Nonlinear Advection-Diffusion Models of Traffic Flow: a Numerical Study

The first-order degenerate parabolic traffic flow dynamics are the simplest extension of the Lighthill, Whitham, and Richards (LWR) model which aim at correcting the discrepancies between the LWR model and the observation collected from real data. In addition, the nonlinearity and degeneracy of these models are designed to address the fundamental criticism of linear diffusively-corrected kinematic-wave models. While several first-order methods have been proposed in the literature, the predictive capabilities of these models has not been sufficiently studied with respect to real data. The goal of this work is to conduct an investigation of the performance of several first-order models, validating with a real data set. The models will be evaluated by their capability of creating a consistent Fundamental Diagram as well as their ability to predict the state of the traffic.