Multi-channel ALOHA and CSMA medium-access protocols: Markovian description and large deviations

TL;DR

This paper models multi-channel ALOHA and CSMA protocols using Markov chains, deriving formulas for throughput, analyzing rare events with large deviations, and providing explicit probabilistic descriptions of system performance over time.

Contribution

It introduces explicit formulas and a Markov chain model for analyzing throughput and rare events in multi-channel ALOHA and CSMA protocols.

Findings

Explicit large-time throughput formulas

Ergodic Markov chain for probabilistic analysis

Large deviation asymptotics for rare events

Abstract

We consider a multi-channel communication system under ALOHA and CSMA protocols, resepctively, in continuous time. We derive probabilistic formulas for the most important quantities: the numbers of sending attempts and the number of successfully delivered messages in a given time interval. We derive (1) explicit formulas for the large-time limiting throughput, (2) introduce an explicit and ergodic Markov chain for a deeper probabilistic analysis, and use this to (3) derive exponential asymptotics for rare events for these quantities in the limit of large time, via large-deviation principles.