Analysis of Average Consensus Algorithm for Asymmetric Regular Networks
For researchers studying average consensus in wireless sensor networks, this work provides a more realistic modeling approach by incorporating asymmetric links, which are common in practice but often ignored.
This paper models wireless sensor networks as directed graphs to account for asymmetric links, deriving explicit convergence rate formulas for regular network topologies. Numerical results confirm the accuracy of the directed graph model and analyze the impact of asymmetry, network size, and dimension on convergence.
Average consensus algorithms compute the global average of sensor data in a distributed fashion using local sensor nodes. Simple execution, decentralized philosophy make these algorithms suitable for WSN scenarios. Most of the researchers have studied the average consensus algorithms by modeling the network as an undirected graph. But, WSNs in practice consist of asymmetric links and the undirected graph cannot model the asymmetric links. Therefore, these studies fail to study the actual performance of consensus algorithms on WSNs. In this paper, we model the WSN as a directed graph and derive the explicit formulas of the ring, torus, $r$-nearest neighbor ring, and $m$-dimensional torus networks. Numerical results subsequently demonstrate the accuracy of directed graph modeling. Further, we study the effect of asymmetric links, the number of nodes, network dimension, and node overhead on the convergence rate of average consensus algorithms.