Tandem queues with bulk arrivals, infinitely many servers and correlated service times

A system of GI^x/G/∞ queues in tandem is considered where the service times of a customer are correlated but the service time vectors for customers are independently and identically distributed. It is shown 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 moments. Numerical experiments for a two-station tandem queueing system demonstrate a somewhat counter-intuitive result that the transient covariance of the joint occupancy level decreases as the covariance of the service times increases. It is also shown that the analysis is valid for a network of GI^x/SM/∞ queues.