Control of mobile ad hoc networks

We show that the per node overhead of traffic control in a mobile ad hoc network with N nodes with density v moving at average speed v can be made proportional to root nu N nu). In this case route between source and destination has a bounded strectch factor compared to optimal route. Since by Gupta and Kumar scaling property the per node traffic cannot be larger than some O((1)/(logN)). Therefore there is a maximal network size which depends of speed upsilon and node density. We show that we moderate hypotheses (location aware nodes) this size can be significantly large.