Equilibrium analysis of a partially observable priority queue

This study considers a single-server Markovian queue with preemptive priority discipline. In front of a server, two queues are formed: a normal queue for ordinary customers and a priority queue for priority customers. When a customer arrives, they can observe the length of the normal queue, but not the priority queue. By considering the length of the normal queue and the expected waiting time in the priority queue, an arriving customer will choose either the priority queue by paying a priority fee or the normal queue for free. We investigate the customers’ equilibrium strategies. Specifically, we find the necessary and sufficient conditions for a threshold-type strategy to be an equilibrium. We also investigate the stability of equilibria. In addition, we examine the effect of information disclosure regarding the length of the priority queue on equilibrium behavior.