Dynamic Scheduling in a Many-Server Multi-Class System: The Role of Customer Impatience in Large Systems

Abstract

We study optimal scheduling of customers in service systems, such as call centers. In such systems, customers typically hang up and abandon the system after waiting for a long time for their service to commence. Such abandonments are detrimental for the system, and so managers typically use scheduling as a tool to mitigate it. In this paper we study the interplay between customer impatience and scheduling decisions when managing heterogeneous customer classes. Specifically, our focus is on general patience distributions, in which a customer's instantaneous propensity to abandon may change over time. We find that incorporating these temporal changes into the scheduling decisions can lead to a significant improvement in the system performance. Formally, we solve the underlying Diffusion Control Problem for these systems, and characterize near-optimal scheduling policies. One of our main results is that for a class of parameters, we establish sufficient conditions for both the optimality and non-optimality of threshold policies, which are widely used due to their ease of implementation.