Journal of Applied Mathematics and Stochastic Analysis
Volume 2008 (2008), Article ID 396871, 20 pages
Research Article

Analysis of MAP/PH(1), PH(2)/2 Queue with Bernoulli Vacations

B. Krishna Kumar,1 R. Rukmani,2 and V. Thangaraj3

1Department of Mathematics, College of Engineering, Anna University, Chennai 600 025, India
2Department of Mathematics, Pachaiyappa's College, Chennai 600 030, India
3Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600 005, India

Received 13 June 2008; Accepted 5 October 2008

Academic Editor: Ho Lee

Copyright © 2008 B. Krishna Kumar 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 two-heterogeneous-server queueing system with Bernoulli vacation in which customers arrive according to a Markovian arrival process (MAP). Servers returning from vacation immediately take another vacation if no customer is waiting. Using matrix-geometric method, the steady-state probability of the number of customers in the system is investigated. Some important performance measures are obtained. The waiting time distribution and the mean waiting time are also discussed. Finally, some numerical illustrations are provided.