Routing for Fairness and Efficiency in a Queueing Model with Reentry and Continuous Customer Classes.

This paper presents a new framework to study customer routing fairness and efficiency in managing queueing systems with reentry; this framework is motivated by applications in healthcare and criminal justice. Each customer's reentry probability is captured by a proportional hazard model that depends on the type of service offered and the customer's continuous risk score, which is drawn from group-dependent distributions. Unlike the machine learning literature that focuses on fairness in classification with group-dependent risk distributions, we account for fairness directly in the resource allocation captured via the routing decisions. We derive an explicit analytical characterization of the system's efficiency and fairness for two policies: group-unaware and group-aware routing policies. Through the comparison, we quantify the fairness-efficiency trade-off. This trade-off generates useful insights for decision makers into how the cost of fairness depends on different system parameters and when caution should be taken for fairness considerations.