Optimal Routing in Closed Queuing Networks

Abstract

In this paper, we establish criteria and propose algorithms for the optimal routing of traffic in closed queuing networks. The objective is to maximize total throughput or (equivalently) to minimize overall average delay. We show that delay is convex over the set of routing patterns in networks with a single class of customers. This enables us to develop a downhill technique for finding the global minimum. The efficiency of our algorithm rests on the fact that the steepest descent direction is readily obtained at each iteration from the MVA algorithm. For multiple-class networks a counterexample is presented to show that convexity does not hold. The technique, however, can still be used to obtain local minima. The algorithm is applied to the optimization of routing in flow-controlled packet-switched networks. Several numerical examples are presented. © 1983, ACM. All rights reserved.