Lagrangian formulation of multiclass 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, in which 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 multiclass model, in contrast to a mixed-class model, treats different types of vehicles (e.g., passenger cars and trucks or vehicles with different origins or destinations, or both) differently. The Lagrangian coordinate system is combined with a multiclass model, and a Lagrangian formulation of the kinematic wave model for multiple user classes is proposed. It is shown that the advantages of the Lagrangian formulation also apply for the multiclass model. Simulations based on the Lagrangian formulation result in more accurate solutions than simulations based on the Eulerian formulation.