Poisson Flows on Markov Step Processes

摘要

A Markov step process Z equipped with a possible non-denumerable state space x can model a variety of queueing, communication and computer networks. The analysis of such networks can be facilitated if certain traffic flows consist of mutually independent Poisson processes. A multivariate N is Poisson (i.e., composed of mutually independent Poisson streams N sub i) if each r sub i (Z) is stationary, and r sub i(Z(t)) is independent of N(t) for each i and each t greater than or = 0. The latter is already much less restrictive than the independent of N(t) and Z(t), but it is able to find even weaker hypotheses which are both necessary and sufficient for N to be Poisson.