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:
82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |
60K25 | Queueing theory (aspects of probability theory) |
90B20 | Traffic problems in operations research |
60K30 | Applications of queueing theory (congestion, allocation, storage, traffic, etc.) |