Reservation Policies in Queues: Advance Deposits, Spot Prices, and Capacity Allocation

At firms such as restaurants, customers either make reservations in advance or join queues on the spot. Reservation holders may not show up, and walk‐ins have to wait. Using a game‐theoretic model between the firm and customers, this paper studies the following: (i) reservation deposits and service prices, and (ii) capacity allocation between reservations and walk‐ins. We have three main results: (i) When reservation no‐shows lead to wasted capacity that cannot be reallocated, the firm should front‐load all charges into the reservation deposit; (ii) The firm should charge a lower service price to reservation‐holders than to walk‐in customers when it decides to serve both; (iii) Less capacity should be allocated for reservations as the potential market size grows; with sufficiently large potential demand, the firm should stop taking reservations. Our results follow from key operational tradeoffs between reservations and queues: reservations permit 100% utilization, but queues operate at less than 100%; however, reservations have constant returns to scale, while queues enjoy increasing returns.