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,...
- Autores:
- 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
- Rights
- License
- Restringido (Acceso a grupos específicos)
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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 |
_version_ |
1814167737849610240 |