Equitable Staffing in Heterogenous Queueing Systems: A Framework for Delay-Minimizing Resource Allocation

Abstract

Public resources are fundamentally limited in capacity, and delays in access are often unavoidable. Traditional approaches to resource planning typically ask: how many resources are needed to reduce delay? However, this question becomes significantly more complex when a single resource system must be partitioned into multiple, structurally distinct subsystems—such as by gender, geographic region, or urgency of need. Each of these subsystems exhibits its own demand profile and delay behavior, yet they all draw from a common, shared resource pool. In such environments, we cannot make staffing decisions for each group in isolation. The overall system functions as an interconnected whole, and performance in one subsystem is inherently tied to the behaviors of the others. This thesis presents a queueing-theoretic framework for analyzing and staffing such group-structured public resource systems. Rather than minimizing delay within each group independently, we propose a method for balancing delay across heterogeneous subsystems in a way that reflects their joint use of limited capacity. We term this approach equitable staffing—a strategy that allocates resources not merely in proportion to demand, but with sensitivity to delay patterns across groups. Applications to gender-partitioned restrooms and regionally-deployed ambulance fleets demonstrate how this framework can guide system-aware staffing decisions, ensuring both fairness and efficiency in public resource design.