SUMMARY A queue at which arrivals occur randomly in batches of fixed size r and for which the service times are independent negative exponential variates is considered. Expressions are obtained for the moments of the transient waiting time distribution and the distribution of the number of customers in the system just before the n th batch arrives. The distribution of the number of customers served in a busy period is also determined.
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Peter J. Brockwell (1963) studied this question.
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