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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.

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
Full Text: DOI EuDML