Asymptotic Variance of Departures in Critically Loaded Queues

摘要

In the study of queueing systems, the analysis of departure processes has played an important role. Following Burke's theorem, stating that departures of a stationary M/M/1 queue form a Poisson process, many papers have dealt with properties of inter-departure times, departure counting processes, and approximations. In this paper we contribute to the analysis of VarD(t) by considering the 'critically loaded' GI/G/1 queue. This critically loaded regime, in which the mean inter-arrival time equals the mean service time, is relevant from a practical standpoint (as in many real-life situations queues are saturated or close to saturation). Moreover, it is mathematically interesting since it leads to counterintuitive results in line with the BRAVO (Balancing Reduces Asymptotic Variance of Outputs) effect observed previously in finite-capacity birth-death queues.