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The network throughput is an important performance criteria for the packet ring networks. Since maximizing the network throughput can lead to severe bias in bandwidth allocation among all flows, fairness should be imposed to prevent bandwidth starvation. The challenge here, therefore, is the joint optimization of the network throughput and fairness. In this paper, we present the optimal bandwidth assignment scheme to decompose this optimization problem into two tasks, one for finding fair bandwidth assignment and the other for finding the optimal routing. The network throughput is maximized under the fairness constraints when these tasks are performed iteratively.