Tomasz Nycz - Academia.edu (original) (raw)

Papers by Tomasz Nycz

The paper proposes steady state and transient state diffusion approximation models for the design... more The paper proposes steady state and transient state diffusion approximation models for the design and performance evaluation of multichannel communication networks. We concentrate on \(G/G/c/c+K\) queueing model and highlight some its applications together with numerical examples to illustrate how this models can be used.

Das Future SOC Lab am HPI ist eine Kooperation des Hasso-Plattner-Instituts mit verschiedenen Ind... more Das Future SOC Lab am HPI ist eine Kooperation des Hasso-Plattner-Instituts mit verschiedenen Industriepartnern. Seine Aufgabe ist die Ermoglichung und Forderung des Austausches zwischen Forschungsgemeinschaft und Industrie. Am Lab wird interessierten Wissenschaftlern eine Infrastruktur von neuester Hard- und Software kostenfrei fur Forschungszwecke zur Verfugung gestellt. Dazu zahlen teilweise noch nicht am Markt verfugbare Technologien, die im normalen Hochschulbereich in der Regel nicht zu finanzieren waren, bspw. Server mit bis zu 64 Cores und 2 TB Hauptspeicher. Diese Angebote richten sich insbesondere an Wissenschaftler in den Gebieten Informatik und Wirtschaftsinformatik. Einige der Schwerpunkte sind Cloud Computing, Parallelisierung und In-Memory Technologien. In diesem Technischen Bericht werden die Ergebnisse der Forschungsprojekte des Jahres 2015 vorgestellt. Ausgewahlte Projekte stellten ihre Ergebnisse am 15. April 2015 und 4. November 2015 im Rahmen der Future SOC Lab ...

Sensors

The increasing use of Software-Defined Networks brings the need for their performance analysis an... more The increasing use of Software-Defined Networks brings the need for their performance analysis and detailed analytical and numerical models of them. The primary element of such research is a model of a SDN switch. This model should take into account non-Poisson traffic and general distributions of service times. Because of frequent changes in SDN flows, it should also analyze transient states of the queues. The method of diffusion approximation can meet these requirements. We present here a diffusion approximation of priority queues and apply it to build a more detailed model of SDN switch where packets returned by the central controller have higher priority than other packets.

Zmienne natężenie ruchu generowanego przez aplikacje internetowe, np. multimedialne, a także przy... more Zmienne natężenie ruchu generowanego przez aplikacje internetowe, np. multimedialne, a także przyjęta przez protokół TCP zasada regulacji natężenia transmisji w funkcji wykrytego obciążenia sieci, określanego na podstawie strat lub czasu transmisji, powodują, że natężenie transmisji internetowych jest permanentnie zmienne w czasie, a zmiany natężenia i dynamika tych zmian muszą być uwzględnione w ocenie algorytmów sterowania ruchem i unikania przeciążeń. Modelowanie struktur w Internecie wymaga z kolei dostosowania istniejących metod i modeli do analizy bardzo dużych konfiguracji sieciowych. Niniejsza praca bada pod kątem obliczeń numerycznych znany model matematyczny, umożliwiający analizę stanów nieustalonych w stanowisku obsługi i ich sieci, wykorzystujący metodę aproksymacji dyfuzyjnej. Zbadano wpływ poszczególnych parametrów modelu i rozmiaru sieci na całkowity czas obliczeń, a więc na skalowalność metody.

W artykule przedstawiono model kolejkowy służący do oceny funkcjonowania dużego systemu siecioweg... more W artykule przedstawiono model kolejkowy służący do oceny funkcjonowania dużego systemu sieciowego, w skład którego wchodzi rozbudowany system bazodanowy. Opisywany system jest systemem rzeczywistym. Zebrane wyniki pracy systemu posłużyły do budowy modelu działania aplikacji interakcyjnych, na podstawie łańcuchów Markowa, aproksymacji dyfuzyjnej i symulacji zdarzeń dyskretnych. Porównanie ich z rzeczywistymi wynikami umożliwiło sprawdzenie przydatności użytych metod w rzeczywistych warunkach.

