In this paper we introduce and evaluate a method for optimizing the router arbitration policy in point- to-point networks. These networks use multiple high- speed, low-cost routers to rapidly switch data directly between data sources and destinations. We assume that routers use an arbitration algorithm that has the ability to assign different priorities to different links thus controlling the distribution of available bandwidth among channels. We propose an analytical method that allows us to determine the correct priorities for channels so as to achieve fair arbitration thus mini- mizing latency, increasing throughput and eliminating tree saturation.In our study we used data generated by a simulation tool to validate the proposed analytical model for determining the weights (priorities) of router ports and to evaluate the resulting performance improvements. Link usage statistics were recorded by the simulator for the purpose of performing a detailed investigation of congestion effects and especially tree saturation. The method was applied to the ServerNet TM System Area Network (SAN), developed by Tandem Computers Inc.