Distributed protocol for determining when averaging consensus is reached

Distributed averaging over a large network is a well studied problem that converges asymptotically; however, existing protocols does not provide a way for each node to distributively detect the occurrence of convergence. In this paper a method is developed to distributively determine when the consensus has reached within a given error margin. In absence of such a method all nodes in the network keep running the required computation and communication even if the consensus value are within acceptable tolerance, which is not preferable as in large-scale distributed networks resources like power are limited. Furthermore, this extra communication can cause signal interference with other critical information. This distributed detection takes finite time and occurs at each node simultaneously.