Journal of Applied Mathematics and Stochastic Analysis
Volume 2004 (2004), Issue 4, Pages 337-357

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

U. C. Gupta and Karabi Sikdar

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.


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.