Quasi-birth-and-death processes with restricted transitions and its applications

In this paper, we identify a class of quasi-birth-and-death (QBD) processes where the transitions to higher (respectively lower) levels are restricted to occur only from (respectively to) a subset of the phase space. These restrictions induce a specific structure in the or matrix of the QBD process,...

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Tipo de recurso:
Fecha de publicación:
2010
Institución:
Universidad del Rosario
Repositorio:
Repositorio EdocUR - U. Rosario
Idioma:
eng
OAI Identifier:
oai:repository.urosario.edu.co:10336/28471
Acceso en línea:
https://doi.org/10.1016/j.peva.2010.04.003
https://repository.urosario.edu.co/handle/10336/28471
Palabra clave:
Markov chains
Quasi-birth-and-death processes
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network_acronym_str EDOCUR2
network_name_str Repositorio EdocUR - U. Rosario
repository_id_str
spelling 80035202600420ab075-a640-42a6-8323-60ddd335b3632020-08-28T15:48:16Z2020-08-28T15:48:16Z2010-05-31In this paper, we identify a class of quasi-birth-and-death (QBD) processes where the transitions to higher (respectively lower) levels are restricted to occur only from (respectively to) a subset of the phase space. These restrictions induce a specific structure in the or matrix of the QBD process, which can be exploited to reduce the time required to compute these matrices. We show how this reduction can be achieved by first defining and solving a censored process, and then solving a Sylvester matrix equation. To illustrate the applicability and computational gains obtained with this approach, we consider several examples where the referred structures either arise naturally or can be induced by adequately modeling the system at hand. The examples include the general MAP/PH/1 queue, a priority queue with two customer classes, an overflow queueing system and a wireless relay node.application/pdfhttps://doi.org/10.1016/j.peva.2010.04.003ISSN: 0166-5316EISSN: 1872-745Xhttps://repository.urosario.edu.co/handle/10336/28471engElsevier141No. 2126Performance EvaluationVol. 68Performance Evaluation, ISSN: 0166-5316;EISSN: 1872-745X, Vol. 68, No. 2 (February 2011); pp. 126-141https://www.sciencedirect.com/science/article/abs/pii/S0166531610000684Restringido (Acceso a grupos específicos)http://purl.org/coar/access_right/c_16ecPerformance Evaluationinstname:Universidad del Rosarioreponame:Repositorio Institucional EdocURMarkov chainsQuasi-birth-and-death processesQuasi-birth-and-death processes with restricted transitions and its applicationsProcesos de cuasi nacimiento y muerte con transiciones restringidas y sus aplicacionesarticleArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501Pérez, Juan F.Van Houdt, Benny10336/28471oai:repository.urosario.edu.co:10336/284712021-09-23 12:56:40.6https://repository.urosario.edu.coRepositorio institucional EdocURedocur@urosario.edu.co
dc.title.spa.fl_str_mv Quasi-birth-and-death processes with restricted transitions and its applications
dc.title.TranslatedTitle.spa.fl_str_mv Procesos de cuasi nacimiento y muerte con transiciones restringidas y sus aplicaciones
title Quasi-birth-and-death processes with restricted transitions and its applications
spellingShingle Quasi-birth-and-death processes with restricted transitions and its applications
Markov chains
Quasi-birth-and-death processes
title_short Quasi-birth-and-death processes with restricted transitions and its applications
title_full Quasi-birth-and-death processes with restricted transitions and its applications
title_fullStr Quasi-birth-and-death processes with restricted transitions and its applications
title_full_unstemmed Quasi-birth-and-death processes with restricted transitions and its applications
title_sort Quasi-birth-and-death processes with restricted transitions and its applications
dc.subject.keyword.spa.fl_str_mv Markov chains
Quasi-birth-and-death processes
topic Markov chains
Quasi-birth-and-death processes
description In this paper, we identify a class of quasi-birth-and-death (QBD) processes where the transitions to higher (respectively lower) levels are restricted to occur only from (respectively to) a subset of the phase space. These restrictions induce a specific structure in the or matrix of the QBD process, which can be exploited to reduce the time required to compute these matrices. We show how this reduction can be achieved by first defining and solving a censored process, and then solving a Sylvester matrix equation. To illustrate the applicability and computational gains obtained with this approach, we consider several examples where the referred structures either arise naturally or can be induced by adequately modeling the system at hand. The examples include the general MAP/PH/1 queue, a priority queue with two customer classes, an overflow queueing system and a wireless relay node.
publishDate 2010
dc.date.created.spa.fl_str_mv 2010-05-31
dc.date.accessioned.none.fl_str_mv 2020-08-28T15:48:16Z
dc.date.available.none.fl_str_mv 2020-08-28T15:48:16Z
dc.type.eng.fl_str_mv article
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_6501
dc.type.spa.spa.fl_str_mv Artículo
dc.identifier.doi.none.fl_str_mv https://doi.org/10.1016/j.peva.2010.04.003
dc.identifier.issn.none.fl_str_mv ISSN: 0166-5316
EISSN: 1872-745X
dc.identifier.uri.none.fl_str_mv https://repository.urosario.edu.co/handle/10336/28471
url https://doi.org/10.1016/j.peva.2010.04.003
https://repository.urosario.edu.co/handle/10336/28471
identifier_str_mv ISSN: 0166-5316
EISSN: 1872-745X
dc.language.iso.spa.fl_str_mv eng
language eng
dc.relation.citationEndPage.none.fl_str_mv 141
dc.relation.citationIssue.none.fl_str_mv No. 2
dc.relation.citationStartPage.none.fl_str_mv 126
dc.relation.citationTitle.none.fl_str_mv Performance Evaluation
dc.relation.citationVolume.none.fl_str_mv Vol. 68
dc.relation.ispartof.spa.fl_str_mv Performance Evaluation, ISSN: 0166-5316;EISSN: 1872-745X, Vol. 68, No. 2 (February 2011); pp. 126-141
dc.relation.uri.spa.fl_str_mv https://www.sciencedirect.com/science/article/abs/pii/S0166531610000684
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_16ec
dc.rights.acceso.spa.fl_str_mv Restringido (Acceso a grupos específicos)
rights_invalid_str_mv Restringido (Acceso a grupos específicos)
http://purl.org/coar/access_right/c_16ec
dc.format.mimetype.none.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Elsevier
dc.source.spa.fl_str_mv Performance Evaluation
institution Universidad del Rosario
dc.source.instname.none.fl_str_mv instname:Universidad del Rosario
dc.source.reponame.none.fl_str_mv reponame:Repositorio Institucional EdocUR
repository.name.fl_str_mv Repositorio institucional EdocUR
repository.mail.fl_str_mv edocur@urosario.edu.co
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