ON A FUNCTIONAL EQUATION ARISING IN THE BROADCAST CHANNEL ANALYSIS OF A PROTOCOL FOR A MULTI-ACCESS

We analyse a stack protocol of the Capetanakis-Tsybakov-Mikhailov type for resolving collisions in a random multiple-access channel. We obtain a functional equation for the generating function of the expected collision resolution interval (CRI) durations, which is non-local with a noncommutative iteration semigroup. Using Mellin transform techniques and geometric properties of the iteration semigroup we show that for amval rates smaller than a fixed threshold, the mean CRI duration for n initial colliders is asymptotically proportional to n. Ergodicity conditions are also demonstrated. ASYMPTOTIC ANALYSIS; FUNCTIONAL EQUATION; MELLIN TRANSFORM; I PROTOCOL; RANDOM ACCESS; TREE ALGORITHM