A random multiple-access protocol with spatial interactions

A random multiple-access protocol with spatial interactions

Bordenave Charles, Foss Serguei, and Shneer Vsevolod

Source: J. Appl. Probab. Volume 46, Number 3 (2009), 844-865.

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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Primary Subjects: 60K25, 90B15

Secondary Subjects: 68R10

Keywords: ALOHA protocol; spatial interaction; stability of processes; fluid limits

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.jap/1253279855
Digital Object Identifier: doi:10.1239/jap/1253279855
Zentralblatt MATH identifier: 05611421
Mathematical Reviews number (MathSciNet): MR2562325

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