The queue length in an <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">G</Emphasis>/1 batch arrival retrial queue

An M/G/1 retrial queue with batch arrivals is studied. The queue length K _μ 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 K _μ are investigated through the relation between K _∞ and its service times.