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

A Markovian queue with two heterogeneous servers and multiple vacations

Dequan Yue 1, , Jun Yu 1, and  Wuyi Yue 2,

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.
Keywords: Queueing system, matrix-geometric solution, multiple vacations, stochastic decomposition., heterogeneous servers.
Mathematics Subject Classification: Primary: 60K25; Secondary: 90B2.
Citation: Dequan Yue, Jun Yu, Wuyi Yue. A Markovian queue with two heterogeneous servers and multiple vacations. Journal of Industrial and Management Optimization, 2009, 5 (3) : 453-465. doi: 10.3934/jimo.2009.5.453
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