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We consider an M/G/1 retrial queue, where the service time distribution has a finite exponential moment. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. The result is obtained by investigating analytic properties of probability generating functions for the queue size and the server state.

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No abstract

In this paper, we are concerned with the analysis of the queue length and waiting time distributions in a batch arrival M X /G/1 retrial queue. Necessary and sufficient conditions are obtained for the existence of the moments of the queue length and waiting time distributions. We also provide recursive formulas for the higher order moments of the queue length and waiting time distributions.