Publication:
Closed queueing networks under congestion: non-bottleneck independence and bottleneck convergence

dc.affiliation.dptoUC3M. Departamento de Estadísticaes
dc.contributor.authorAnselmi, Jonatha
dc.contributor.authorD'Auria, Bernardo
dc.contributor.authorWalton, Neil
dc.contributor.editorUniversidad Carlos III de Madrid. Departamento de Estadística
dc.date.accessioned2012-06-21T10:45:57Z
dc.date.available2012-06-21T10:45:57Z
dc.date.issued2012-06
dc.description.abstractWe analyze the behavior of closed product-form queueing networks when the number of customers grows to infinity and remains proportionate on each route (or class). First, we focus on the stationary behavior and prove the conjecture that the stationary distribution at non-bottleneck queues converges weakly to the stationary distribution of an ergodic, open product-form queueing network. This open network is obtained by replacing bottleneck queues with per-route Poissonian sources whose rates are determined by the solution of a strictly concave optimization problem. Then, we focus on the transient behavior of the network and use fluid limits to prove that the amount of fluid, or customers, on each route eventually concentrates on the bottleneck queues only, and that the long-term proportions of fluid in each route and in each queue solve the dual of the concave optimization problem that determines the throughputs of the previous open network.
dc.description.sponsorshipThe second author is partially supported by the Spanish Ministry of Education and Science Grants MTM2010-16519, SEJ2007-64500 and RYC-2009- 04671
dc.format.mimetypeapplication/pdf
dc.identifier.repecws121711
dc.identifier.urihttps://hdl.handle.net/10016/14625
dc.identifier.uxxiDT/0000000967
dc.language.isoeng
dc.relation.ispartofseriesUC3M Working papers. Statistics and Econometrics
dc.relation.ispartofseries12-11
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España
dc.rights.accessRightsopen access
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.ecienciaEstadística
dc.subject.otherClosed queueing networks
dc.subject.otherProduct-form
dc.subject.otherAsymptotic independence
dc.subject.otherFluid limit
dc.subject.otherLarge population
dc.titleClosed queueing networks under congestion: non-bottleneck independence and bottleneck convergence
dc.typeworking paper*
dc.type.hasVersionSMUR*
dspace.entity.typePublication
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