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Shared-medium ATM switches are favored by the industry among other families of ATM switches. In this paper, four variations of a new distributed scheme are proposed for the arbitration of a shared bus of an ATM switch. The proposed bus arbitration schemes are based on learning automata. Taking advantage of the bursty nature of ATM traffic, the new arbitration scheme shows a superb performance compared to the time division multiple access, TDMA, scheme.