Abstract-One of the most crucial aspects of an algorithm design for the wireless sensors networks is the failure tolerance. A high natural robustness and an effectively bounded execution time are factors that can significantly optimize the overall energy consumption and therefore, a great emphasis is laid on these aspects in many applications from the area of the wireless sensor networks. This paper addresses the robustness of the optimized Best Constant weights of Average Consensus with a stopping criterion (i.e. the algorithm is executed in a finite time) and their five variations with a lower mixing parameter (i.e. slower variants) to random communication breakdowns modeled as a stochastic event of a Bernoulli distribution. We choose three metrics, namely the deviation of the least precise final estimates from the average, the convergence rate expressed as the number of the iterations for the consensus, and the deceleration of each initial setup, in order to evaluate the robustness of various initial setups of Best Constant weights under a varying failure probability and over 30 random geometric graphs of either a strong or a weak connectivity. Our contribution is to find the most robust initial setup of Best Constant weights according to numerical experiments executed in Matlab. Finally, the experimentally obtained results are discussed, compared to the results from the error-free executions, and our conclusions are compared with the conclusions from related papers.Index Terms-Distributed computing, Average Consensus algorithm, Best Constant weights, communication breakdowns, failure analysis.
I. INTRODUCTIONIRELESS Sensor Networks (abbreviated as WSNs) is a technology with a wide usage in the field of the realtime detection of global events and monitoring [1]. Manuscript received March 15, 2018; revised August 20, 2018. Date of publication September 4, 2018. Prof. Nikola Rožić has been coordinating the review of this manuscript and approved it for publication.Martin Kenyeres and Radim Burget are with Department of Telecommunications, Brno University of Technology, Technicka 12, Brno, burget@feec.vutbr.cz).Jozef Kenyeres is with Sipwise GmbH, Europaring F15, 2345 Brunn am Gebirge, Austria. (e-mail: jkenyeres@sipwise.com).Research described in this paper was financed by the National Sustainability Program under grant LO1401. For the research, infrastructure of the SIX Center was used.Digital Object Identifier (DOI): 10.24138/jcomss.v14i3.487These networks consist of power and computationally constrained devices (labeled as nodes) situated in a geographical area in order to sense important information about a particular physical quantity, process it, share the measured data with other nodes and make a meaningful decision on the observed quantity [2]. Due to their specific character, the WSNs find the usage in various applications such as military surveillance, a natural disaster detection, industrial automation, inventory tracking, an acoustic detection, wildlife applications, medical systems, target tracking,...