TANDEM QUEUES WITH BULK ARRIVALS, INFINITELY MANY SERVERS AND CORRELATED SERVICE TIMES

A system of GI(x)/G/infinity queues in tandem is considered where the service times of a customer are correlated but the service time vector s for customers are independently and identically distributed. It is s hown that the binomial moments of the joint occupancy distribution can be generated by a sequence of renewal equations. The distribution of the joint occupancy level is then expressed in terms of the binomial m oments. Numerical experiments for a two-station tandem queueing system demonstrate a somewhat counterintuitive result that the transient cov ariance of the joint occupancy level decreases as the covariance of th e service times increases. It is also shown that the analysis is valid for a network of GI(x)/SM/infinity queues.