An analysis of a contention resolution algorithm

Summary A single multiaccess channel is studied with the outcome of a transmission being either idle, success, or collision (ternary channel). Packets involved in a collision must be retransmitted, and an efficient way to solve a collision is known in the literature as Gallager-Tsybakov-Mikhailov algorithm. Performance analysis of the algorithm is quite hard. In fact, it bases on a numerical solution of some recurrence equations and on a numerical evaluation of some series. The obvious drawback of it is lack of insight into the behavior of the algorithm. We shall present a new approach of looking at the algorithm and discuss some attempts of analyzing its performance. In particular, expected lengths of a resolution interval and a conflict resolution interval as well as throughput of the algorithm will be discussed using asymptotic approximation and a small input rate approximation.