Mathematics, 2021

The paper addresses two issues: (i) modeling dynamic flows transmitted in vast TCP/IP networks an... more The paper addresses two issues: (i) modeling dynamic flows transmitted in vast TCP/IP networks and (ii) modeling the impact of energy-saving algorithms. The approach is based on the fluid-flow approximation, which applies first-order differential equations to analyze the evolution of queues and flows. We demonstrate that the effective implementation of this method overcomes the constraints of storing large data in numerical solutions of transient problems in vast network topologies. The model is implemented and executed directly in a database system. It can analyze transient states in topologies of more than 100,000 nodes, i.e., the size which was not considered until now. We use it to investigate the impact of an energy-saving algorithm on the performance of a vast network. We find that it reduces network congestion and save energy costs but significantly lower network throughput.

Streszczenie. Zmienne natezenie ruchu generowanego przez aplikacje internetowe, np. multimedialne... more Streszczenie. Zmienne natezenie ruchu generowanego przez aplikacje internetowe, np. multimedialne, a takze przyjeta przez protokol TCP zasada regulacji natezenia transmisji w funkcji wykrytego obciązenia sieci, określanego na podstawie strat lub czasu transmisji, powodują, ze natezenie transmisji internetowych jest permanentnie zmienne w czasie, a zmiany natezenia i dynamika tych zmian muszą byc uwzglednione w ocenie algorytmow sterowania ruchem i unikania przeciązen. Modelowanie struktur w Internecie wymaga z kolei dostosowania istniejących metod i modeli do analizy bardzo duzych konfiguracji sieciowych. Niniejsza praca bada pod kątem obliczen numerycznych znany model matematyczny, umozliwiający analize stanow nieustalonych w stanowisku obslugi i ich sieci, wykorzystujący metode aproksymacji dyfuzyjnej. Zbadano wplyw poszczegolnych parametrow modelu i rozmiaru sieci na calkowity czas obliczen, a wiec na skalowalnośc metody. Slowa kluczowe: aproksymacja dyfuzyjna

Theoretical and Applied Informatics, 2008

Artykul przedstawia model stacji obslugi typu G/G/N/N – a wiec stacji zawierającej N rownoleglych... more Artykul przedstawia model stacji obslugi typu G/G/N/N – a wiec stacji zawierającej N rownoleglych kanalow obslugi, bez mozliwości tworzenia kolejki, ze strumieniem wejściowym o dowolnym rozkladzie odstepow czasu pomiedzy nadejściem kolejnych klientow i z dowolnym rozkladem czasow obslugi. Zastosowanie metody aproksymacji dyfuzyjnej pozwala na opis zarowno stanow ustalonych, jak i nieustalonych (co jest niewykonalne przy zastosowaniu dokladnych klasycznych metod teorii kolejek) pracy takiego stanowiska. Dokladnośc metody jest oceniona przy uzyciu dwu przykladow numerycznych, gdzie wyniki aproksymacji są porownane z wynikami symulacji. Symulacja stanow nieustalonych oznacza powtorzenie wiele tysiecy razy symulowanego przebiegu i uśrednienie wszystkich uzyskanych trajektorii. Opracowany model pojedynczego stanowiska moze byc latwo rozwiniety do sieci o dowolnej topologii zawierającej stanowiska stanowiska G/G/N/N oraz G/G/1/N. Przyklady numeryczne pokazują tez mozliwości zastosowania m...

Varying intensity of traffic generated by Internet applications such as multimedia, together with... more Varying intensity of traffic generated by Internet applications such as multimedia, together with the TCP protocol rules to regulate the intensity of the detected transmission as a function of network load which is determined on the basis of loss or transmission time, cause that the intensity of Internet broadcasts is continuously variable in time, therefore intensity changes and dynamics of these changes must be included in the evaluation of algorithms for traffic control and congestion avoidance. Modeling of the structures on the Internet, in turn, requires adaptation of existing methods and models for the analysis of very large network configurations. This paper examines the numerical calculations for well-known mathematical model that allows analysis of transient states at the service station and their networks, using the diffusion approximation method. The influence of various parameters of the model and size of the network to the total computation time was investigated, and th...

