  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.
