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On the existence of finite-dimensional filters for Markov-modulated traffic
Published online by Cambridge University Press: 14 July 2016
Abstract
A Markov-modulated Poisson process (MMPP) is a Poisson process whose rate 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, and 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 relevance of the result is that it rules out the existence of simple finite descriptions of queueing networks with MMPP inputs.
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- Copyright © Applied Probability Trust 1994
Footnotes
Research supported by Direction des Recherches, Etudes, et Techniques, France, at the University of California, Berkeley.
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