Performance analysis for the Geom/G/1 queue with single working vacation

Authors:
Xiuli Xu;Yance Li;Naishuo Tian
Affiliations:
Yanshan University, Qinhuangdao, China;Yanshan University, Qinhuangdao, China;Yanshan University, Qinhuangdao, China
Venue:
Proceedings of the 5th International Conference on Queueing Theory and Network Applications
Year:
2010

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Abstract

In this paper, we analyzed a Geom/G/1 queue with single working vacation. Firstly, we obtained the M/G/1-type structure matrix of the two-dimensional embedded Markov chain. Using the matrix analysis method, highly complicated PGF of the stationary queue size is firstly derived. Furthermore, we got the stochastic decomposition formulae for the PGF of the stationary queue size and the stationary waiting time. Finally, several numerical examples are presented to verify these results.