Theoretical and Applied Informatics, 2008

The article presents a diffusion approximation model applied to investigate the behaviour of prio... more The article presents a diffusion approximation model applied to investigate the behaviour of priority queues. Diffusion approximation allows us to include in queueing models fairly general assumptions. First of all it gives us a tool to consider in a natural way transient states of queues, which is vary rare in classical queueing models. Then we may consider input streams with general interarrival time distributions and servers with general service time distributions. Single server models may be easily incorporated into the network of queues. Here, we apply the diffusion approximation formalism to study transient and steady-state behaviour of G/G/1 and G/G/1/N priority preemptive models. The models can be easily converted to nonpreemptive queueing discipline. Also the introduction of self-similar traffic is possible. The models may be useful in performance evaluation of mechanisms to differentiate the quality of service e.g. in WiMAX, metro networks, etc.

Lecture Notes in Electrical Engineering, 2015

The article presents an approach to numerical modeling of dynamics of flows in wide area TCP/IP c... more The article presents an approach to numerical modeling of dynamics of flows in wide area TCP/IP computer networks with the use of SAP HANA in-memory database. The aim is to explore the possibility of transforming a broadly known modeling method—fluid-flow approximation—into database language, overcoming this way the need to develop dedicated solutions and to transmit the results from the application to the database. We implemented the model logic into SQL procedures and performed mathematical calculations for an exemplary vast topology. The experiments show that the database engine may be used to perform all model computations.

Communications in Computer and Information Science, 2015

The paper defines a method to extract a part of a graph, which corresponding to a network (Intern... more The paper defines a method to extract a part of a graph, which corresponding to a network (Internet) topology covering a certain area. The method refers to data gathered within Opte Project and describing the Internet topology. The extracted parts of graphs have been analyzed in terms of the number of neighbours, longest path length and existence of cycles. Then the resulting topologies are used to model transient behaviour of wide area networks with the use of fluid-flow approximation.

Computer and Information Sciences II, 2011

The article presents a queueing model for performance evaluation of a large database system at an... more The article presents a queueing model for performance evaluation of a large database system at an assurance company. The system includes a server with a database and a local area network with a number of terminals where the company employees run applications that introduce documents or retrieve them from the database. We discuss a model of clients activities. Measurements were collected inside the working system: the phases at each users application performance were identified and their duration was measured. The collected data are used to construct a synthetic model of applications activities which is then applied to predict the system behaviour in case of the growth of the number of users. We apply simulation, Markov and diffusion models—their comparison, based on real data, may better verify the utility of particular methods than usual academic examples.

2009 IEEE Symposium on Computers and Communications, 2009

The article discusses the use of the diffusion approximation in transient analysis of queueing mo... more The article discusses the use of the diffusion approximation in transient analysis of queueing models applied to investigate some aspects of Internet transmissions. In classical queuing theory, the analysis of transient states is complex and practically does not go far beyond MIMII queue and its modifications. However, the time dependent flows in computer networks and especially in Internet focus our interest on transient-state analysis, which is necessary to investigate the dynamics of TCP flows cooperating with active queue management or to see the changes of priority queues which assure the differentiated QoS. With the use of GIGIIIN and GIGIIINIPRIOR models, we present the potentials of the diffusion approximation and compare it with alternative methods: Markovian queues solved numerically, fluid-flow approximation and simulation. We mention briefly an original software we dispose to use these methods.

2009 1st International Conference on Wireless Communication, Vehicular Technology, Information Theory and Aerospace & Electronic Systems Technology, 2009

The article makes a contribution to QoS of service models discussing the way the performance of p... more The article makes a contribution to QoS of service models discussing the way the performance of priority disciplines may be studied under assumption of time-dependent and correlated traffic. First we present how self-similar traffic is introduced to diffusion approximation models and then we apply this approach in case of priority queues. Diffusion approximation allows us to include in queueing models fairly general assumptions. It gives us a tool to consider in a natural way transient states of queues, which is vary rare in classical queueing models. Then we may consider input streams with general interarrival time distributions and servers with general service time distributions. Single server models may be easily incorporated into the network of queues. The presented approach may be useful in performance evaluation of mechanisms to differentiate the quality of service in WiMax.

Communications in Computer and Information Science, 2014

The paper presents a comparison of two approaches to queuing models used in performance evaluatio... more The paper presents a comparison of two approaches to queuing models used in performance evaluation of computer networks: diffusion approximation and fluid-flow approximation. Both methods are well known and are used alternatively in similar problems but the differences between their results and the errors they introduce when applied to TCP driven time dependent flows were not sufficiently investigated.

