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Average consensus algorithms compute the global average of sensor data in adistributed fashion using local sensor nodes. Simple execution, decentralizedphilosophy make these algorithms suitable for WSN scenarios. Most of theresearchers have studied the average consensus algorithms by modeling thenetwork as an undirected graph. But, WSNs in practice consist of asymmetriclinks and the undirected graph cannot model the asymmetric links. Therefore,these studies fail to study the actual performance of consensus algorithms onWSNs. In this paper, we model the WSN as a directed graph and derive theexplicit formulas of the ring, torus, $r$-nearest neighbor ring, and$m$-dimensional torus networks. Numerical results subsequently demonstrate theaccuracy of directed graph modeling. Further, we study the effect of asymmetriclinks, the number of nodes, network dimension, and node overhead on theconvergence rate of average consensus algorithms.

Analysis of Average Consensus Algorithm for Asymmetric Regular Networks