In this paper, we analyze the customers’ strategic behavior in an \(\varvec{M/M/1}\) queue with differentiated vacations. The server takes a type 1 vacation after a busy period and a type 2 vacation when it returns from a vacation (type 1 or type 2) and finds the system still empty. The customers decide whether to join or not the queue based on a reward-cost structure and the available information on the system state. We consider two cases: the partially unobservable and the fully unobservable queues. For each case, we derive the corresponding Nash equilibrium and social optimal strategies along with the stationary behavior of the system. Through numerical results, we show the effect of some system parameters and information levels on the optimal strategies, social benefit, throughput as well as the price of anarchy.
