Communications in Mathematical Sciences

Vlasov-Fokker-Plank Models for Multilane Traffic Flow

Reinhard Illner, Axel Klar, and Thorsten Materne

Abstract

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

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

Dates
First available in Project Euclid: 7 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.cms/1118150395

Mathematical Reviews number (MathSciNet)
MR1979839

Zentralblatt MATH identifier
1153.82335

Citation

Illner, Reinhard; Klar, Axel; Materne, Thorsten. Vlasov-Fokker-Plank Models for Multilane Traffic Flow. Commun. Math. Sci. 1 (2003), no. 1, 1--12. https://projecteuclid.org/euclid.cms/1118150395


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