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Vlasov-Fokker-Planck models for multilane traffic flow. (English) Zbl 1153.82335
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:
82C31Stochastic methods in time-dependent statistical mechanics
60K25Queueing theory
90B20Traffic problems
60K30Applications of queueing theory