Rational Abandonment from Observable Priority Queues: Equilibrium Strategy, Performance, and Pricing Implications

Observable priority queues, where some customers are served ahead of others, are prevalent in many service systems, ranging from the entertainment industry to emergency departments (EDs). In this paper, we study the rational abandonment behavior of utility-maximizing customers in the context of an observable two-class priority queue and identify novel performance and pricing implications. We first characterize the structure of the rational abandonment strategy and show that it has a threshold-based last-come, first-abandon structure. We then examine the steady-state performance of the system under the rational abandonment strategy and in contrast with an exogenous abandonment model commonly used in the literature. We show that using the exogenous abandonment model could result in highly suboptimal decisions when considering capacity planning to meet target waiting times and/or abandonment rates. We further investigate optimal pricing strategies under rational abandonment. Our results highlight the importance of the timing of payments. We show that welfare maximization requires charging only a service fee and no entrance fee. In contrast, revenue maximization generally requires a combination of both an entrance and a service fee. Furthermore, welfare-maximizing prices always involve abandonment, whereas revenue maximization may require pricing strategies that prevent abandonment. Finally, we discuss the implications of our results for our motivating applications, including the perils of charging nonurgent ED patients upfront. This paper was accepted by Baris Ata, stochastic models and simulation. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.01924 .