  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
Erdos-Renyi 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 Erdos-Renyi random networks result in an
asymptotic agreement over the network, an analytical characterization of the
distribution of the asymptotic consensus value is still 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.
