On queueing systems with renewal departure processes

Abstract

It is proved that, for a large class of stable stationary queueing systems with renewal arrival processes and without losses, a necessary condition for the departure process also to be a renewal process is that its interval distribution be the same as that of the arrival process. This result is then applied to the classicalGI/G/squeueing systems. In particular, alternative proofs of known characterizations of theM/G/1 andGI/M/1 systems are given, as well as a characterization of theGI/G/∞ system. In the course of the proofs, sufficient conditions for the existence of all the moments of the stationary queue-size distributions of both theGI/G/1 andGI/G/∞ systems are derived.