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In this paper we consider a local computer network in which users communicate with each other over a single bus. We develop window search algorithms with which to implement random access protocols on the bus. Two protocols, one nonadaptive and the other adaptive are described. The maximum throughputs and throughput-delay tradeoffs are provided for both. These protocols show significant improvement over previous random access protocols used in local computer networks. We also consider the problem of allowing new users to join the system.