A Queueing Approximation of MMPP/PH/1

We consider the well-studied MMPP/PH/1 queue and illustrate a method to find an almost equivalent model, the MTCP/PH/1. MTCP stands for Markovian TransitionCounting Process. It is a counting process that has similar characteristics to MMPP (Markov Modulated Poisson Process). We prove that for a class of MMPPs there is an equivalent class of MTCPs. We then use this property to suggest an approximation for MMPP/PH/1 in terms of the first two moments. We numerically show that the steady state characteristics of MMPP/PH/1 are well approximated by the associated MTCP/PH/1 queue. Our numerical analysis leaves some open problems on bounds of the approximations. Of independent interest, this paper also contains a lemma on the workload expression of MAP/PH/1 queues which to the best of our knowledge has not appeared elsewhere.