Geometric connectivity of vehicular ad hoc networks: Analytical characterization

Advances in wireless communications are facilitating the development of inter-vehicle communication systems that will benefit mobility and safety objectives. Recently, these systems, referred as vehicular ad hoc networks (VANETs), are gaining significant prominence from both government agencies and private organizations. VANETs are characterized by high vehicle mobility, unexpected driver behavior and variable traffic environment which bring forth challenges to maintain good connectivity. This study considers VANETs as a nominal system with disturbance. Under the nominal system, the traffic space headway is assumed to follow an approved traffic flow distributions, such as exponential distribution. Disturbance is then used to capture a set of uncertain traffic flow events caused by driver behavior and changes in traffic flow. In addition, robustness factor is incorporated to present the impact of probabilistic disturbance events that disrupt the node connectivity. Under constant disturbance conditions, the lower bound of reachable neighbors for each vehicle to maintain a high connectivity is analytically derived. Furthermore, we obtain the relationship between the number of nodes in a VANET and the reachable neighbors under which the network is asymptotically connected. Finally, in variable disturbance situations, the interaction between robustness factor and macroscopic traffic parameters are investigated based on the simulation data. The validation results demonstrate that the proposed analytical characterization can approximate VANET connectivity very well. Our results facilitate the understanding of VANET connectivity on a freeway segment under different traffic conditions.