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Application of Neuts’ method to vacation models with bulk arrivals. (English) Zbl 0742.60098
Summary: This paper studies a single server infinite capacity queueing system with Poisson arrivals of customers groups of random size and a general service time distribution, the server of which applies a general exhaustive service vacation policy. A computational method is applied to obtain the steady state distributions of the queue of a post-departure or inactive phase termination epoch at a post-departure epoch and at an arbitrary epoch. Relations between these distributions are given. As special cases, we consider two hybrid vacation models: the $$(T(SV),N)$$-policy and the $$(T(MV);N)$$-policy. In particular, when the service time distribution is of phase type, explicit results can be obtained for the $$N$$-policy. We show this by a simple example.
MSC:
 60K25 Queueing theory (aspects of probability theory) 90B22 Queues and service in operations research