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Sib. Èlektron. Mat. Izv., 2016, Volume 13, Pages 16–25 (Mi semr653)  

Probability theory and mathematical statistics

Stability and instability of a random multiple access model with adaptive energy harvesting

S. Fossab, D. Kimc, A. Turlikovd

a Heriot-Watt University, EH14 4AS, Edinburgh, UK
b S.L. Sobolev Institute of Mathematics and Novosibirsk State University, 630090, Novosibirsk, Russia
c Kazakh National Research Technical University named after K. I. Satpaev and “EcoRisk” LLP, Satpaev str. 22, 050013, Almaty, Kazakhstan
d St.-Petersburg University of Aerospace Instrumentation, B. Morskaya 67, 190000, St.-Petersburg, Russia

Abstract: We introduce a model for the classical synchronised multiple access system with a single transmission channel and a randomised transmission protocol (ALOHA). We assume in addition that there is an energy harvesting mechanism, and any message transmission requires a unit of energy. Units of energy arrive randomly and independently of anything else. We analyze stability and instability conditions for this model.

Keywords: random multiple access, stochastic energy harvesting, (in)stability, ALOHA algorithm, generalized Foster criterion.

Funding Agency Grant Number
Ministry of Education and Science of the Republic of Kazakhstan 0770/GF3
The authors thank the grant 0770/GF3 of Kazakhstan Ministry of Education and Science.


DOI: https://doi.org/10.17377/semi.2016.12.002

Full text: PDF file (583 kB)
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UDC: 519.724
MSC: 60K25;90B15
Received November 30, 2015, published February 2, 2016
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Citation: S. Foss, D. Kim, A. Turlikov, “Stability and instability of a random multiple access model with adaptive energy harvesting”, Sib. Èlektron. Mat. Izv., 13 (2016), 16–25

Citation in format AMSBIB
\Bibitem{FosKimTyu16}
\by S.~Foss, D.~Kim, A.~Turlikov
\paper Stability and instability of a random multiple access model with adaptive energy harvesting
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 16--25
\mathnet{http://mi.mathnet.ru/semr653}
\crossref{https://doi.org/10.17377/semi.2016.12.002}


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