A Markovian queue with two heterogeneous servers and multiple vacations

Dequan Yue; Jun Yu; Wuyi Yue

doi:10.3934/jimo.2009.5.453

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2009, Volume 5, Issue 3: 453-465. Doi: 10.3934/jimo.2009.5.453

This issue Previous Article M/M/3/3 and M/M/4/4 retrial queues Next Article Analysis of discrete-time space priority queue with fuzzy threshold

A Markovian queue with two heterogeneous servers and multiple vacations

1.
Department of Statistics, College of Sciences, Yanshan University, Qinhuangdao 066004
2.
Department of Intelligence and Informatics, Konan University, Kobe 658-8501

Received: September 2008

Revised: November 2008

Published: July 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 60K25; Secondary: 90B22.

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