Approximation of a class of Markov-modulated Poisson processes with a large state-space.

Persistent Link:
http://hdl.handle.net/10150/184828
Title:
Approximation of a class of Markov-modulated Poisson processes with a large state-space.
Author:
Sitaraman, Hariharakrishnan.
Issue Date:
1989
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Many queueing systems have an arrival process that can be modeled by a Markov-modulated Poisson process. The Markov-modulated Poisson process (MMPP) is a doubly stochastic Poisson process in which the arrival rate varies according to a finite state irreducible Markov process. In many applications of MMPPs, the point process is constructed by superpositions or similar constructions, which lead to modulating Markov processes with a large state space. Since this limits the feasibility of numerical computations, a useful problem is to approximate an MMPP represented by a large Markov process by one with fewer states. We focus our attention in particular, to approximating a simple but useful special case of the MMPP, namely the Birth and Death Modulated Poisson process. In the validation stage, the quality of the approximation is examined in relation to the MMPP/G/1 queue.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Queuing theory.; Poisson processes.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Systems and Industrial Engineering; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Neuts, Marcel F.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleApproximation of a class of Markov-modulated Poisson processes with a large state-space.en_US
dc.creatorSitaraman, Hariharakrishnan.en_US
dc.contributor.authorSitaraman, Hariharakrishnan.en_US
dc.date.issued1989en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractMany queueing systems have an arrival process that can be modeled by a Markov-modulated Poisson process. The Markov-modulated Poisson process (MMPP) is a doubly stochastic Poisson process in which the arrival rate varies according to a finite state irreducible Markov process. In many applications of MMPPs, the point process is constructed by superpositions or similar constructions, which lead to modulating Markov processes with a large state space. Since this limits the feasibility of numerical computations, a useful problem is to approximate an MMPP represented by a large Markov process by one with fewer states. We focus our attention in particular, to approximating a simple but useful special case of the MMPP, namely the Birth and Death Modulated Poisson process. In the validation stage, the quality of the approximation is examined in relation to the MMPP/G/1 queue.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectQueuing theory.en_US
dc.subjectPoisson processes.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineSystems and Industrial Engineeringen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorNeuts, Marcel F.en_US
dc.contributor.committeememberYakowitz, Sidney J.en_US
dc.contributor.committeememberLamond, Bernard F.en_US
dc.identifier.proquest9004979en_US
dc.identifier.oclc703278254en_US
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