On the Modified Supplementary Variable Technique for a Discrete-Time GI/G/1 Queue with Multiple Vacations

초록

This work suggests a new analysis approach for a discrete-time GI/G/1 queue with multiple vacations. The method used is called a modified supplementary variable technique and our result is an exact transform-free expression for the steady state queue length distribution. Utilizing this result, we propose a simple two-momentapproximation for the queue length distribution. From this, approximations for the mean queue length and the probabilities of the number of customers in the system are also obtained. To evaluate the approximations, we conduct numerical experiments which show that our approximations are remarkably simple yet provide fairly good performance, especially for a Bernoulli arrival process.

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