Equilibrium strategy of a processor-sharing system with discriminatory discipline

We study the equilibrium strategies of a processor-sharing service system with discriminatory discipline. We consider both cases that customer can or cannot observe how many customers in the system upon arrival. Respectively, we obtain a threshold strategy for each class of customers in the observable case, and the customer´s equilibrium arrival rate in the unobservable case. And further, we derive the bounds of the service price and give an effective algorithm to calculate the optimal service price to maximize the service provider´s profit. Finally, some numerical examples are given to verify our results.