Artalejo, Jesús R. and Gómez-Corral, Antonio and Qi-Ming , He
(2010)
*Markovian arrivals in stochastic modelling: a survey and some new results.*
Sort: Statistics and Operations Research Transactions, 34
(2).
pp. 101-156.
ISSN 1696-2281

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## 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, non-homogeneous 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.

Item Type: | Article |
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Uncontrolled Keywords: | Discrete-Time; Stationary Distributions; Transition Matrices; Inventory Problems; Additive Processes; Markovian arrival process; batch arrivals; marked process; phase-type distribution; BSDE approach |

Subjects: | Sciences > Mathematics > Stochastic processes |

ID Code: | 15069 |

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