Fluid Limits for Multiclass Many-Server Queues with General Reneging Distributions and Head-of-the-Line Scheduling

Abstract

We describe a fluid model with time-varying input that approximates a multiclass many-server queue with general reneging distribution and multiple customer classes (specifically, the multiclass G/GI/N+GI queue). The system dynamics depend on the policy, which is a rule for determining when to serve a given customer class. The class of admissible control policies are those that are head-of-the-line (HL) and nonanticipating. For a sequence of many-server queues operating under admissible HL control policies and satisfying some mild asymptotic conditions, we establish a tightness result for the sequence of fluid scaled queue state descriptors and associated processes and show that limit points of such sequences are fluid model solutions almost surely. The tightness result together with the characterization of distributional limit points as fluid model solutions almost surely provides a foundation for the analysis of particular HL control policies of interest. We leverage these results to analyze a set of admissible HL control policies that we introduce, called weighted random buffer selection (WRBS), and an associated WRBS fluid model that allows multiple classes to be partially served in the fluid limit (which is in contrast to previously analyzed static priority policies).