Application of dynamic programming to priority assignment in a class of queueing systems with impatient customers

This paper deals with the problem of allocating attention among multiple tasks in a supervisory control system. The situation is modeled in the framework of a single server priority queueing system. Using Bellman's principle of optimality, a functional equation for the optimal, state dependent, nonpreemptive priority policy is obtained. The optimal policy is contrasted with an easily computable, suboptimal threshold policy, based on heavy traffic approximation. It is concluded that the utility of the optimal policy is significant at medium to high traffic intensities, and that the heavy traffic, suboptimal policy should be of considerable use in this regard. Several modifications of the single server model, as well as extensions to multiple, interacting sever models are pointed out.