Multi-class fundamental diagrams from the Prigogine-Herman-Boltzmann equation

Our aim in this paper is to establish a theoretical fundamental diagram for a multi-class traffic flow from a gas-kinetic-like traffic model. We start with a multi-class generalization of the Prigogine-Herman-Boltzmann equation to construct the fundamental relation for this system. We show that there exists a critical density which depends on the relative concentration of slow and fast users and describe a procedure to find the threshold value. Finally, our flow-density relation for a two-class mixture of vehicles is contrasted with empirical data in the literature.