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International Journal of Stochastic Analysis
Volume 2012 (2012), Article ID 145867, 16 pages
http://dx.doi.org/10.1155/2012/145867
Research Article

An M/M/2 Queueing System with Heterogeneous Servers Including One with Working Vacation

1Department of Mathematics, Cochin University of Science and Technology, Cochin 682022, India
2Department of Mathematics, Government College, Chittur, Palakkad 678104, India

Received 24 February 2012; Accepted 13 May 2012

Academic Editor: Ho Lee

Copyright © 2012 A. Krishnamoorthy and C. Sreenivasan. 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

This paper analyzes an M/M/2 queueing system with two heterogeneous servers, one of which is always available but the other goes on vacation in the absence of customers waiting for service. The vacationing server, however, returns to serve at a low rate as an arrival finds the other server busy. The system is analyzed in the steady state using matrix geometric method. Busy period of the system is analyzed and mean waiting time in the stationary regime computed. Conditional stochastic decomposition of stationary queue length is obtained. An illustrative example is also provided.