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Consider n stations sharing a single communications channel. Each station has a buffer of length one. If the arrival rate of station i is ri, then 1 -n,(lrr ) is shown to be an upper bound (over all policies) on the throughput of the channel. Moreover, an optimal policy always exists and is stationary and periodic. The throughput of two policies, the random -policy and the goldenratio pofiq, are analyzed for a finite and infinite number of stations. The latter is shown to approach a limit whichdoi:10.1109/tac.1984.1103619 fatcat:4migb7cxbzhw3nliev6secbhza