Abstract: In this paper, we study the tail behavior of the stationary queue length of an M/G/1 retrial queue which is batch arrived and have subexponential service time by using stochastic decomposition. Then we obtain the correlation between the stationary queue length tail distribution of an M/G/1 retrial queue with batch arrival and the  stationary queue length tail distribution in the corresponding standard M/G/1 queue with batch arrival. Our results for subexponential tails also can be applied to regularly varying tails. Therefore, we get the regularly varying tail asymptotics for the stationary queue length.

Key words: retrial queue, tail asymptotics, stochastic decomposition, subexponential, regular variation