Analysis of loss networks with routing
Autor(a) principal: | |
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Data de Publicação: | 2006 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.1/11814 |
Resumo: | This paper analyzes stochastic networks consisting of finite capacity nodes with different classes of requests which move according to some routing policy. The Markov processes describing these networks do not, in general, have reversibility properties, so the explicit expression of their invariant distribution is not known. Kelly's limiting regime is considered: the arrival rates of calls as well as the capacities of the nodes are proportional to a factor going to infinity. It is proved that, in limit, the associated rescaled Markov process converges to a deterministic dynamical system with a unique equilibrium point characterized by a nonstandard fixed point equation. |
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Analysis of loss networks with routingModelStochastic networksHeavy traffic limitsAsymptotic dynamical systemsFixed point equationsThis paper analyzes stochastic networks consisting of finite capacity nodes with different classes of requests which move according to some routing policy. The Markov processes describing these networks do not, in general, have reversibility properties, so the explicit expression of their invariant distribution is not known. Kelly's limiting regime is considered: the arrival rates of calls as well as the capacities of the nodes are proportional to a factor going to infinity. It is proved that, in limit, the associated rescaled Markov process converges to a deterministic dynamical system with a unique equilibrium point characterized by a nonstandard fixed point equation.Institute of Mathematical StatisticsSapientiaAntunes, NelsonFricker, ChristineRobert, PhilippeTibi, Danielle2018-12-07T14:58:01Z2006-112006-11-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/11814eng1050-516410.1214/105051606000000466info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-24T10:23:40Zoai:sapientia.ualg.pt:10400.1/11814Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:03:15.877922Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Analysis of loss networks with routing |
title |
Analysis of loss networks with routing |
spellingShingle |
Analysis of loss networks with routing Antunes, Nelson Model Stochastic networks Heavy traffic limits Asymptotic dynamical systems Fixed point equations |
title_short |
Analysis of loss networks with routing |
title_full |
Analysis of loss networks with routing |
title_fullStr |
Analysis of loss networks with routing |
title_full_unstemmed |
Analysis of loss networks with routing |
title_sort |
Analysis of loss networks with routing |
author |
Antunes, Nelson |
author_facet |
Antunes, Nelson Fricker, Christine Robert, Philippe Tibi, Danielle |
author_role |
author |
author2 |
Fricker, Christine Robert, Philippe Tibi, Danielle |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Sapientia |
dc.contributor.author.fl_str_mv |
Antunes, Nelson Fricker, Christine Robert, Philippe Tibi, Danielle |
dc.subject.por.fl_str_mv |
Model Stochastic networks Heavy traffic limits Asymptotic dynamical systems Fixed point equations |
topic |
Model Stochastic networks Heavy traffic limits Asymptotic dynamical systems Fixed point equations |
description |
This paper analyzes stochastic networks consisting of finite capacity nodes with different classes of requests which move according to some routing policy. The Markov processes describing these networks do not, in general, have reversibility properties, so the explicit expression of their invariant distribution is not known. Kelly's limiting regime is considered: the arrival rates of calls as well as the capacities of the nodes are proportional to a factor going to infinity. It is proved that, in limit, the associated rescaled Markov process converges to a deterministic dynamical system with a unique equilibrium point characterized by a nonstandard fixed point equation. |
publishDate |
2006 |
dc.date.none.fl_str_mv |
2006-11 2006-11-01T00:00:00Z 2018-12-07T14:58:01Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.1/11814 |
url |
http://hdl.handle.net/10400.1/11814 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1050-5164 10.1214/105051606000000466 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Institute of Mathematical Statistics |
publisher.none.fl_str_mv |
Institute of Mathematical Statistics |
dc.source.none.fl_str_mv |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799133267080773632 |