An Asymptotically Optimal Push-Pull Method for Multicasting Over a Random Network

The authors consider all cast and multicast flow problems where either all of the nodes or only a subset of the nodes may be in session. Traffic from each node in the session has to be sent to every other node in the session. If the session does not consist of all the nodes, the remaining nodes act as relays. The nodes are connected by undirected links whose capacities are independent and identically distributed random variables. They study the asymptotics of the capacity region (with network coding) in the limit of a large number of nodes, and show that the normalized sum rate converges to a constant almost surely.