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On vacation models with bulk arrivals. (English) Zbl 0701.60099
Summary: We consider a single server infinite capacity queueing system with Poisson arrivals of customer groups of random size and a general service time distribution, the server of which applies a general exhaustive service vacation policy. We are concerned with the steady-state distributions of the queue length at a post-departure epoch and at an arbitrary epoch. We give a probabilistic proof of a relation between each of these distributions and the corresponding one in the bulk arrival model without server vacations. Specific types of vacation policies are then considered.

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research