On the value function of a priority queue with an application to a controlled polling model

We give a closed-form expression for the discounted weighted queue length a nd switching costs of a two-class single-server queueing model under a pree mptive priority rule. These expressions are used to do a single step of pol icy iteration in a polling model with a dynamically controlled switching ru le, starting from the preemptive priority rule. Numerical experiments show that this leads to a policy that performs well.