Markov-modulated and feedback fluid queues

Research output: ThesisPhD Thesis - Research UT, graduation UTAcademic

Abstract

In the last twenty years the field of Markov-modulated fluid queues has received considerable attention. In these models a fluid reservoir receives and/or releases fluid at rates which depend on the actual state of a background Markov chain. In the first chapter of this thesis we give a short introduction on how the stationary distribution for such a model is usually found, as well as a literature overview on Markov-modulated and related uid queues. The rest of the thesis is concerned with �nding stationary distributions for some types of fluid models that have received little or no attention until now. The two main contributions are the following. 1. We focus on models in which the state space of the regulating Markov process is infinitely large, either denumerable or not. Regarding the first type, we mainly look into regulating processes that are of birth-death type. We present procedures to find the stationary distribution, using the theory of orthogonal polynomials. In the nondenumerable case, we look into simple systems of fluid queues, in which one fluid queue regulates the behaviour of another (one example being a fluid tandem queue). 2. We look into models in which the state of the fluid reservoir in quences the behaviour of the regulating process, so that the latter does not constitute a Markov process. We call suchlike systems feedback fluid queues, to emphasize the two-way dependence between fluid reservoir and regulating process.
LanguageUndefined
Supervisors/Advisors
  • Supervisor
  • van Doorn, Erik Alexander, Advisor
Award date4 Dec 1998
Place of PublicationEnschede
Publisher
Print ISBNs90-3651248-4
Publication statusPublished - 4 Dec 1998

Keywords

  • IR-29630
  • METIS-140264

Cite this

Scheinhardt, Willem R.W.. / Markov-modulated and feedback fluid queues. Enschede : Universiteit Twente, 1998. 155 p.
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Markov-modulated and feedback fluid queues. / Scheinhardt, Willem R.W.

Enschede : Universiteit Twente, 1998. 155 p.

Research output: ThesisPhD Thesis - Research UT, graduation UTAcademic

TY - THES

T1 - Markov-modulated and feedback fluid queues

AU - Scheinhardt, Willem R.W.

PY - 1998/12/4

Y1 - 1998/12/4

N2 - In the last twenty years the field of Markov-modulated fluid queues has received considerable attention. In these models a fluid reservoir receives and/or releases fluid at rates which depend on the actual state of a background Markov chain. In the first chapter of this thesis we give a short introduction on how the stationary distribution for such a model is usually found, as well as a literature overview on Markov-modulated and related uid queues. The rest of the thesis is concerned with �nding stationary distributions for some types of fluid models that have received little or no attention until now. The two main contributions are the following. 1. We focus on models in which the state space of the regulating Markov process is infinitely large, either denumerable or not. Regarding the first type, we mainly look into regulating processes that are of birth-death type. We present procedures to find the stationary distribution, using the theory of orthogonal polynomials. In the nondenumerable case, we look into simple systems of fluid queues, in which one fluid queue regulates the behaviour of another (one example being a fluid tandem queue). 2. We look into models in which the state of the fluid reservoir in quences the behaviour of the regulating process, so that the latter does not constitute a Markov process. We call suchlike systems feedback fluid queues, to emphasize the two-way dependence between fluid reservoir and regulating process.

AB - In the last twenty years the field of Markov-modulated fluid queues has received considerable attention. In these models a fluid reservoir receives and/or releases fluid at rates which depend on the actual state of a background Markov chain. In the first chapter of this thesis we give a short introduction on how the stationary distribution for such a model is usually found, as well as a literature overview on Markov-modulated and related uid queues. The rest of the thesis is concerned with �nding stationary distributions for some types of fluid models that have received little or no attention until now. The two main contributions are the following. 1. We focus on models in which the state space of the regulating Markov process is infinitely large, either denumerable or not. Regarding the first type, we mainly look into regulating processes that are of birth-death type. We present procedures to find the stationary distribution, using the theory of orthogonal polynomials. In the nondenumerable case, we look into simple systems of fluid queues, in which one fluid queue regulates the behaviour of another (one example being a fluid tandem queue). 2. We look into models in which the state of the fluid reservoir in quences the behaviour of the regulating process, so that the latter does not constitute a Markov process. We call suchlike systems feedback fluid queues, to emphasize the two-way dependence between fluid reservoir and regulating process.

KW - IR-29630

KW - METIS-140264

M3 - PhD Thesis - Research UT, graduation UT

SN - 90-3651248-4

PB - Universiteit Twente

CY - Enschede

ER -

Scheinhardt WRW. Markov-modulated and feedback fluid queues. Enschede: Universiteit Twente, 1998. 155 p.