Analysis of the M/G/1 queue with exponentially working vacations--a matrix analytic approach

Authors:
Ji-Hong Li;Nai-Shuo Tian;Zhe George Zhang;Hsing Paul Luh
Affiliations:
College of Economics and Management, Yanshan University, Qinhuangdao, China 066004;College of Science, Yanshan University, Qinhuangdao, China 066004;Dept. of Decision Sciences, Western Washington University, Bellingham, USA 98225 and Faculty of Business Administration, Simon Fraser University, Burnaby, Canada;Department of Mathematical Sciences, National ChengChi University, Taipei, Taiwan
Venue:
Queueing Systems: Theory and Applications
Year:
2009

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Abstract

In this paper, an M/G/1 queue with exponentially working vacations is analyzed. This queueing system is modeled as a two-dimensional embedded Markov chain which has an M/G/1-type transition probability matrix. Using the matrix analytic method, we obtain the distribution for the stationary queue length at departure epochs. Then, based on the classical vacation decomposition in the M/G/1 queue, we derive a conditional stochastic decomposition result. The joint distribution for the stationary queue length and service status at the arbitrary epoch is also obtained by analyzing the semi-Markov process. Furthermore, we provide the stationary waiting time and busy period analysis. Finally, several special cases and numerical examples are presented.