Communications in Computer and Information Science, 2014

Communications in Computer and Information Science, 2013

Transient queue analysis is needed to model the influence of time-dependent flows on congestion i... more Transient queue analysis is needed to model the influence of time-dependent flows on congestion in computer networks. It may be applied to the networks performance evaluation and the analysis of the transmissions quality of service. However, the exact queuing theory gives us only few practically useful results, concerning mainly M/M/1 and M/M/1/N queues. The article presents potentials of three approaches: Markovian queues solved numerically, the diffusion approximation, and fluid-flow approximation. We mention briefly a software we implemented to use these methods and summarise our experience with it.

2009 Fifth Advanced International Conference on Telecommunications, 2009

ABSTRACT The article presents a diffusion approximation model applied to investigate the behaviou... more ABSTRACT The article presents a diffusion approximation model applied to investigate the behaviour of priority queues. Diffusion approximation allows us to include in queueing models fairly general assumptions. First of all it gives us a tool to consider in a natural way transient states of queues, which is vary rare in classical queueing models. Then we may consider input streams with general interarrival time distributions and servers with general service time distributions. Single server models may be easily incorporated into the network of queues. Here, we apply the diffusion approximation formalism to study transient and steady-state behavior of G/G/1 and G/G/1/N priority preemptive models. The models can be easily converted to nonpreemptive queueing discipline. Also the introduction of self-similar traffic is possible. The models may be useful in performance evaluation of mechanisms to differentiate the quality of service e.g. in WiMAX, metro networks, etc.

Lecture Notes in Electrical Engineering, 2010

ABSTRACT The article presents a diffusion approximation model applied to investigate queues with ... more ABSTRACT The article presents a diffusion approximation model applied to investigate queues with Finite capacity. Usually it is assumed that the size of a queue is limited by the maximum number of customers allowed to the system. Here, we assume that the size of customers is random (i.e. we consider batch arrivals with an arbitrary batch size distribution) and the constraint is given by the total volume of the queue. It is more adequate if we consider the queues of packets in e.g. IP routers where the volume of a buffer where packets are stored is limited and the size of packets is variable.

The paper proposes steady state and transient state diffusion approximation models for the design... more The paper proposes steady state and transient state diffusion approximation models for the design and performance evaluation of multichannel communication networks. We concentrate on \(G/G/c/c+K\) queueing model and highlight some its applications together with numerical examples to illustrate how this models can be used.

Das Future SOC Lab am HPI ist eine Kooperation des Hasso-Plattner-Instituts mit verschiedenen Ind... more Das Future SOC Lab am HPI ist eine Kooperation des Hasso-Plattner-Instituts mit verschiedenen Industriepartnern. Seine Aufgabe ist die Ermoglichung und Forderung des Austausches zwischen Forschungsgemeinschaft und Industrie. Am Lab wird interessierten Wissenschaftlern eine Infrastruktur von neuester Hard- und Software kostenfrei fur Forschungszwecke zur Verfugung gestellt. Dazu zahlen teilweise noch nicht am Markt verfugbare Technologien, die im normalen Hochschulbereich in der Regel nicht zu finanzieren waren, bspw. Server mit bis zu 64 Cores und 2 TB Hauptspeicher. Diese Angebote richten sich insbesondere an Wissenschaftler in den Gebieten Informatik und Wirtschaftsinformatik. Einige der Schwerpunkte sind Cloud Computing, Parallelisierung und In-Memory Technologien. In diesem Technischen Bericht werden die Ergebnisse der Forschungsprojekte des Jahres 2015 vorgestellt. Ausgewahlte Projekte stellten ihre Ergebnisse am 15. April 2015 und 4. November 2015 im Rahmen der Future SOC Lab ...

Sensors

The increasing use of Software-Defined Networks brings the need for their performance analysis an... more The increasing use of Software-Defined Networks brings the need for their performance analysis and detailed analytical and numerical models of them. The primary element of such research is a model of a SDN switch. This model should take into account non-Poisson traffic and general distributions of service times. Because of frequent changes in SDN flows, it should also analyze transient states of the queues. The method of diffusion approximation can meet these requirements. We present here a diffusion approximation of priority queues and apply it to build a more detailed model of SDN switch where packets returned by the central controller have higher priority than other packets.

