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Evaluation of Natural Robustness of Best Constant Weights to Random Communication Breakdowns

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.