Subexponential asymptotics of the BMAP/GI/1 queue

Abstract

This paper considers the stationary queue length and waiting time distributions in a FIFO BMAP/GI/1 queue with heavy-tailed service times and that with heavy-tailed batch sizes. In each case, we provide sufficient conditions under which the stationary queue length and waiting time distributions are subexponential. Furthermore, we obtain asymptotic relationships between the tail distributions of the stationary queue length and waiting time.