Settling time bounds forM/G/1 queues

This paper addresses the question of how long it takes for anM/G/1 queue, starting empty, to approach steady state. A coupling technique is used to derive bounds on the variation distance between the distribution of number in the system at timet and its stationary distribution. The bounds are valid for allt. This research was supported in part by a grant from the AT&T Foundation and NSF grant DCR-8351757.