Abstract
Summary It has been proved by Burke (1956) and Reich (1957) that the output process of a single server queue with a Poisson input process and negative exponential distribution for service time is again a Poisson process with the same parameter as the input process. In this paper single server queues with a Poisson input process and a general class of service time distribution are considered. It is shown that successive interdeparture intervals are independent in the limit only in the case the service time is negative exponential. It is shown also that if the size of the waiting room is taken into account as in Finch (1958) then successive departure intervals are not independent in the limit even when the service time is negative exponential.
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