A Random Multiple Access Protocol with Spatial Interactions

Details A Random Multiple Access Protocol with Spatial Interactions A Random Multiple Access Protocol with Spatial Interactions

2006-12-20

arxiv.org/abs/math/0612583v2

Mathematics

Probability

29 pages

Scientific paper

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. Further, 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.

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