July  2009, 5(3): 453-465. doi: 10.3934/jimo.2009.5.453

A Markovian queue with two heterogeneous servers and multiple vacations

1. 

Department of Statistics, College of Sciences, Yanshan University, Qinhuangdao 066004, China

2. 

Department of Intelligence and Informatics, Konan University, Kobe 658-8501

Received  September 2008 Revised  November 2008 Published  June 2009

In this paper, we study an M/M/2 queueing system with multiple vacations where the service rates of the servers are not identical. This queuing system has been analyzed as a quasi-birth and death process by Kumar and Madheswari (2005). However, by expressing the rate matrix explicitly, we have obtained a explicit expression of the stationary distribution of the queue length. The conditional stochastic decomposition properties of the queue length and the waiting time have been also established for such a system.
Citation: Dequan Yue, Jun Yu, Wuyi Yue. A Markovian queue with two heterogeneous servers and multiple vacations. Journal of Industrial & Management Optimization, 2009, 5 (3) : 453-465. doi: 10.3934/jimo.2009.5.453
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