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

Multi-class 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 (1) expressing a controller’s optimism level toward ambiguity, and (2) utilizing incoming data in order 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 cµ-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 (ED) setting, and demonstrate the benefits of using our framework for improving current patient flow policies.