Priority assignment using dynamic programming for a class of queueing systems

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, preempt resume priority policy is obtained, and an efficient recursive technique is proposed for its computation. The optimal policy is contrasted with an easily computed, suboptimal threshold policy based on heavy traffic approximations. 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 these cases. Several modifications and/or extensions of the single server model to multiple interacting server models are pointed out.