Connectivity dynamics for vehicular ad-hoc networks in signalized road systems

In this paper, we analyze the connectivity dynamics of vehicular ad-hoc networks in a generic signalized urban route. Given the velocity profile of an urban route as a function of space and time, we utilize a fluid model to characterize the general vehicular traffic flow, and a stochastic model to capture the randomness of individual vehicle. From the fluid and stochastic models, we can acquire respectively the densities of the mean number of vehicles along the road and the corresponding distribution. With the knowledge of the vehicular density dynamics, we determine the probability that the communication network is fully connected, i.e., each node can communicate with every other node through a multi-hop path, and the problem is also investigated for a general case of a k-connected network. To closely approximate the practical road conditions, we use a density-dependent velocity profile to approximate vehicle interactions and capture the shockwave propagation at traffic signals. We confirm the accuracy of the connectivity analysis through simulations and show that the analytical results are good approximations even when vehicles interact with each other as their movement is controlled by traffic lights. We also illustrate that system engineering and planning for optimizing connectivity in the communication networks can be carried out with the results in this paper.