Overlap times in the G/G/1 queue via Laplace transforms

Abstract In this paper, we analyze the steady-state maximum overlap time distribution in the G/G/1 queue. Our methodology exploits Laplace-Stieltjes transforms with a novel decomposition of the maximum overlap time. Explicit expressions are provided for the special cases of the M/G/1 and G/M/1 queues. We also study the steady-state distribution of the minimum overlap time of a customer with its two adjacent customers. We show a novel relationship between the minimum, maximum and the steady-state waiting time.