On the exact distribution of the iostropic planar point processes of phase type (Q1975673)

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.