A random multiple-access protocol with spatial interactions

Charles Bordenave, Serguei Foss, Vsevolod Shneer

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


We analyse an ALOHA-type random multiple-access protocol where users have local interactions. We show that the fluid model of the system workload satisfies a certain differential equation. We obtain a sufficient condition for the stability of this differential equation and deduce from that a sufficient condition for the stability of the protocol. We discuss the necessary condition. Furthermore, for the underlying Markov chain, we estimate the rate of convergence to the stationary distribution. Then we establish an interesting and unexpected result showing that the main diagonal is locally unstable if the input rate is sufficiently small. Finally, we consider two generalisations of the model. © Applied Probability Trust 2009.

Original languageEnglish
Pages (from-to)844-865
Number of pages22
JournalJournal of Applied Probability
Issue number3
Publication statusPublished - 2009


  • Aloha protocol
  • Fluid limits
  • Spatial interaction
  • Stability of processes


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