The space and time dynamics of moving vehicles regulated by traffic signals governs the node connectivity and communication capability of vehicular ad hoc networks (VANETs) in urban environments. However, none of the previous studies on node connectivity has considered such dynamics with the presence of traffic lights and vehicle interactions. In fact, most of them assume that vehicles are distributed homogeneously throughout the geographic area, which is unrealistic. We introduce in this paper a stochastic traffic model for VANETs in signalized urban road systems. The proposed model is a composite of the fluid model and stochastic model. The former characterizes the general flow and evolution of the traffic stream so that the average density of vehicles is readily computable, while the latter takes into account the random behavior of individual vehicles. As the key contribution of this paper, we attempt to approximate vehicle interactions and capture platoon formations and dissipations at traffic signals through a density-dependent velocity profile. The stochastic traffic model with approximation of vehicle interactions is evaluated with extensive simulations, and the distributional result of the model is validated against real-world empirical data in London. 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 knowledge of the mean vehicular density dynamics and its probability distribution from the stochastic traffic model, we determine the degree of connectivity in the communication network and illustrate that system engineering and planning for optimizing both the transport (in terms of congestion) and communication networks (in terms of connectivity) can be carried out with the proposed model.

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