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Synchronizing Travelling and Waiting Processes: Customer Strategy with an Online Reservation System

Online reservation system allows customers to join a queue and virtually wait for service before arriving on site. For example, some platforms have been designed to collect the information of restaurants and show the real-time congestion levels (e.g., Nowait). We consider a model in which customers must travel from their location to the service site incurring a travelling cost. Upon arrival to the service site the customer may have to wait until the customers ahead finish their service. When customers intend to book service online, they are informed about their positions in the queue at the time of booking, so that they make their decision whether or not to join the queue taking into account both their travelling time and expected waiting time. Intuitively, the more time customers spend on travelling to the site, the less time they have to wait in line. Therefore, there exists a tradeoff between the travelling and waiting cost. We show that if the travelling cost is sufficiently high, the attraction of the service is decreasing in the distance between the customer and service location; and if the travelling cost is negligible, the attraction of the service is increasing in the distance. With such customers behavior, the optimal location strategy of a service site heavily relies on the conditions of the travelling and benefit of the service.