Poisson Flows on Markov Step Processes,
MICHIGAN UNIV ANN ARBOR COMPUTER INFORMATION AND CONTROL ENGINEERING PROGRAM
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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 iZt is independent of Nt for each i and each t greater than or 0. The latter is already much less restrictive than the independent of Nt and Zt, but it is able to find even weaker hypotheses which are both necessary and sufficient for N to be Poisson.
- Statistics and Probability