Abstract

In a queueing network with a single server and r service nodes, a non-preemptive non-idling policy chooses a node to service at each service completion epoch. Under the assumptions of independent Poisson arrival processes, fixed routing probabilities, and linear holding cost rates, we apply Whistle's method for Arm-acquiring bandits to show that for minimizing discounted cost or long-run average cost the optimal policy is an index policy. We also give explicit expressions for those priority indices.