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Markovian arrivals in stochastic modelling: a survey and some new results

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hdl:2099/11244
Document typeArticle
Defense date2010
PublisherInstitut d'Estadística de Catalunya
Rights accessOpen Access
This work is protected by the corresponding intellectual and industrial property rights.
Except where otherwise noted, its contents are licensed under a Creative Commons license
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Attribution-NonCommercial-NoDerivs 3.0 Spain
Abstract
This 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.
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.
ISSN1696-2281
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