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Article: Decay properties and quasi-stationary distributions for stopped Markovian bulk-arrival and bulk-service queues

TitleDecay properties and quasi-stationary distributions for stopped Markovian bulk-arrival and bulk-service queues
Authors
KeywordsDecay parameter
Invariant measures
Quasi-stationary distributions
Stopped Markovian bulk-arrival and bulk-service queues
Issue Date2010
PublisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0257-0130
Citation
Queueing Systems, 2010, v. 66 n. 3, p. 275-311 How to Cite?
AbstractWe consider decay properties including the decay parameter, invariant measures and quasi-stationary distributions for a Markovian bulk-arrival and bulk-service queue which stops when the waiting line is empty. Investigating such a model is crucial for understanding the busy period and other related properties of the Markovian bulk-arrival and bulk-service queuing processes. The exact value of the decay parameter λ C is first obtained. We show that the decay parameter can be easily expressed explicitly. The invariant measures and quasi-distributions are then revealed. We show that there exists a family of invariant measures indexed by λ ∈ [0,λ C]. We then show that under some mild conditions there exists a family of quasi-stationary distributions also indexed by λ ∈ [0,λ C]. The generating functions of these invariant measures and quasi-stationary distributions are presented. We further show that this stopped Markovian bulk-arrival and bulk-service queueing model is always λ C-transient. Some deep properties regarding λ C-transience are examined and revealed. The clear geometric interpretation of the decay parameter is explained. A few examples are then provided to illustrate the results obtained in this paper. © 2010 Springer Science+Business Media, LLC.
Persistent Identifierhttp://hdl.handle.net/10722/129372
ISSN
2015 Impact Factor: 0.875
2015 SCImago Journal Rankings: 1.146
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorChen, Aen_HK
dc.contributor.authorLi, Jen_HK
dc.contributor.authorHou, Zen_HK
dc.contributor.authorNg, KWen_HK
dc.date.accessioned2010-12-23T08:36:24Z-
dc.date.available2010-12-23T08:36:24Z-
dc.date.issued2010en_HK
dc.identifier.citationQueueing Systems, 2010, v. 66 n. 3, p. 275-311en_HK
dc.identifier.issn0257-0130en_HK
dc.identifier.urihttp://hdl.handle.net/10722/129372-
dc.description.abstractWe consider decay properties including the decay parameter, invariant measures and quasi-stationary distributions for a Markovian bulk-arrival and bulk-service queue which stops when the waiting line is empty. Investigating such a model is crucial for understanding the busy period and other related properties of the Markovian bulk-arrival and bulk-service queuing processes. The exact value of the decay parameter λ C is first obtained. We show that the decay parameter can be easily expressed explicitly. The invariant measures and quasi-distributions are then revealed. We show that there exists a family of invariant measures indexed by λ ∈ [0,λ C]. We then show that under some mild conditions there exists a family of quasi-stationary distributions also indexed by λ ∈ [0,λ C]. The generating functions of these invariant measures and quasi-stationary distributions are presented. We further show that this stopped Markovian bulk-arrival and bulk-service queueing model is always λ C-transient. Some deep properties regarding λ C-transience are examined and revealed. The clear geometric interpretation of the decay parameter is explained. A few examples are then provided to illustrate the results obtained in this paper. © 2010 Springer Science+Business Media, LLC.en_HK
dc.languageengen_US
dc.publisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0257-0130en_HK
dc.relation.ispartofQueueing Systemsen_HK
dc.rightsThe original publication is available at www.springerlink.comen_US
dc.subjectDecay parameteren_HK
dc.subjectInvariant measuresen_HK
dc.subjectQuasi-stationary distributionsen_HK
dc.subjectStopped Markovian bulk-arrival and bulk-service queuesen_HK
dc.titleDecay properties and quasi-stationary distributions for stopped Markovian bulk-arrival and bulk-service queuesen_HK
dc.typeArticleen_HK
dc.identifier.emailNg, KW: kaing@hkucc.hku.hken_HK
dc.identifier.authorityNg, KW=rp00765en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s11134-010-9194-xen_HK
dc.identifier.scopuseid_2-s2.0-78049373040en_HK
dc.identifier.hkuros183561en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-78049373040&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume66en_HK
dc.identifier.issue3en_HK
dc.identifier.spage275en_HK
dc.identifier.epage311en_HK
dc.identifier.isiWOS:000283558600003-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridChen, A=7403392194en_HK
dc.identifier.scopusauthoridLi, J=35317934900en_HK
dc.identifier.scopusauthoridHou, Z=7201896669en_HK
dc.identifier.scopusauthoridNg, KW=7403178774en_HK
dc.identifier.citeulike8122709-

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