On the Maximal Shortest Path in a Connected Component in V2V

TL;DR

This paper models the probability distribution of the number of hops in the maximal shortest path within a connected vehicle network on a single lane, applicable to various traffic conditions and validated with real road data.

Contribution

It provides a general formulation for the distribution of shortest path hops in VANETs under arbitrary traffic assumptions, including Poisson models for medium and dense networks.

Findings

Distribution derived for Poisson traffic in medium/dense networks

Model validated with Madrid road traces

Results useful for evaluating diffusion protocols

Abstract

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.