Modelling urban traffic dynamics based upon the variational formulation of kinematic waves

This paper presents a dynamic traffic modelling framework based on the variational formulation of kinematic waves. We compare the effectiveness of this relatively recent numerical method with the traditional Godunov-based cell transmission method on various aspects including modelling shocks, dispersion of vehicle platoons, moving bottlenecks, and traffic characteristics with respect to real-world observations made in Central London, UK. The results suggest that the variational method is able to produce high-quality estimates both theoretically and empirically. This study opens up a new research direction in the area of urban traffic modelling and optimisation.