Large network consensus is robust to packet losses and interferences

In many randomized consensus algorithms, the constraint of average preservation may not be enforced at every time step, resulting in an error between the average of the initial conditions and the current average. We have recently shown that under mild conditions on the distribution of the update matrices, the mean square error has an upper bound inversely proportional to the size of the network. In this work, we consider the case of consensus with packet losses and interferences. Using an extension of our results taking correlations into account, we show that the MSE induced by losses and interferences can be estimated by such a bound: hence we argue that larger networks are naturally more robust, in terms of accuracy, to packet losses and interferences. Our results hold for general networks, without restrictive assumptions on its topology.