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 non-commutative iteration semigroup. Using Mellin transform techniques and geometric properties of the iteration semigroup we show that for arrival rates smaller than a fixed threshold, the mean CRI duration for n initial colliders is asymptotically proportional to n. Ergodicity conditions are also demonstrated.
Carrier Sensing Multiple Access with Collision Resolution (CSMA/CR) Protocol for Next-Generation Wireless LAN