WIAS Preprint No. 2985, (2022)

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


Authors

  • König, Wolfgang
    ORCID: 0000-0002-7673-4364
  • Shafigh, Helia
    ORCID: 0009-0003-8160-9204

2020 Mathematics Subject Classification

  • 60K35 82C21

Keywords

  • Communication system, random medium access strategies, throughput, multi-channel ALOHA protocol, CSMA, Markov chains, Markov renewal process, large deviations

DOI

10.20347/WIAS.PREPRINT.2985

Abstract

We consider a multi-channel communication system under ALOHA and CSMA protocols, resepc- tively, 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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