Convergence Analysis for Regular Wireless Consensus Networks

TL;DR

This paper analyzes the convergence behavior of average consensus algorithms in wireless sensor networks with regular graph topologies, deriving analytical expressions for optimal parameters and convergence time.

Contribution

It provides new analytical formulas for optimal consensus parameters in r-nearest neighbor networks and their higher-dimensional generalizations, aiding network performance management.

Findings

Analytical expressions for optimal consensus parameters are derived.

Convergence time depends on network dimension, number of nodes, and transmission radius.

Results are validated through simulations showing agreement with theoretical predictions.

Abstract

Average consensus algorithms can be implemented over wireless sensor networks (WSN), where global statistics can be computed using communications among sensor nodes locally. Simple execution, robustness to global topology changes due to frequent node failures and underlying distributed philosophy has made consensus algorithms more suitable to WSNs. Since these algorithms are iterative in nature, their performance is characterized by convergence speed. We study the convergence of the average consensus algorithms for WSNs using regular graphs. We obtained the analytical expressions for optimal consensus and convergence parameters which decides the convergence time for r-nearest neighbor cycle and torus networks. We have also derived the generalized expression for optimal consensus and convergence parameters for m-dimensional r-nearest neighbor torus networks. The obtained analytical results agree with the simulation results and shown the effect of network dimension, number of nodes and transmission radius on convergence time. This work provides the basic analytical tools for managing and controlling the performance of average consensus algorithm in the finite sized practical networks.