Journal of Applied Mathematics and Stochastic Analysis
Volume 2004 (2004), Issue 4, Pages 337-357
doi:10.1155/S1048953304403025
A finite capacity bulk service queue with single vacation and Markovian arrival process
Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
Received 29 March 2004; Revised 11 June 2004
Copyright © 2004 U. C. Gupta and Karabi Sikdar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.