Probability theory and mathematical statistics

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

S. Foss^ab, D. Kim^c, A. Turlikov<sup>d

a</sup> 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.

UDC: 519.724

MSC: 60K25;90B15

Received November 30, 2015, published February 2, 2016

Language: English

DOI: 10.17377/semi.2016.12.002