A finite capacity bulk service queue with single vacation and Markovian arrival process

U. C. Gupta and Karabi Sikdar

International Journal of Stochastic Analysis, 2004, vol. 2004, 1-21

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 (ATM) 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. Finally, some performance measures such as loss probability and average queue length are discussed. Numerical results are also presented in some cases.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:720694

DOI: 10.1155/S1048953304403025

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