Journal of Applied Mathematics and Stochastic Analysis
Volume 2005 (2005), Issue 3, Pages 353-373

Complete analysis of MAP/G/1/N queue with single (multiple) vacation(s) under limited service discipline

U. C. Gupta,1 A. D. Banik,1 and S. S. Pathak2

1Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
2Department of Electronics and Electrical Communication Engineering, Indian Institute of Technology, Kharagpur 721302, India

Received 25 June 2004; Revised 4 February 2005

Copyright © 2005 U. C. Gupta et al. 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.


We consider a finite-buffer single-server queue with Markovian arrival process (MAP) where the server serves a limited number of customers, and when the limit is reached it goes on vacation. Both single- and multiple-vacation policies are analyzed and the queue length distributions at various epochs, such as pre-arrival, arbitrary, departure, have been obtained. The effect of certain model parameters on some important performance measures, like probability of loss, mean queue lengths, mean waiting time, is discussed. The model can be applied in computer communication and networking, for example, performance analysis of token passing ring of LAN and SVC (switched virtual connection) of ATM.