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Application of Neuts’ method to bulk queueing models with vacations. (English) Zbl 0827.90057
Summary: We study a single server infinite capacity queueing system in which customers, arriving in groups according to a Poisson process, are served in batches under the usual service rule. The server applies a general exhaustive service vacation policy. Computational results for the queue length at a post-departure or inactive phase termination epoch, at a post-departure epoch and at an arbitrary epoch are given. In particular, we consider a vacation model where the decision of whether to take a vacation or not, in a given inactive phase, is allowed to depend on the number of vacations already taken in this inactive phase and the number of customers waiting, compared to a specified number \(N\). As special cases, it includes the \((T(SV); N)\)-policy and the \((T(MV); N)\)-policy. We discuss two applications in the analysis of production, computer and communication systems. A simple numerical example is also considered.
90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
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