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.