Zmienne natężenie ruchu generowanego przez aplikacje internetowe, np. multimedialne, a także przy... more Zmienne natężenie ruchu generowanego przez aplikacje internetowe, np. multimedialne, a także przyjęta przez protokół TCP zasada regulacji natężenia transmisji w funkcji wykrytego obciążenia sieci, określanego na podstawie strat lub czasu transmisji, powodują, że natężenie transmisji internetowych jest permanentnie zmienne w czasie, a zmiany natężenia i dynamika tych zmian muszą być uwzględnione w ocenie algorytmów sterowania ruchem i unikania przeciążeń. Modelowanie struktur w Internecie wymaga z kolei dostosowania istniejących metod i modeli do analizy bardzo dużych konfiguracji sieciowych. Niniejsza praca bada pod kątem obliczeń numerycznych znany model matematyczny, umożliwiający analizę stanów nieustalonych w stanowisku obsługi i ich sieci, wykorzystujący metodę aproksymacji dyfuzyjnej. Zbadano wpływ poszczególnych parametrów modelu i rozmiaru sieci na całkowity czas obliczeń, a więc na skalowalność metody.

W artykule przedstawiono model kolejkowy służący do oceny funkcjonowania dużego systemu siecioweg... more W artykule przedstawiono model kolejkowy służący do oceny funkcjonowania dużego systemu sieciowego, w skład którego wchodzi rozbudowany system bazodanowy. Opisywany system jest systemem rzeczywistym. Zebrane wyniki pracy systemu posłużyły do budowy modelu działania aplikacji interakcyjnych, na podstawie łańcuchów Markowa, aproksymacji dyfuzyjnej i symulacji zdarzeń dyskretnych. Porównanie ich z rzeczywistymi wynikami umożliwiło sprawdzenie przydatności użytych metod w rzeczywistych warunkach.

Mathematics, 2021

The paper addresses two issues: (i) modeling dynamic flows transmitted in vast TCP/IP networks an... more The paper addresses two issues: (i) modeling dynamic flows transmitted in vast TCP/IP networks and (ii) modeling the impact of energy-saving algorithms. The approach is based on the fluid-flow approximation, which applies first-order differential equations to analyze the evolution of queues and flows. We demonstrate that the effective implementation of this method overcomes the constraints of storing large data in numerical solutions of transient problems in vast network topologies. The model is implemented and executed directly in a database system. It can analyze transient states in topologies of more than 100,000 nodes, i.e., the size which was not considered until now. We use it to investigate the impact of an energy-saving algorithm on the performance of a vast network. We find that it reduces network congestion and save energy costs but significantly lower network throughput.

Streszczenie. Zmienne natezenie ruchu generowanego przez aplikacje internetowe, np. multimedialne... more Streszczenie. Zmienne natezenie ruchu generowanego przez aplikacje internetowe, np. multimedialne, a takze przyjeta przez protokol TCP zasada regulacji natezenia transmisji w funkcji wykrytego obciązenia sieci, określanego na podstawie strat lub czasu transmisji, powodują, ze natezenie transmisji internetowych jest permanentnie zmienne w czasie, a zmiany natezenia i dynamika tych zmian muszą byc uwzglednione w ocenie algorytmow sterowania ruchem i unikania przeciązen. Modelowanie struktur w Internecie wymaga z kolei dostosowania istniejących metod i modeli do analizy bardzo duzych konfiguracji sieciowych. Niniejsza praca bada pod kątem obliczen numerycznych znany model matematyczny, umozliwiający analize stanow nieustalonych w stanowisku obslugi i ich sieci, wykorzystujący metode aproksymacji dyfuzyjnej. Zbadano wplyw poszczegolnych parametrow modelu i rozmiaru sieci na calkowity czas obliczen, a wiec na skalowalnośc metody. Slowa kluczowe: aproksymacja dyfuzyjna

