Queueing problems with arrivals in general stresm and phase type service

This paper deals with the steady state behaviour of a discrete time, single channel, first-come-first-served queueing problem wherein the service phases at two consecutive time-marks are correlated but the arrivals occur in General Stream. Probability Generating functions for the number of phases are obtained under two different models each with assumption that the service phases at two consecutive time marks are (i) correlated and (ii) uncorrelated. For each case the mean queue lengths when the number of phases demanded by an arriving unit is one, are derived. Some particular cases are discussed.