Probability theory and mathematical statistics

Spatially decentralized protocols in random multiple access networks

M. G. Chebunin^ab, E. I. Prokopenko^ab, A. S. Tarasenko<sup>ab

a</sup> Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
^b Novosibirsk State University, str. Pirogova, 2, 630090, Novosibirsk, Russia

Abstract: We analyse a spatial ALOHA-type random multiple-access protocol in a stochastic network with local interactions. We formulate and prove a stability criterion and provide convergence rates to stationarity. Finally, we compare various ALOHA-type protocols in a symmetric network.

Keywords: ALOHA protocol, random multiple access, spatial interactions, spatially decentralized protocol, positive recurrence, (in)stability, Foster criterion.

UDC: 621.394.74

MSC: 60K25;90B15

Received January 22, 2018, published February 12, 2018

DOI: 10.17377/semi.2018.15.014

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