Theoretical and Applied Informatics, 2008

Artykul przedstawia model stacji obslugi typu G/G/N/N – a wiec stacji zawierającej N rownoleglych... more Artykul przedstawia model stacji obslugi typu G/G/N/N – a wiec stacji zawierającej N rownoleglych kanalow obslugi, bez mozliwości tworzenia kolejki, ze strumieniem wejściowym o dowolnym rozkladzie odstepow czasu pomiedzy nadejściem kolejnych klientow i z dowolnym rozkladem czasow obslugi. Zastosowanie metody aproksymacji dyfuzyjnej pozwala na opis zarowno stanow ustalonych, jak i nieustalonych (co jest niewykonalne przy zastosowaniu dokladnych klasycznych metod teorii kolejek) pracy takiego stanowiska. Dokladnośc metody jest oceniona przy uzyciu dwu przykladow numerycznych, gdzie wyniki aproksymacji są porownane z wynikami symulacji. Symulacja stanow nieustalonych oznacza powtorzenie wiele tysiecy razy symulowanego przebiegu i uśrednienie wszystkich uzyskanych trajektorii. Opracowany model pojedynczego stanowiska moze byc latwo rozwiniety do sieci o dowolnej topologii zawierającej stanowiska stanowiska G/G/N/N oraz G/G/1/N. Przyklady numeryczne pokazują tez mozliwości zastosowania m...

Varying intensity of traffic generated by Internet applications such as multimedia, together with... more Varying intensity of traffic generated by Internet applications such as multimedia, together with the TCP protocol rules to regulate the intensity of the detected transmission as a function of network load which is determined on the basis of loss or transmission time, cause that the intensity of Internet broadcasts is continuously variable in time, therefore intensity changes and dynamics of these changes must be included in the evaluation of algorithms for traffic control and congestion avoidance. Modeling of the structures on the Internet, in turn, requires adaptation of existing methods and models for the analysis of very large network configurations. This paper examines the numerical calculations for well-known mathematical model that allows analysis of transient states at the service station and their networks, using the diffusion approximation method. The influence of various parameters of the model and size of the network to the total computation time was investigated, and th...

Theoretical and Applied Informatics, 2008

The article presents a diffusion approximation model applied to investigate the behaviour of prio... more The article presents a diffusion approximation model applied to investigate the behaviour of priority queues. Diffusion approximation allows us to include in queueing models fairly general assumptions. First of all it gives us a tool to consider in a natural way transient states of queues, which is vary rare in classical queueing models. Then we may consider input streams with general interarrival time distributions and servers with general service time distributions. Single server models may be easily incorporated into the network of queues. Here, we apply the diffusion approximation formalism to study transient and steady-state behaviour of G/G/1 and G/G/1/N priority preemptive models. The models can be easily converted to nonpreemptive queueing discipline. Also the introduction of self-similar traffic is possible. The models may be useful in performance evaluation of mechanisms to differentiate the quality of service e.g. in WiMAX, metro networks, etc.

Lecture Notes in Electrical Engineering, 2015

The article presents an approach to numerical modeling of dynamics of flows in wide area TCP/IP c... more The article presents an approach to numerical modeling of dynamics of flows in wide area TCP/IP computer networks with the use of SAP HANA in-memory database. The aim is to explore the possibility of transforming a broadly known modeling method—fluid-flow approximation—into database language, overcoming this way the need to develop dedicated solutions and to transmit the results from the application to the database. We implemented the model logic into SQL procedures and performed mathematical calculations for an exemplary vast topology. The experiments show that the database engine may be used to perform all model computations.

Communications in Computer and Information Science, 2015

The paper defines a method to extract a part of a graph, which corresponding to a network (Intern... more The paper defines a method to extract a part of a graph, which corresponding to a network (Internet) topology covering a certain area. The method refers to data gathered within Opte Project and describing the Internet topology. The extracted parts of graphs have been analyzed in terms of the number of neighbours, longest path length and existence of cycles. Then the resulting topologies are used to model transient behaviour of wide area networks with the use of fluid-flow approximation.

Computer and Information Sciences II, 2011

The article presents a queueing model for performance evaluation of a large database system at an... more The article presents a queueing model for performance evaluation of a large database system at an assurance company. The system includes a server with a database and a local area network with a number of terminals where the company employees run applications that introduce documents or retrieve them from the database. We discuss a model of clients activities. Measurements were collected inside the working system: the phases at each users application performance were identified and their duration was measured. The collected data are used to construct a synthetic model of applications activities which is then applied to predict the system behaviour in case of the growth of the number of users. We apply simulation, Markov and diffusion models—their comparison, based on real data, may better verify the utility of particular methods than usual academic examples.

