Variance analysis of randomized consensus in switching directed networks

In this paper, we study the asymptotic properties of distributed consensus algorithms over switching directed random networks. More specifically, we focus on consensus algorithms over independent and identically distributed, directed Erdös-Rényi random graphs, where each agent can communicate with any other agent with some exogenously specified probability p. While it is well-known that consensus algorithms over Erdös-Rényi random networks result in an asymptotic agreement over the network, an analytical characterization of the distribution of the asymptotic consensus value remains an open question. In this paper, we provide closed-form expressions for the mean and variance of the asymptotic random consensus value, in terms of the size of the network and the probability of communication p. We also provide numerical simulations that illustrate our results.