Advance Selling and Upgrading in Priority Queues

Problem definition: 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. Customers who purchase tickets in advance 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. Methodology/results: 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 revenue. We investigate two pricing schemes, both with and without upgrading options, under different scenarios depending on the proportion of customers who have access to advance ticket purchasing. When all customers have access to advance ticket purchasing, our findings indicate that the advance-and-spot selling scheme yields the same maximum revenue as the scheme that includes the upgrading option if the spot regular ticket price is not too large; thus, the upgrading option becomes unnecessary. Otherwise, allowing upgrading generates more revenue (and social welfare). Interestingly, although upgrading options offer consumers greater flexibility, they reduce consumer surplus in scenarios where upgrading increases revenue. When some customers only purchase tickets on the spot, our numerical analysis shows that allowing upgrading results in higher revenue when the probability of high system congestion is large and highlights cases when the revenue gap is significant. Finally, we extend our analysis to account for customers’ balking behavior and the additional waiting time incurred when purchasing tickets on the spot, providing a robust check on scheme comparison. Managerial implications: Our paper is one of the first to investigate—in the context of queueing economics—the advance selling strategy together with upgrading option, taking into account arrival rate uncertainty. 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. Funding: Financial support from the National Natural Science Foundation of China [Grants 72101248, 72471215, 72122019, 72471005, and 72031006] is gratefully acknowledged. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0410 .