ON THE EXISTENCE OF FINITE-DIMENSIONAL FILTERS FOR MARKOV-MODULATED TRAFFIC

A Markov-modulated Poisson process (MMPP) is a Poisson process whose r ate is a finite Markov chain. The Poisson process is a simple MMPP. An MMPP/M/1 queue is a queue with MMPP arrivals, an infinite capacity, a nd a single exponential server. We prove that the output of an MMPP/M/ 1 queue is not an MMPP process unless the input is Poisson. We derive this result by analyzing the structure of the non-linear filter of the state given the departure process of the queue. The practical relevan ce of the result is that it rules out the existence of simple finite d escriptions of queueing networks with MMPP inputs.