The M/G/1-type markov chain with restricted transitions and its application to queues with batch arrivals
We consider M/G/1-type Markov chains where a transition that decreases the value of the level triggers the phase to a small subset of the phase space. We show how this structure—referred to as restricted downward transitions—can be exploited to speed up the computation of the stationary probability...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2011
- Institución:
- Universidad del Rosario
- Repositorio:
- Repositorio EdocUR - U. Rosario
- Idioma:
- eng
- OAI Identifier:
- oai:repository.urosario.edu.co:10336/27086
- Acceso en línea:
- https://doi.org/10.1017/S0269964811000155
https://repository.urosario.edu.co/handle/10336/27086
- Palabra clave:
- M/G/1-type Markov chains
G matrix
Computation
- Rights
- License
- Restringido (Acceso a grupos específicos)
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80035202-1420ab075-a640-42a6-8323-60ddd335b363-12020-08-19T14:40:57Z2020-08-19T14:40:57Z2011-07-21We consider M/G/1-type Markov chains where a transition that decreases the value of the level triggers the phase to a small subset of the phase space. We show how this structure—referred to as restricted downward transitions—can be exploited to speed up the computation of the stationary probability vector of the chain. To this end we define a new M/G/1-type Markov chain with a smaller block size, the G matrix of which is used to find the original chain's G matrix. This approach is then used to analyze the BMAP/PH/1 queue and the BMAP[2]/PH[2]/1 preemptive priority queue, yielding significant reductions in computation time.application/pdfhttps://doi.org/10.1017/S0269964811000155ISSN: 0269-9648EISSN: 1469-8951https://repository.urosario.edu.co/handle/10336/27086engCambridge University Press517No. 4487Probability in the Engineering and Informational SciencesVol. 25Probability in the Engineering and Informational Sciences, ISSN: 0269-9648;EISSN: 1469-8951, Vol.25, No.4 (2011); pp. 487-517https://www.cambridge.org/core/journals/probability-in-the-engineering-and-informational-sciences/article/mg1type-markov-chain-with-restricted-transitions-and-its-application-to-queues-with-batch-arrivals/F4A45829C200EF53BD97AAC8FA558B8DRestringido (Acceso a grupos específicos)http://purl.org/coar/access_right/c_16ecProbability in the Engineering and Informational Sciencesinstname:Universidad del Rosarioreponame:Repositorio Institucional EdocURM/G/1-type Markov chainsG matrixComputationThe M/G/1-type markov chain with restricted transitions and its application to queues with batch arrivalsLa cadena de Markov tipo M / G / 1 con transiciones restringidas y su aplicación a colas con llegadas por lotesarticleArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501Pérez, Juan F.Van Houdt, Benny10336/27086oai:repository.urosario.edu.co:10336/270862021-06-03 00:50:05.415https://repository.urosario.edu.coRepositorio institucional EdocURedocur@urosario.edu.co |
| dc.title.spa.fl_str_mv |
The M/G/1-type markov chain with restricted transitions and its application to queues with batch arrivals |
| dc.title.TranslatedTitle.spa.fl_str_mv |
La cadena de Markov tipo M / G / 1 con transiciones restringidas y su aplicación a colas con llegadas por lotes |
| title |
The M/G/1-type markov chain with restricted transitions and its application to queues with batch arrivals |
| spellingShingle |
The M/G/1-type markov chain with restricted transitions and its application to queues with batch arrivals M/G/1-type Markov chains G matrix Computation |
| title_short |
The M/G/1-type markov chain with restricted transitions and its application to queues with batch arrivals |
| title_full |
The M/G/1-type markov chain with restricted transitions and its application to queues with batch arrivals |
| title_fullStr |
The M/G/1-type markov chain with restricted transitions and its application to queues with batch arrivals |
| title_full_unstemmed |
The M/G/1-type markov chain with restricted transitions and its application to queues with batch arrivals |
| title_sort |
The M/G/1-type markov chain with restricted transitions and its application to queues with batch arrivals |
| dc.subject.keyword.spa.fl_str_mv |
M/G/1-type Markov chains G matrix Computation |
| topic |
M/G/1-type Markov chains G matrix Computation |
| description |
We consider M/G/1-type Markov chains where a transition that decreases the value of the level triggers the phase to a small subset of the phase space. We show how this structure—referred to as restricted downward transitions—can be exploited to speed up the computation of the stationary probability vector of the chain. To this end we define a new M/G/1-type Markov chain with a smaller block size, the G matrix of which is used to find the original chain's G matrix. This approach is then used to analyze the BMAP/PH/1 queue and the BMAP[2]/PH[2]/1 preemptive priority queue, yielding significant reductions in computation time. |
| publishDate |
2011 |
| dc.date.created.spa.fl_str_mv |
2011-07-21 |
| dc.date.accessioned.none.fl_str_mv |
2020-08-19T14:40:57Z |
| dc.date.available.none.fl_str_mv |
2020-08-19T14:40:57Z |
| 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/10.1017/S0269964811000155 |
| dc.identifier.issn.none.fl_str_mv |
ISSN: 0269-9648 EISSN: 1469-8951 |
| dc.identifier.uri.none.fl_str_mv |
https://repository.urosario.edu.co/handle/10336/27086 |
| url |
https://doi.org/10.1017/S0269964811000155 https://repository.urosario.edu.co/handle/10336/27086 |
| identifier_str_mv |
ISSN: 0269-9648 EISSN: 1469-8951 |
| dc.language.iso.spa.fl_str_mv |
eng |
| language |
eng |
| dc.relation.citationEndPage.none.fl_str_mv |
517 |
| dc.relation.citationIssue.none.fl_str_mv |
No. 4 |
| dc.relation.citationStartPage.none.fl_str_mv |
487 |
| dc.relation.citationTitle.none.fl_str_mv |
Probability in the Engineering and Informational Sciences |
| dc.relation.citationVolume.none.fl_str_mv |
Vol. 25 |
| dc.relation.ispartof.spa.fl_str_mv |
Probability in the Engineering and Informational Sciences, ISSN: 0269-9648;EISSN: 1469-8951, Vol.25, No.4 (2011); pp. 487-517 |
| dc.relation.uri.spa.fl_str_mv |
https://www.cambridge.org/core/journals/probability-in-the-engineering-and-informational-sciences/article/mg1type-markov-chain-with-restricted-transitions-and-its-application-to-queues-with-batch-arrivals/F4A45829C200EF53BD97AAC8FA558B8D |
| 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 |
Cambridge University Press |
| dc.source.spa.fl_str_mv |
Probability in the Engineering and Informational Sciences |
| 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_ |
1814167514179960832 |