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dc.contributor.authorArtalejo, Jesús R.
dc.contributor.authorGómez-Corral, Antonio
dc.contributor.authorHe, Qi-Ming
dc.date.accessioned2011-11-02T19:01:03Z
dc.date.available2011-11-02T19:01:03Z
dc.date.issued2010
dc.identifier.citationArtalejo, Jesús R.; Gómez-Corral, Antonio; He, Qi-Ming. Markovian arrivals in stochastic modelling: a survey and some new results. "SORT", vol. 34, núm. 2, p. 101-144.
dc.identifier.issn1696-2281
dc.identifier.urihttp://hdl.handle.net/2099/11244
dc.description.abstractThis paper aims to provide a comprehensive review on Markovian arrival processes (MAPs), which constitute a rich class of point processes used extensively in stochastic modelling. Our starting point is the versatile process introduced by Neuts (1979) which, under some simplified notation, was coined as the batch Markovian arrival process (BMAP). On the one hand, a general point process can be approximated by appropriate MAPs and, on the other hand, the MAPs provide a versatile, yet tractable option for modelling a bursty flow by preserving the Markovian formalism. While a number of well-known arrival processes are subsumed under a BMAP as special cases, the literature also shows generalizations to model arrival streams with marks, nonhomogeneous settings or even spatial arrivals. We survey on the main aspects of the BMAP, discuss on some of its variants and generalizations, and give a few new results in the context of a recent state-dependent extension.
dc.format.extent56 p.
dc.language.isoeng
dc.publisherInstitut d'Estadística de Catalunya
dc.relation.ispartofSORT. 2010, vol. 34, núm. 2
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica
dc.subject.lcshMarkov processes
dc.subject.lcshStochastic processes
dc.subject.otherMarkovian arrival process
dc.subject.otherBatch arrivals
dc.subject.otherMarked process
dc.subject.otherPhase-type distribution
dc.subject.otherBSDE approach
dc.titleMarkovian arrivals in stochastic modelling: a survey and some new results
dc.typeArticle
dc.subject.lemacMarkov, Processos de
dc.subject.lemacProcessos estocàstics
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::60 Probability theory and stochastic processes::60J Markov processes
dc.subject.amsClassificació AMS::60 Probability theory and stochastic processes::60G Stochastic processes
dc.rights.accessOpen Access
local.citation.authorArtalejo, Jesús R.; Gómez-Corral, Antonio; He, Qi-Ming
local.citation.publicationNameSORT
local.citation.volume34
local.citation.number2
local.citation.startingPage101
local.citation.endingPage144


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