SOME RESULTS FOR INFINITE SERVER POISSON QUEUES
CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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A generalization of the MGinfinity 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 Wt, the number of people being served at t, and St, the number of people who have completed service by t, are distributed as compound Poisson laws. The distributions of the traffic time average the integral from 0 to T of the quantity WtdtT and the occupation time 0t the amount of time 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 time average are also discussed in the time homogeneous case.
- Operations Research