Modeling the Impact of Mobility on the Connectivity of Vehicular Networks in Large-Scale Urban Environments

The connectivity of moving vehicles is one of the key metrics in vehicular ad hoc networks (VANETs) that critically influences the performance of data transmission. Due to lack of in-depth analysis of real-world vehicular mobility traces, we do not understand the connectivity in realistic large-scale urban scenarios. Specifically, the mechanism of how the mobility of networked vehicles impacts the network connectivity remains unknown. In this paper, we aim to unveil the underlying relationship between the mobility and connectivity of VANETs. To achieve this goal, we employ some key topology metrics, including component speed and component size, to characterize mobility and connectivity. In our investigation of a large-scale real-world urban mobility trace data set, we discover, to our surprise, that there exists a dichotomy in the relationship between component speed and size. This dichotomy indicates that mobility destroys the connectivity with a power-law decline when the component speed is larger than a threshold; otherwise, it has no apparent impact on connectivity. Based on this observation, we propose a mathematical model to characterize this relationship, which agrees well with empirical results. Our findings thus offer a comprehensive understanding of the relationship between mobility and connectivity in urban vehicular scenarios, and based on this, helpful guidelines can be provided in the design and analysis of VANETs.