RT Journal Article
T1 Markovian arrivals in stochastic modelling: a survey and some new results
A1 Artalejo Rodríguez, Jesús Manuel
A1 Gómez-Corral, Antonio
A1 Qi-Ming, He
AB 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.
PB Institut d'Estadística de Catalunya (Idescat)
SN 1696-2281
YR 2010
FD 2010-07
LK https://hdl.handle.net/20.500.14352/42154
UL https://hdl.handle.net/20.500.14352/42154
LA eng
NO Government of Spain (Ministry of Science and Innovation)
NO European Commission
DS Docta Complutense
RD 11 abr 2025