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Zbl 1153.82335
Illner, Reinhard; Klar, Axel; Materne, Thorsten
Vlasov-Fokker-Planck models for multilane traffic flow. (English)
[J] Commun. Math. Sci. 1, No. 1, 1-12 (2003). ISSN 1539-6746

Summary: 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.

MSC 2000:: *82C31 Stochastic methods in time-dependent statistical mechanics
60K25 Queueing theory
90B20 Highway traffic
60K30 Appl. of queueing theory

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