Connectivity Analysis of a Mobile Vehicular Ad Hoc Network with Dynamic Node Population

Network connectivity is a critical metric for the planning, design, and evaluation of ad hoc networks. In this paper, the connectivity properties of a linear vehicular ad hoc network (VANET) with high speed mobile nodes and dynamic node populations are investigated. The nodes are assumed to be arriving at the network following a Poisson distribution, and the speed of each node is modeled as a wide sense stationary ergodic random process. Based on these assumptions, a new mobility model is developed to represent the steady state node distributions in terms of random node locations and random node populations. The mobility model accurately captures the statistical properties of a mobile network with rapidly changing network topologies and network densities. Exact closed-form connectivity probability expressions are developed with the assistance of the volume of an n-dimensional hypercube intersected by an n-dimensional hyperplane. The impacts of key network parameters, such as node arrival rate, random node speed, and node transmission range, are incorporated in the analytical expressions. The results can be used to determine the transmission power that can ensure network connectivity while minimizing interference in a VANET.