The queue length in an M/G/1 batch arrival retrial queue

An M/G/1 retrial queue with batch arrivals is studied. The queue length Kμ is decomposed into the sum of two independent random variables. One corresponds to the queue length K∞ of a standard M/G/1 batch arrival queue, and another is compound-Poisson distributed. In the case of the distribution of the batch size being light-tailed, the tail asymptotics of Kμ are investigated through the relation between K∞ and its service times.

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