Communications in Mathematical Sciences

Volume 1 (2003)

Number 1

Vlasov-Fokker-Plank Models for Multilane Traffic Flow

Pages: 1 – 12

DOI: http://dx.doi.org/10.4310/CMS.2003.v1.n1.a1

Authors

Reinhard Illner

Axel Klar

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.

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