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A finite capacity bulk service queue with single vacation and Markovian arrival process. (English) Zbl 1084.60054
From the authors’ abstract: Vacation time queues with Markovian arrival process (MAP) are mainly useful in modeling and performance analysis of telecommunication networks based on asynchronous transfer mode environment. This paper analyzes a single-server finite capacity queue wherein service is performed in batches of maximum size “\(b\)” with a minimum threshold “\(a\)” and arrivals are governed by MAP. The server takes a single vacation when he finds less than “\(a\)” customers after service completion. The distributions of buffer contents at various epochs (service completion, vacation termination, departure, arbitrary and pre-arrival) have been obtained. Also, some performance measures such as loss probability and average queue length are discussed, and some numerical results are presented.

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