Estimating the multiplicities of conflicts in multiple access channels

A conflict of multiplicity k occurs when k stations transmit simultaneously to a multiple access channel. As a result, all stations receive feedback indicating whether k is 0, 1, or is ≥ 2. If k = 1 the transmission succeeds, whereas if k ≥ 2 all the transmissions fail. In general, no a priori information about k is available. We present and analyze an algorithm that enables the conflicting stations to cooperatively compute a statistical estimate of k, at small cost, as a function of the feedback elicited during its execution. An algorithm to resolve a conflict among two or more stations controls the retransmissions of the conflicting stations so that each eventually transmits singly to the channel. Combining our estimation algorithm with a binary tree algorithm leads to a hybrid algorithm that resolves conflicts faster on average than any other reported to date.