On the maximal shortest path in a connected component in V2V

In this work, a VANET (Vehicular Ad-hoc NETwork) is considered to operate on a simple lane, without infrastructure. The arrivals of vehicles are assumed to be general with any traffic and speed assumptions. The vehicles communicate through the shortest path. In this paper, we study the probability distribution of the number of hops on the maximal shortest path in a connected component of vehicles. The general formulation is given for any assumption of road traffic. Then, it is applied to calculate the z-transform of this distribution for medium and dense networks in the Poisson case. Our model is validated with the Madrid road traces of the Universitat Politècnica de Catalunya. These results may be useful for example when evaluating diffusion protocols through the shortest path in a VANET, where not only the mean but also the other moments are needed to derive accurate results.