Redistributing Priority Payments in Service Systems

Abstract

Problem Definition: We study a service system in which each customer has a random waiting cost and must choose between two queues: regular (no cost) or priority (for a fee). Social preferences may make customers more willing to purchase priority if the payments are redistributed to compensate inconvenienced customers.
Methodology/Results: We study the impact of the recipient of the priority payment---the service provider or the inconvenienced customers in the regular queue---on customer priority-purchasing decisions. To determine the waiting-cost-dependent optimal strategies, we first establish structural results at a sample-path level and then prove that they generalize. With no redistribution, we show that the equilibrium obeys a cost-dependent, increasing-threshold structure. We then prove that the same structure prevails with redistribution. We also prove that redistribution results in fewer priority purchases because compensating regular-queue customers makes priority relatively less attractive. We then study both settings in the lab. Subjects were not biased to purchase priority more often in the compensation treatment, failing to display a social preference. Instead, the aggregate number of priority purchases aligned closely with theory in both treatments, i.e., more priority purchases occurred in the no-compensation treatment. When subjects made mistakes, across both treatments they were more likely to incorrectly choose the regular queue than they were to incorrectly choose the priority queue.
Managerial Implications: Our theoretical results can help service providers predict priority purchasing patterns for better capacity planning. That our experiments align closely with the theory reinforces the value of these predictions. Moreover, for systems (like city congestion tolls) whose implicit goal is to achieve fewer purchases, our results imply that a system planner can disincentivize purchases merely by redistributing proceeds. Finally, subject tendency to under-purchase priority relative to the theory suggests that customers may have an intrinsic preference for the "free" option (the regular queue).

Keywords: priority queues, behavioral operations, strategic queueing, social norms, behavioral queueing