Advance Selling and Upgrading in Priority Queues

We study advance selling and upgrading in a priority queue setting that emerges in the amusement park industry. Customers choose to buy fast-track or regular tickets depending on their heterogeneous waiting costs. At the park entrance, customers can choose tickets based on the observed congestion levels. Advance tickets are cheaper, but customers suffer from congestion uncertainty. Upgrading options allow customers to purchase regular tickets in advance and upgrade on-site if the congestion turns out to be high. The seller's objective is to find the optimal pricing scheme to maximize revenue. We analyze a two-stage model in a queueing game framework. Under full coverage and fixed regular ticket prices, the seller sets the priority ticket prices to maximize the extra revenue. We find that if all customers arrive in advance, in many cases advance-and-spot selling without upgrading achieves the upper bound---the optimal extra revenue from the state-dependent priority pricing, hence the upgrading option is not necessary. On the other hand, if some customers arrive on the spot, allowing upgrading is more likely to generate more revenue. In scenarios where upgrading increases the revenue, the upgrading options, despite offering consumers greater flexibility, hurt consumer surplus. Our paper is one of the first to investigate—in the context of queueing economics—the advance selling strategy together with upgrading. Our results offer guidance on selling scheme design for ticket sellers, and provide one economic explanation for the various pricing policies seen in the amusement park industry