  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 Polit\`ecnica 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.
