Data-Driven Percentile Optimization for Multiclass Queueing Systems with Model Ambiguity: Theory and Application

Abstract

Multiclass queueing systems widely used in operations research and management typically experience ambiguity in real-world settings in the form of unknown parameters. For such systems, we incorporate robustness in the control policies by applying a data-driven percentile optimization technique that allows for (a) expressing a controller’s optimism level toward ambiguity and (b) utilizing incoming data to learn the true system parameters. We show that the optimal policy under the percentile optimization objective is related to a closed-form, priority-based policy. We also identify connections between the optimal percentile optimization and c µ-like policies, which, in turn, enables us to establish effective but easy-to-use heuristics for implementation in complex systems. Using real-world data collected from a leading U.S. hospital, we also apply our approach to a hospital emergency department setting and demonstrate the benefits of using our framework for improving current patient flow policies.