Distributed stopping for average consensus in directed graphs via a randomized event-triggered strategy

We consider how an iterative strategy for asymptotic average consensus in a directed graph (digraph) can be adapted so that the nodes can determine, in a distributed manner, a stopping criterion that allows them to terminate the execution of the iteration when approximate average consensus has been reached. The nodes are said to have reached approximate average consensus when each of them has a value that is close to the desirable average (in a way that we precisely define). The algorithm we propose can be used in practical settings to cap the number of transmissions that are required in order to reach (approximate) average consensus.