A multi-class traffic flow model – an extension of the Lighthill, Whitham & Richard model with heterogeneous drivers

In this paper, a multi-class traffic flow model as an extension of the Lighthill, Whitham and Richards (LWR) model with heterogeneous drivers is formulated. The model takes into account the distribution of heterogeneous drivers characterized by their choice of speeds in a traffic stream, which models the dynamic behavior of heterogeneous users whereby faster vehicles could overtake slower ones under uncongested condition as well as congested condition (though less easily), and slower vehicles would slow down the faster ones. Numerical simulations show that the model can predict many of the puzzling traffic flow phenomena such as the two-capacity (or reverse-lambda) regimes that occurred in the fundamental diagram, hysteresis and platoon dispersion.