A Model of Rational Retrials in Queues

Consumers often have to join a queue before they can obtain a service; however, they suffer disutility in waiting for the service. When consumers can self-organize the timing of their service visits, they may avoid long queues and choose to retry later. Nevertheless, the existing research on decision-making in queues has focused mainly on join or balk decisions, while acknowledging that some consumers may postpone their visits and retry later. We study an observable queue in which consumers make rational join, balk and (costly) retry decisions upon their arrival. Retrial attempts could be costly due to factors such as transportation costs, retrial hassle and visit fees. We characterize the equilibrium under such retrial behavior, and study its welfare effects. With the additional option to retry, consumer welfare could worsen compared to the welfare in a system without retrials. Surprisingly, self-interested consumers retry too little (in equilibrium compared to the socially optimal policy) when the retrial cost is low, and retry too much when the retrial cost is high. We explore the impact of customers who have emergency needs and do not have the flexibility to retry or balk. We find that the presence of these “critical” arrivals typically destroys consumer welfare, even that their welfare is increased by the presence of the “regular” consumers who make join, balk, or retry decisions.