Rational Abandonment from Priority Queues: Equilibrium Strategy and Pricing Implications

Observable priority queues are prevalent in practice and create incentives for utility-maximizing customers to abandon after joining. However, the literature has so far ignored this behavior and the resulting system control issues. This paper studies the rational abandonment behavior of utility-maximizing customers in the context of an observable two-class priority queue, and identifies novel implications. We characterize the equilibrium abandonment strategy of low-priority customers and show that it has a threshold structure that depends on the fee structure. We then consider pricing as a means to control the balking and abandonment behavior, both under welfare maximization and revenue maximization. Our pricing 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. This two-fee structure is equivalent to charging only upon entrance but offering a partial cancellation refund. Moreover, charging only an entrance fee may generate more or less revenue than charging only a service fee, but the performance of the latter policy is more robust. This appears to be the first paper that (i) gives an analytical characterization of equilibrium abandonment behavior in observable priority queues, and (ii) studies pricing for any queueing system in presence of rational customer abandonment.