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

Wolfgang König; Helia Shafigh

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arXiv · 2212.08588

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

Wolfgang König·Helia Shafigh

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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.

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Wolfgang König, Helia Shafigh. 2022-12-16. Multi-channel ALOHA and CSMA medium-access protocols: Markovian description and large deviations. https://arxiv.org/abs/2212.08588

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