Self-stabilizing Consensus Average Algorithm in Distributed Sensor Networks

One important issue in sensor networks that has received renewed interest recently is average consensus, i.e., computing the average of n sensor measurements, where nodes iteratively exchange data with their neighbors and update their own data accordingly until reaching convergence to the right parameters estimate. In this paper, we introduce an efficient self-stabilizing algorithm to achieve/ensure the convergence of node states to the average of the initial measurements of the network. We prove that the convergence of the fusion process is finite and express an upper bound of the actual number of moves/iterations required by the algorithm. This means that our algorithm is guaranteed to reach a stable situation where no load will be sent from one sensor node to another. We also prove that the load difference between any two sensor nodes in the network is within $\frac{\varepsilon}{D}\times\left\lfloor\frac{D+1}{2}\right\rfloorε is the prescribed global equilibrium threshold (this threshold is given by the system) and D is the diameter of the network.