On the exact distribution of the iostropic planar point processes of phase type
type: Item
instance of: scholarly article
title: On the exact distribution of the iostropic planar point processes of phase type
zbMATH Open document ID: 0980.60055
DOI: 10.1016/S0377-0427(99)00282-4
author: Marie-Ange Remiche
published in: Journal of Computational and Applied Mathematics
publication date: 2002-02-24T00:00:00Z
review text: The definition of the isotropic phase planar process [see \textit{G. Latouche} and \textit{V. Ramaswami}, in: Teletraffic contributions for the information age, 381-390 (1997)] is as follows. Let \(\{(L(t), Y(t)\), \(t\in R^2\}\) be a stationary Markovian arrival process, with single arrivals, taking its value on the state space \(N\times M\), with \(M=\{1,\dots, m\}\) where \(m\) is finite. \(L(t)\) is called the level in which the process lies at time \(t\) and \(Y(t)\) the phase of the process. The author develops several analytical expressions of the moments and the exact distribution of the numbers of points in any polar rectangle of the plane. This paper is the first step towards a complete determination of the finite-dimensional distribution of the process.
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 60D05
zbMATH DE Number: 1437654
zbMATH Keywords: Markovian arrival process
zbMATH Keywords: matrix-analytic method
zbMATH Keywords: planar point processes
reviewed by: Viktor Ohanyan
MaRDI profile type: Publication
cites work: Q3883242
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cites work: Asymptotic poisson distribution in isotropic ph planar point processes
description: scientific article; zbMATH DE number 1437654