Stochastic Order Relationships Between GI/G/k Systems

Abstract

Consider two GI/G/k queueing systems in which the second system has stochastically larger interarrival times and/or stochastically shorter service times than the first system. In this paper we find sufficient conditions under which this implies stochastically shorter waiting time, virtual waiting time, queue size, and imbedded queue size, for the second system as compared to the first.