Estimating the multiplicities of conflicts to speed their resolution in multiple access channels

Abstract

New, improved algorithms are proposed for regulating access to a multiple-access channel, a common channel shared by many geographically distributed computing stations. A conflict of multiplicity n occurs when n stations transmit simultaneously to the channel. As a result, all stations receive feedback indicating whether n is 0, 1, or ≥2. If n = 1, the transmission succeeds; whereas if n ≥ 2, all the transmissions fail. Algorithms are presented and analyzed that allow the conflicting stations to compute a stochastic estimate n * of n , cooperatively, 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 one of our estimation algorithms with a tree algorithm (of Capetanakis, Hayes, and Tsybakov and Mikhailov) then leads to a hybrid algorithm for conflict resolution. Several efficient combinations are possible, the most efficient of which resolves conflicts about 20 percent faster on average than any of the comparable algorithms reported to date.