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

Abstract

One of the most crucial aspects of an algorithmdesign for the wireless sensors networks is the failure tolerance.A high natural robustness and an effectively bounded executiontime are factors that can significantly optimize the overall energyconsumption and therefore, a great emphasis is laid on theseaspects in many applications from the area of the wireless sensornetworks. This paper addresses the robustness of the optimizedBest Constant weights of Average Consensus with a stoppingcriterion (i.e. the algorithm is executed in a finite time) and theirfive variations with a lower mixing parameter (i.e. slowervariants) to random communication breakdowns modeled as a stochastic event of a Bernoulli distribution. We choose threemetrics, namely the deviation of the least precise final estimatesfrom the average, the convergence rate expressed as the numberof the iterations for the consensus, and the deceleration of eachinitial setup, in order to evaluate the robustness of various initialsetups of Best Constant weights under a varying failureprobability and over 30 random geometric graphs of either astrong or a weak connectivity. Our contribution is to find themost robust initial setup of Best Constant weights according tonumerical experiments executed in Matlab. Finally, theexperimentally obtained results are discussed, compared to theresults from the error-free executions, and our conclusions arecompared with the conclusions from related papers.

Keywords

• distributed computing
• average consensus
• best constant weights
• communication breakdowns
• failure analysis