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Distribution of decentralized optimization convergence bounds in energy harvesting wireless sensor networks
Author(s) -
Roseveare Nicholas J.,
Alam S. M. Shafiul,
Natarajan Balasubramaniam
Publication year - 2016
Publication title -
transactions on emerging telecommunications technologies
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.366
H-Index - 47
ISSN - 2161-3915
DOI - 10.1002/ett.3099
Subject(s) - lagrange multiplier , wireless sensor network , convergence (economics) , probabilistic logic , mathematical optimization , computer science , wireless , energy (signal processing) , energy harvesting , upper and lower bounds , stochastic process , topology (electrical circuits) , mathematics , telecommunications , computer network , statistics , mathematical analysis , combinatorics , artificial intelligence , economics , economic growth
Abstract In this paper, we attempt to uncover the fundamental limitations of implementing decentralized optimization in an energy harvesting sensor network by quantifying the impact of stochastic energy availability on convergence. Specifically, the discrete energy quanta being harvested by a network of wireless sensors are modelled via a marked Poisson process. The wireless sensors are involved in updating the Lagrange multipliers associated with the constraints for a decentralized concave optimization problem. The convergence of the corresponding Lagrange dual function is monotonically dependent upon the maximum delay in communication. The probabilistic nature of the harvested energy quanta results in a random crossover with respect to the minimum energy threshold required for successful communication. As a consequence, we investigate the probabilistic behaviour of the Lagrange dual function convergence bound under the effect of random delay considering single/multi‐hop communication among neighbouring sensors. The maximum delay distribution is derived for both deterministic and stochastic models for the energy harvested at sensor nodes. Simulation shows the efficacy of the theoretical distributions in modelling the delay dependent Lagrange dual function convergence bound behaviour. Copyright © 2016 John Wiley & Sons, Ltd.