An achievability result for random networks

We analyze a network of nodes in which pairs communicate over a shared wireless medium. We are interested in the maximum total aggregate traffic flow that is possible through the network. Our model differs substantially from the many existing approaches in that the channel connections in our network are entirely random: we assume that, rather than being governed by geometry and a decay law, the strength of the connections between nodes is drawn independently from a common distribution. Such a model is appropriate for environments where the first order effect that governs the signal strength at a receiving node is a random event (such as the existence of an obstacle), rather than the distance from the transmitter. We show that the aggregate traffic flow is a strong function of the channel distribution. In particular, we show that for certain distributions, the aggregate traffic flow scales at least as n/(log n)
^v
for some fixed v > 0, which is significantly larger than the O(radic/n) results obtained for many geometric models