Communications in Mathematical Sciences

Vlasov-Fokker-Plank Models for Multilane Traffic Flow

Reinhard Illner, Axel Klar, and Thorsten Materne


Systems of equations of Vlasov-Fokker-Planck type are suggested for multilane traffic flow. The equations include nonlocal and time-delayed braking and acceleration terms with rates depending on the densities and relative speeds. The braking terms include lane-change probabilities. It is shown that simple natural assumptions on the structure of these probabilities lead to multivalued fundamental diagrams, consistent with traffic observations. Lane-changing behavior is the critical ingredient in such bifunctions.

Article information

Commun. Math. Sci., Volume 1, Number 1 (2003), 1-12.

First available in Project Euclid: 7 June 2005

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Illner, Reinhard; Klar, Axel; Materne, Thorsten. Vlasov-Fokker-Plank Models for Multilane Traffic Flow. Commun. Math. Sci. 1 (2003), no. 1, 1--12.

Export citation