Connectivity of vehicular ad hoc networks with continuous node distribution patterns

The connectivity of vehicular ad hoc networks (VANets) can be affected by the special distribution patterns, usually dependent and non-uniform, of vehicles in a transportation network. In this study, we introduce a new framework for computing the connectivity in a VANet for continuous distribution patterns of communication nodes on a line in a transportation network. Such distribution patterns can be estimated from traffic densities obtained through loop detectors or other detectors. When communication nodes follow homogeneous Poisson distributions, we obtain a new closed-form solution to connectivity; when distribution patterns of communication nodes are given by spatial renewal processes, we derive an approximate closedform solution to the connectivity; and when communication nodes follow non-homogeneous Poisson distributions, we propose a recursive model of connectivity. For a shock-wave traffic, we demonstrate the consistency between analytical results with those simulated with ns-2, acommunication simulator. With the developed models, we also discuss the impacts on connectivity of road-side stations and different distribution patterns of vehicles. Given continuous traffic conditions, the connectivity model could be helpful for designing routing protocols in VANets and implementing vehicle-infrastructure integration systems. Limitations and future research related to this study are discussed in the conclusion section.