Distributed average consensus with stochastic communication failures

We consider a distributed average consensus algorithm over a network in which communication links fail with independent probability. Convergence in such stochastic networks is defined in terms of the variance of deviation from average. We characterize the decay factor of the variance in terms of the eigenvalues of a Lyapunov-like matrix recursion. We give expressions for the decay factors in the asymptotic limits of small failure probability and large networks. We also present a simulation-free method for computing the decay factor for any particular graph instance and use this method to study the behavior of various network examples as a function of link failure probability.