Lagrangian formulation of a multi-class kinematic wave model

The kinematic wave model is often used in simulation tools to describe dynamic traffic flow and to estimate and predict traffic states. Discretization of the model is generally based on Eulerian coordinates, which are fixed in space. However, the Lagrangian coordinate system, where the coordinates move with the velocity of the vehicles, results in more accurate solutions. Furthermore, if the model includes multiple user classes it describes real traffic more accurately. Such a multi-class model, in contrast to a mixed-class model, treats different types of vehicles (eg. passenger cars and trucks or vehicles with different origins and/or destinations) differently. We combine the Lagrangian coordinate system with a multi-class model and propose a Langrangian formulation of the kinematic wave model for multiple user classes. We show that the advantages of the Lagrangian formulation also apply for the multi-class model. Simulations based on the Lagrangian formulation result in more accurate solutions than simuations based on the Eulerian formulation.