In contemporary macroscopic traffic flow modeling, a distinction between user-classes is rarely made. However, it is envisaged that both the accuracy and the explanatory ability of macroscopic traffic flow models can be improved significantly by distinguishing classes and their specific driving characteristics. In this article, we derive such a multiple user-class traffic flow model. Starting point for the derivation of the macroscopic flow model is the user-class specific phase-space density, which can be considered as a generalization of the traditional density. The gas-kinetic equations describing the dynamics of the multiclass Phase-Space Density (MUC-PSD) are governed by various, interacting processes, such as acceleration towards a class-specific desired velocity, deceleration caused by vehicle interactions and the influence of lane changing. The gas-kinetic equations serve as the foundation of the proposed macroscopic traffic flow models, describing the dynamics of the class-dependent spatial density, velocity and velocity variance. The modeling approach yields explicit relations for both the velocity and the velocity variance. These equilibrium relations show competing processes: on the one hand, drivers accelerate towards their class-dependent desired velocity, while on the other hand, they need to decelerate due to interactions with vehicles from their own class and asymmetric interactions with vehicles from other classes. Using the operationalized model, macroscopic simulations provide insight into the model behavior for different scenarios.
