Stochastic traffic and connectivity dynamics for vehicular ad-hoc networks in signalized road systems

In the design and planning of vehicular ad-hoc networks, road-side infrastructure nodes are commonly used to improve the overall connectivity and communication capability of the networks, however, to determine the locations to install the infrastructure nodes for optimal performance based on the ever-changing density and connectivity dynamics of moving vehicles remains to be a challenging issue. In this paper, we introduce a stochastic traffic model to capture the space and time dynamics of vehicles in signalized urban road systems to identify poorly-connected regions for infrastructure node placements. To closely approximate the practical road conditions, we propose a density-dependent velocity profile to approximate vehicle interactions and capture platoons formation and dissipation at traffic signals. Numerical results are presented to evaluate the stochastic traffic model. In general, we show that the fluid model can adequately describe the mean behavior of the traffic stream, while the stochastic model can approximate the probability distribution well even when vehicles interact with each other as their movement is controlled by traffic lights. With the understandings of the vehicular density dynamics from the proposed model, we illustrate that connectivity dynamics of vehicles can be determined and consequent system engineering and planning can be carried out.