Optimal control of a queueing system with two interacting service stations and three classes of impatient tasks

The problem of task selection and service priority is studied for a queueing network with two interacting service stations and three classes of impatient tasks. By using stochastic dynamic programming, a functional equation for the optimal, state-dependent priority assignment policy is derived. Properties of the optimal cost-to-go functions and the optimal policy are established through inductive proofs. It is shown that the optimal policy is governed by two switching surfaces in the three-dimensional state space (one dimension for each task class). For the infinite-time-horizon case, the optimal policy is shown to be stationary. In this case, the optimal cost-to-go function and switching surfaces are obtained numerically by using the overrelaxed Gauss-Seidel method. Sensitivities of the optimal policy with respect to key system parameters are also investigated.<>