A Closed Queueing Network with Strategic Service Differentiation.

We consider a service system with a single server, exponentially distributed service time, and two types of service rates – high and low. A customer chooses to obtain a high rate or a low rate service, and then the customer is active for an exponentially distributed period of time with a given high or low rate, respectively, and returns to the queue to be served again. Customers strategically choose a service type in order to maximize their long-run activity time. We investigate which strategies of the customers are socially optimal and explore conditions for Nash equilibria. We examine symmetric and asymmetric strategies, as well as behavioral strategies. We focus on the game with two customers. We prove an equivalence of the conditions for the existence of pure and mixed equilibria to those in the behavioral model, though the value of the mixed equilibrium strategy differs from the value of the behavioral equilibrium strategy for the same parameters. We show that a pure asymmetric equilibrium does not exist, a pure asymmetric strategy cannot be socially optimal, and a pure symmetric equilibrium always exists.