Limiting Distribution of the Collision Resolution Interval

The authors use the theory of probability metrics to study the asymptotic normality of the collision resolution intervals in the CTM multi-access protocol under general conditions on the number of retransmitted messages and of new arrivals during the collision slots. The main result establishes stability of the central limit theorem for the CTM algorithm. The authors provide extensive simulation results investigating the extent to which the mean of the collision resolution interval eventually becomes unstable for increasing values of n, the number of users who initially collide. The normal fit is numerically investigated and is shown to be quite satisfactory and stable with respect to moderate perturbations and n greater than or equal to 50.