On the bias vector of a two-class preemptive priority queue

We give a closed-form expression for the long-run average cost and the bias vector in a two-class exponential preemptive resume priority queue with holding and switching costs. The bias vector is the sum of a quadratic function of the number of customers in each priority class and an exponential function of the number of customers in the high priority class. We use this result to perform a single step of the policy iteration algorithm in the model where the switches of the server from one priority class to the other can be controlled. It is numerically shown that the policy resulting from the application of a single step of the policy iteration algorithm is close to the optimal policy.