCH:)16 b(A)g(distributed)g(load)h(sharing) 655 2458 y(batc)n(h)27 b(system.)e(T)-6 b(ec)n(hnical)27 b(Rep)r(ort)f(CSRI-286)g(\(April\),)f(Computer)h(Systems)f(Researc)n(h) h(Institute,)655 2541 y(Univ)n(ersit)n(y)e(of)f(T)-6 b(oron)n(to.)531 2632 y Fa(W)e(ang,)25 b(Y.-T.)i(and)e(Morris,)h(R.)g (J.)71 b Fw(1985.)95 b(Load)25 b(sharing)f(in)g(distributed)g(systems.) f Fu(IEEE)28 b(T)-5 b(r)l(ans-)655 2715 y(actions)26 b(on)g(Computers)k(c-94)p Fw(,)24 b(3)f(\(Marc)n(h\),)h(204{217.)531 2807 y Fa(Za)l(y)l(as,)i(E.)g(R.)71 b Fw(1987.)96 b(A)n(ttac)n(king)27 b(the)f(pro)r(cess)f(migration)f(b)r(ottlenec)n(k.)i(In)g Fu(11th)h(A)n(CM)g(Symp)l(osium)655 2890 y(on)f(Op)l(er)l(ating)g (Systems)g(Principles)j Fw(\(1987\),)c(pp.)f(13{24.)531 2981 y Fa(Zhang,)c(Y.,)g(Hak)o(ozaki,)h(K.,)g(Kamed)o(a,)f(H.,)g(and)g (Shimizu,)f(K.)71 b Fw(1995.)89 b(A)17 b(p)r(erformance)g(comparison) 655 3064 y(of)23 b(adaptiv)n(e)i(and)e(static)h(load)f(balancing)h(in)f (heterogeneous)j(distributed)d(systems.)f(In)h Fu(Pr)l(o)l(c)l(e)l(e)l (dings)655 3147 y(of)j(the)f(28th)i(A)n(nnual)g(Simulation)f(Symp)l (osium)31 b Fw(\(April)23 b(1995\),)i(pp.)e(332{340.)531 3238 y Fa(Zhou,)37 b(S.)70 b Fw(1987.)105 b Fu(Performanc)l(e)35 b(studies)g(for)g(dynamic)g(lo)l(ad)h(b)l(alancing)f(in)g(distribute)l (d)f(systems)p Fw(.)655 3321 y(Ph.D.)23 b(Dissertation,)g(Univ)n(ersit) n(y)h(of)f(California,)f(Berk)n(eley)-6 b(.)531 3413 y Fa(Zhou,)26 b(S.)f(and)h(Ferrari,)g(D.)71 b Fw(1987.)95 b(A)24 b(measuremen)n(t)f(study)i(of)f(load)g(balancing)h(p)r (erformance.)e(In)655 3496 y Fu(IEEE)34 b(7th)f(International)h(Confer) l(enc)l(e)f(on)g(Distribute)l(d)f(Computing)i(Systems)i Fw(\(Octob)r(er)d(1987\),)655 3579 y(pp.)24 b(490{497.)531 3670 y Fa(Zhou,)39 b(S.,)g(W)-8 b(ang,)38 b(J.,)h(Zheng,)g(X.,)g(and)d (Delisle,)k(P.)71 b Fw(1993.)106 b(Utopia:)54 b(a)34 b(load-sharing)h(facil-)655 3753 y(it)n(y)c(for)f(large)h (heterogeneous)i(distributed)e(computing)g(systems.)f Fu(Softwar)l(e)j({)g(Pr)l(actic)l(e)f(and)h(Ex-)655 3836 y(p)l(eienc)l(e)c(23)p Fw(,)24 b(2)g(\(Decem)n(b)r(er\),)g(1305{1336.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF