Optimality equations based performance potentials for a class of controlled closed queueing networks

This paper deals with the performance optimization problem of a class of controlled queueing network systems. We introduce two fundamental concepts: the discounted cost performance potentials and average cost performance potentials, and consider a fundamental relation between the two potentials. Under a general assumption, we establish directly the optimality equation for infinite time horizon average cost model and prove the existence of an optimal solution in a compact action set by using properties of the performance potentials, suggest a policy-optimality algorithm and give a numerical example to illustrate the application of the proposed algorithm.