Connectivity analysis for vehicular ad hoc network based on the Exponential Random Geometric Graphs

Network connectivity is a fundamental requirement for applying the vehicular ad hoc networks (VANETs) to real traffic systems. The high mobility of vehicles results in rapid changes in network topology generating dynamic variation in network connectivity. Therefore, a new approach of using Exponential Random Geometric Graphs (ERGGs) to analyze VANETs connectivity is presented considering the high randomness of vehicles' velocity and headway under the scenario of free flow state on highway. Vehicles enter the highway according to a Poisson distribution, and the headway follows a negative exponential distribution. Assuming that each vehicle is assigned a random speed chosen from normal distribution and maintains the speed while it travels on the highway. The dynamic topology properties, such as one-step transition probability matrix, are derived from ERGGs by analyzing the evolving process of the headway. In addition, the static topology properties such as connectivity probability and communication duration between vehicles are also calculated. The analysis of results agrees with a idealized scenario, which shows the ERGGs can be used to analyze the evolution of network connectivity.