Information propagation speed in bidirectional vehicular delay tolerant networks

In this paper, we provide an analysis of the information propagation speed in bidirectional vehicular delay tolerant networks on highways. We show that a phase transition occurs concerning the information propagation speed, with respect to the vehicle densities in each direction of the highway. We prove that under a certain threshold, information propagates on average at vehicle speed, while above this threshold, information propagates dramatically faster at a speed that increase exponentially when vehicle density increases. We provide the exact expressions of the threshold and of the average propagation speed near the threshold. We show that under the threshold, the information propagates on a distance which is bounded by a sub-linear power law with respect to the elapsed time, in the referential of the moving cars. On the other hand, we show that information propagation speed grows quasi-exponentially with respect to vehicle densities in each direction of the highway, when the densities become large, above the threshold. We confirm our analytical results using simulations carried out in several environments.