Convergence Analysis for Regular Wireless Consensus Networks

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.Comment: 10 pages, 19 figure

Latency of opportunistic forwarding in finite regular wireless networks

In opportunistic forwarding, a node randomly relays packets to one of its neighbors based on local information, without the knowledge of global topology. Each intermediate node continues this process until the packet arrives at its destination. This is particularly attractive in certain types of wireless ad hoc and sensor networks where obtaining accurate knowledge of global topology may be infeasible. However, opportunistic forwarding is hampered by the difficulty to control its performance, particularly, the end-to-end latency. This paper presents new analytical results that shed light on the latency of “random walk”, the simplest type of opportunistic forwarding, for several useful regular network topologies, such as r-nearest cycle that can model variable wireless transmission distance in one dimensional scenario, and a 2D regular torus-type graph that can approximate grid-like deployments. We give new exact and approximation formulas for the maximum expected hitting time of random walk on such topologies