Some Queuing Problems with Phase-Type Service

This paper deals with steady-state behavior of a discrete-time, single-channel, first-come-first-served, queuing problem where the service is accomplished in phases. Probability generating functions for the number of phases are obtained under two different models each with assumptions that the arrivals at two consecutive time-marks are (i) correlated and (ii) uncorrelated. Special cases of importance are discussed. Finally, mean queue length for each model when the number of phases demanded by an arriving unit is one, is derived.