2009 IEEE Symposium on Computers and Communications, 2009

The article discusses the use of the diffusion approximation in transient analysis of queueing mo... more The article discusses the use of the diffusion approximation in transient analysis of queueing models applied to investigate some aspects of Internet transmissions. In classical queuing theory, the analysis of transient states is complex and practically does not go far beyond MIMII queue and its modifications. However, the time dependent flows in computer networks and especially in Internet focus our interest on transient-state analysis, which is necessary to investigate the dynamics of TCP flows cooperating with active queue management or to see the changes of priority queues which assure the differentiated QoS. With the use of GIGIIIN and GIGIIINIPRIOR models, we present the potentials of the diffusion approximation and compare it with alternative methods: Markovian queues solved numerically, fluid-flow approximation and simulation. We mention briefly an original software we dispose to use these methods.

2009 1st International Conference on Wireless Communication, Vehicular Technology, Information Theory and Aerospace & Electronic Systems Technology, 2009

The article makes a contribution to QoS of service models discussing the way the performance of p... more The article makes a contribution to QoS of service models discussing the way the performance of priority disciplines may be studied under assumption of time-dependent and correlated traffic. First we present how self-similar traffic is introduced to diffusion approximation models and then we apply this approach in case of priority queues. Diffusion approximation allows us to include in queueing models fairly general assumptions. It gives us a tool to consider in a natural way transient states of queues, which is vary rare in classical queueing models. Then we may consider input streams with general interarrival time distributions and servers with general service time distributions. Single server models may be easily incorporated into the network of queues. The presented approach may be useful in performance evaluation of mechanisms to differentiate the quality of service in WiMax.

Communications in Computer and Information Science, 2014

The paper presents a comparison of two approaches to queuing models used in performance evaluatio... more The paper presents a comparison of two approaches to queuing models used in performance evaluation of computer networks: diffusion approximation and fluid-flow approximation. Both methods are well known and are used alternatively in similar problems but the differences between their results and the errors they introduce when applied to TCP driven time dependent flows were not sufficiently investigated.

Communications in Computer and Information Science, 2014

Communications in Computer and Information Science, 2013

Transient queue analysis is needed to model the influence of time-dependent flows on congestion i... more Transient queue analysis is needed to model the influence of time-dependent flows on congestion in computer networks. It may be applied to the networks performance evaluation and the analysis of the transmissions quality of service. However, the exact queuing theory gives us only few practically useful results, concerning mainly M/M/1 and M/M/1/N queues. The article presents potentials of three approaches: Markovian queues solved numerically, the diffusion approximation, and fluid-flow approximation. We mention briefly a software we implemented to use these methods and summarise our experience with it.

2009 Fifth Advanced International Conference on Telecommunications, 2009

ABSTRACT The article presents a diffusion approximation model applied to investigate the behaviou... more ABSTRACT The article presents a diffusion approximation model applied to investigate the behaviour of priority queues. Diffusion approximation allows us to include in queueing models fairly general assumptions. First of all it gives us a tool to consider in a natural way transient states of queues, which is vary rare in classical queueing models. Then we may consider input streams with general interarrival time distributions and servers with general service time distributions. Single server models may be easily incorporated into the network of queues. Here, we apply the diffusion approximation formalism to study transient and steady-state behavior of G/G/1 and G/G/1/N priority preemptive models. The models can be easily converted to nonpreemptive queueing discipline. Also the introduction of self-similar traffic is possible. The models may be useful in performance evaluation of mechanisms to differentiate the quality of service e.g. in WiMAX, metro networks, etc.

Lecture Notes in Electrical Engineering, 2010

ABSTRACT The article presents a diffusion approximation model applied to investigate queues with ... more ABSTRACT The article presents a diffusion approximation model applied to investigate queues with Finite capacity. Usually it is assumed that the size of a queue is limited by the maximum number of customers allowed to the system. Here, we assume that the size of customers is random (i.e. we consider batch arrivals with an arbitrary batch size distribution) and the constraint is given by the total volume of the queue. It is more adequate if we consider the queues of packets in e.g. IP routers where the volume of a buffer where packets are stored is limited and the size of packets is variable.