Analysis of contention tree algorithms

The Capetanakis-Tsybakov-Mikhailov (1978, 1979) contention tree algorithm provides an efficient scheme for multiaccessing a broadcast-communication channel. This paper studies the statistical properties of multiple-access contention tree algorithms with ternary feedback for an arbitrary degree of node. The particular quantities under investigation are the number of levels required for a random contender to have successful access, as well as the number of levels and the number of contention frames required to provide access for all contenders. Through classical Fourier analysis approximations to both the average and the variance are calculated as a function of the number of contenders n. It is demonstrated that in the limit of large n these quantities do not converge to a fixed mode, but contain an oscillating term as well.