Scheduling an Overloaded Multiclass Many-Server Queue with Impatient Customers

Abstract

We describe a fluid model with time-varying input that approximates a multiclass many-server queue with time-varying arrivals (specifically, the multiclass G/GI/N +GI queue). We show how to use that fluid model to approximately solve scheduling control problems when the arrival rate remains constant over time. The key is to characterize the invariant states of the fluid model, because they typically provide an approximation to the mean steady-state behavior of the queue under a wide range of scheduling policies. The resulting fluid control problem motivates using a static priority scheduling policy, that is consistent with the simple index rule known as cμ, when the objective is to minimize the long-run average abandonment rate. We end by discussing several open problems.