We derive from a solvable, discrete velocity model of a nonlinear Boltzmann equation the functional relations between the vehicular density ρ(x, t) and the flux J (x, t) which occurs in a popular traffic model first proposed by Greenshields. © 2002 Elsevier Science B,V. All rights reserved.
Hongler, M. O., & Filliger, R. (2002). Mesoscopic derivation of a fundamental diagram of one-lane traffic. Physics Letters, Section A: General, Atomic and Solid State Physics, 301(5–6), 408–412. https://doi.org/10.1016/S0375-9601(02)01082-4