Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 173407, 10 pages
http://dx.doi.org/10.1155/2013/173407
Research Article

The M/M/ Repairable Queueing System with Variable Breakdown Rates

Shengli Lv1 and Jingbo Li2

1School of Science, Yanshan University, Qinhuangdao 066004, China
2College of Mathematics and Information, Hebei Normal University of Science and Technology, Qinhuangdao 066004, China

Received 6 October 2012; Accepted 31 December 2012

Academic Editor: Xiaochen Sun

Copyright © 2013 Shengli Lv and Jingbo Li. 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 considers the M/M/ repairable queuing system. The customers' arrival is a Poisson process. The servers are subject to breakdown according to Poisson processes with different rates in idle time and busy time, respectively. The breakdown servers are repaired by repairmen, and the repair time is an exponential distribution. Using probability generating function and transform method, we obtain the steady-state probabilities of the system states, the steady-state availability of the servers, and the mean queueing length of the model.