Make waiting not to seem like waiting: Capacity management of waiting-area entertainment

To operationalize the psychological principle that “occupied time feels shorter than unoccupied time”, it is common for service providers to offer entertainment options in the waiting areas. Typical examples that put in practice this mechanism include amusement parks, car dealers, airports, hospitals, restaurants, etc. In this paper, we study a queueing system where the server provides entertainment services to waiting customers. Assuming customers are strategic and delay-sensitive, we formulate a game-theoretical model and study customers' equilibrium behavior in response to this mechanism. Because offering waiting-area entertainment incurs extra operational costs, we discuss whether and when this option will benefit the service provider and obtain the optimal entertainment capacity that maximizes the system's profit. Our analysis reveals that this option is appealing if and only if the market size is intermediate and that the optimal capacity of the entertainment is a unimodal function in the market size. Our insights continue to remain valid when the service fee becomes endogenous.