A Queue with Simultaneous Arrivals and Erlang Service Distribution

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Abstract
In this paper the method of generating functions is applied to a queue where the moments of arrival follow a Poisson distribution, but where at each of these moments several persons may arrive simultaneously. Assuming an Erlang distribution for the service times and first-come first-served discipline for the arriving groups, explicit formulas are obtained for the limiting values of the mean number of persons in the queue and in the system, and the mean time that a group of persons who arrive together must wait before one of them is served.

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