Priority Service Pricing with Heterogeneous Customers: Impact of Delay Cost Distribution

This paper studies the priority pricing problem for a single-server queueing system with two priority classes in which customers have different sensitivities to delay. The system makes a fixed-delay announcement to inform arriving customers of the expected delay for each class, whereupon each customer must decide which class to join. Any customer who joins the priority class is charged a fixed priority price. Our examination of customers' joining behavior under any given priority prices reveals that there can be multiple equilibrium delays and that the number of those delays depends on the structure of customers' delay cost distribution. We characterize the stability of these equilibria and show that the system can reach the largest or smallest equilibrium by making a proper initial delay announcement. In addition, we consider two pricing problems to maximize the system's long-run average revenue and social welfare, respectively. The results derived here establish that both the revenue-maximizing price and the social welfare-maximizing price are quite sensitive to the delay cost distribution. Finally, we investigate the influence of the number of priority classes by extending the two-priority-class model to a multiple-priority-class model.