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Title: Analysis of the M/G/1 queue with exponentially working vacations—a matrix analytic approach
Authors: 陸行
Luh,Hsing Paul
Zhang,Zhe George
Contributors: 應數系
Keywords: Working vacations;Embedded Markov chain;M/G/1-type matrix;Stochastic decomposition;Conditional waiting time. 60K25;68M20
Date: 2009.12
Issue Date: 2014-08-05 16:31:35 (UTC+8)
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.
Relation: Queueing Systems,61(2-3),139-166
Data Type: article
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