E-Prints Complutense

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

Impacto

Descargas

Último año



Artalejo, Jesús R. y Gómez-Corral, Antonio y 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

[img]
Vista previa
PDF
Creative Commons License
Esta obra está bajo una licencia de Creative Commons: Reconocimiento - No comercial.

425kB

URL Oficial: http://dialnet.unirioja.es/servlet/articulo?codigo=3352462


URLTipo de URL
http://www.idescat.cat/sort/Institución


Resumen

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.


Tipo de documento:Artículo
Palabras clave:Discrete-Time; Stationary Distributions; Transition Matrices; Inventory Problems; Additive Processes; Markovian arrival process; batch arrivals; marked process; phase-type distribution; BSDE approach
Materias:Ciencias > Matemáticas > Procesos estocásticos
Código ID:15069
Depositado:03 May 2012 08:42
Última Modificación:20 Abr 2015 12:11

Descargas en el último año

Sólo personal del repositorio: página de control del artículo