The c — Server Queue with Constant Service Times and a Versatile Markovian Arrival Process

Abstract

Classical results of C. D. Crommelin on the c-server queue with constant service times and Poisson input are extended to the case of the versatile Markovian arrival process, introduced by the author. The purely probabilistic analysis of a related problem in Markov chains leads to an algorithm for the evaluation of the stationary distributions of the queue length and waiting time at an arbitrary epoch. As an illustration, the algorithmic steps are discussed in detail for the case where the arrivals form a Markov-modulated Poisson process.

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