Equity vs. Efficiency in Service Systems with Differentiated Demand

Abstract

In service systems, the pursuit of efficiency by prioritizing certain groups often raises concerns about equity toward those who are being prioritized. In this paper, we study the efficiency-equity trade-off for a queueing system with two customer classes, distinguished by their arrival rate, urgency level (measured by per-unit-time delay cost), and initial well-being at the time of arrival to the system. We examine two types of policies among all work-conserving and non-preemptive priority policies: the efficient (i.e., utilitarian) policy, which maximizes the system's overall expected utility by prioritizing the urgent customers, and the equitable (i.e., egalitarian) policy, which maximizes the minimum expected utility of individual customers. We fully characterize the equitable policy and show that it agrees with the efficient policy when the system utilization is lower than a threshold and disagrees otherwise. We then explore the efficiency-equity trade-off by analyzing the relative efficiency loss associated with the equitable policy, namely the price of equity (PEQ), and the relative equity loss associated with the efficient policy, namely the price of efficiency (PEF). We show that a slight increase in service capacity can lead to significant improvements in both the PEQ and PEF. We further show that the PEQ is significant when there is a moderate gap in delay cost rates and neither arrival rate significantly outweighs the other. In contrast, the PEF is significant when the delay cost rates are close, and the arrival rate of the urgent class significantly dominates that of the nonurgent class. Our results challenge the perception that efficiency and equity lie at the opposite ends of the spectrum, showing that substantial improvements in one can be achieved with only marginal sacrifices in the other. This implies that in situations where alternative options are limited, such as immigration or healthcare systems, a slight adjustment in service allocation can promote equity while maintaining efficiency to a large extent.

Keywords: service operations, queue, equity, fairness, efficiency, price of fairness