The relations among the queue size distributions at departure, arbitrary and pre-arrival epochs in the MAP/G/1 queue with finite/infinite buffer – an alternative approach

In this paper we consider a single server finite buffer queue wherein arrivals are governed by Markovian arrival process and the service times are arbitrarily distributed. Using the supplementary variable method, the relations among the limiting queue size distributions at post-departure, arbitrary and pre-arrival epochs are obtained. Furthermore, similar results have also been derived for the infinite buffer queue. These relations are consistent with the known results and the method of derivation is simple and elegant.