Optimal pricing of priority services

We consider the problem of a service facility that offers m different priority classes to its n customers, and sets a tariff (price-schedule) to maximize profit. Each customer must use the service facility and will select an output rate and the priority classes used to maximize profit. The problem is formulated as a noncooperative game. We show that equilibrium output rates and assignments to priority classes can be determined by solving the integrated system problem (ISP) that maximizes the joint profit of all agents. The service facility can be represented by a network, and ISP is a traffic assignment problem. A tariff schedule that induces each customer to select the integrated system output rate and assignment is said to be vertically efficient. We show that the server can select vertically efficient tariffs that result in an equilibrium. Optimal pricing for the special case where the service facility is modeled as a priority queue is discussed. Examples are included to illustrate the results.