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A RANDOM MULTIPLE-ACCESS PROTOCOL WITH SPATIAL INTERACTIONS

CHARLES BORDENAVE, SERGUEI FOSS and VSEVOLOD SHNEER
Journal of Applied Probability
Vol. 46, No. 3 (SEPTEMBER 2009), pp. 844-865
Stable URL: http://www.jstor.org/stable/25662464
Page Count: 22
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A RANDOM MULTIPLE-ACCESS PROTOCOL WITH SPATIAL INTERACTIONS
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Abstract

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.

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