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It is shown that, for a ternary feedback random access channel with a Poisson arrival process, is an upper bound to the throughput for all "degenerate intersection" algorithms (DIA's) and first-come first-served algorithms (FCFSA's). As a by-product, the nested FCFSA with the largest throughput is found for the random access channel with a Bernoulli arrival process with parameter . For , this algorithm has the highest throughput over all DIA's and FCFSA's. Lastly, it is shown that. for some values of , a non-DIA, non-FCFSA has a higher throughput than the optimum DIA or FCFSA.