Performance Evaluation of Interval-Searching Conflict Resolution Algorithms

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 (G1M) algorithm. which falls into class of interval-searching contention resolution algorithms. Perfonnance analysis of the algorithm was based on a numerical solution of some recurrence equations and on a numerical evaluation of some series. The obvious drawback of such an analysis is lack of insight into the behaviour 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 resolved 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. Finally, we generalize these results to cover a wider class of interval-searching algorithms.