Some conjectures on the behavior of acknowledgement-based transmission control of random access communication channels

Abstract

A class of acknowledgment-based transmission control algorithms is considered. In the finite population case, we claim that algorithms based on backoff functions which increase faster than linearly but slower than exponentially are stable up to full channel capacity, whereas sublinear, exponential, and superexponential algorithms are not. In addition, comments are made about the nature of the quasistationary behavior in the infinite population case, and about how systems interpolate between the finite and infinite number of station cases. The treatment presented here is nonrigorous, consisting of approximate analytic arguments confirmed by detailed numerical simulations.