Cd Some Results for Infinite Server Poisson Queues

A generalization of the M/G/« queueing system with batch arrivals to one with time dependent arrival rates, service times, and batch size distributions is considered. It is shown that both W(t) , the number of people being served at t , and S(t) , the number of people who have completed service by t , are distributed as compound Poisson laws. The distributions of the traffic time average -1 T T y* U(t)dt and Che occupation time 0(t) (the amount of 0 tine past t until the system becomes empty, under the assumption that no new customers are served after t) are also derived. The limiting proportion of busy time and the asymptotic behavior of the traffic tine average are also discussed in the time homogeneous case.