Descriptors for point processes based on runs: the Markovian arrival process

Marcel F. Neuts

International Journal of Stochastic Analysis, 1996, vol. 9, 1-20

Abstract:

This paper is part of a broader investigation of properties of a point process that can be identified by imagining that the process is involved in a competition for the generation of runs of events. The general purpose of that methodology is to quantify the prevalence of gaps and bursts in realizations of the process. The Markovian arrival process (MAP) is highly versatile in qualitative behavior and its analysis is numerically tractable by matrix-analytic methods. It can therefore serve well as a benchmark process in that investigation. In this paper, we consider the MAP and a regular grid competing for runs of lengths at least r 1 and r 2 , respectively. A run of length r in one of the processes is defined as a string of r successive events occurring without an intervening event in the other process.

This article is dedicated to the memory of Roland L. Dobrushin.

Date: 1996
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://downloads.hindawi.com/journals/IJSA/9/417039.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJSA/9/417039.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:417039

DOI: 10.1155/S104895339600041X

Access Statistics for this article

More articles in International Journal of Stochastic Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().