Abstract
This paper considers an infinite server queue in discrete time in which arrivals are in batches of variable size X and service is provided in batches of fixed size R. We obtain analytical results for the number of busy servers and waiting customers at pre-arrival and arbitrary epochs. For the number of busy servers we obtain a recursive relation for the partial binomial moments and explicit expressions for the marginal binomial moments both in transient and steady states. Special cases are also considered
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