A study of the VANET connectivity by percolation theory

As deploying Vehicular Ad Hoc NETworks (VANETs) costs large amounts of resources, it is crucial that governments and companies make a thorough estimation and comparison of the benefits and the costs. The network connectivity is an important factor we should take care of, because it can greatly affect the performance of VANETs and further affect how much we can benefit from VANETs. We use percolation theory to analyze the connectivity of VANETs. Through theoretical deduction, we discover the quantitative relationship among network connectivity, vehicle density and transmission range. We show that there is a jump of the network connectivity when vehicle density or transmission range is big enough. Simulations conducted in a large scenario validate our theoretical results. Our results have great meanings in the deployment of VANETs in real world. Given vehicle density, our theorem can be used to calculate the minimum transmission range to achieve good network connectivity. As a large transmission range can cause serious collisions in wireless links, it is a tradeoff to choose a proper transmission range. Our analysis can give a hand to this tradeoff and guide the deployment of VANETs in real world.