On queues in discrete regenerative environments, with application to the second of two queues in series

Abstract

Let Un be the time between the nth and (n + 1)th arrivals to a single-server queuing system, and Vn the nth arrival's service time. There are quite a few models in which {Un, Vn, n ≥ 1} is a regenerative sequence. In this paper, some light and heavy traffic limit theorems are proved solely under this assumption; some of the light traffic results, and all the heavy traffic results, are new for two such models treated earlier by the author; and all the results are new for the semi-Markov queuing model.In the last three sections, the results are applied to a single-server queue whose input is the output of a G/G/1 queue functioning in light traffic.