Global Stability of Two-Station Queueing Networks

Abstract

This paper summarizes results of Dai and Vande Vate [15, 14] characterizing explicitly, in terms of the mean service times and average arrival rates, the global pathwise stability region of two-station open multiclass queueing networks with very general arrival and service processes. The conditions for pathwise global stability arise from two intuitively appealing phenomena: virtual stations and push starts. These phenomena shed light on the sources of bottlenecks in complicated queueing networks like those that arise in wafer fabrication facilities. We show that a two-station open multi-class queueing network is globally pathwise stable if and only if the corresponding fluid model is globally weakly stable. We further show that a two-station fluid model is globally (strongly) stable if and only if the average service times are in the interior of the global weak stability region. As a consequence, under stronger distributional assumptions on the arrival and service processes, the queueing network is globally stable in a stronger sense when the mean service times are in the interior of the global pathwise stability region. Namely, the underlying state process of the queueing network is positive Harris recurrent.KeywordsService TimeTraffic IntensityGlobal StabilityFluid ModelFluid LimitThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.