A generalization of the decomposition property in the M/G/1 queue with server vacations

Authors:
Tetsuya Takine;Toshiharu Hasegawa
Affiliations:
Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, Kyoto 606, Japan;Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, Kyoto 606, Japan
Venue:
Operations Research Letters
Year:
1992

Citing 3
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Time-dependent analysis of M/G/1 vacation models with exhaustive service

Queueing Systems: Theory and Applications
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Conditional and unconditional distributions for M/G/1 type queues with server vacations

Queueing Systems: Theory and Applications

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Abstract

This paper considers the M/G/1 queueing systems with server vacations. For a very general class of such systems, Fuhrmann and Cooper have shown that the stationary queue length at a random point in time is distributed as the sum of two independent random variables, one of which is the stationary queue length at a random point in time in the corresponding standard M/G/1 queue. This property is called the stochastic decomposition in the M/G/1 queue with server vacations. In this paper, we show that this decomposition property is also valid for the joint probability distribution of the queue length and the forward recurrence service time.