Hybrid stochastic kinetic description of two-dimensional traffic dynamics
This work provides a more realistic traffic flow model for researchers studying multi-lane traffic dynamics, though it is an incremental extension of existing kinetic models.
The authors developed a hybrid stochastic kinetic model for two-dimensional traffic dynamics that accounts for both lane-changing and same-lane interactions, and validated its speed-density diagrams against real data.
In this work we present a two-dimensional kinetic traffic model which takes into account speed changes both when vehicles interact along the road lanes and when they change lane. Assuming that lane changes are less frequent than interactions along the same lane and considering that their mathematical description can be done up to some uncertainty in the model parameters, we derive a hybrid stochastic Fokker-Planck-Boltzmann equation in the quasi-invariant interaction limit. By means of suitable numerical methods, precisely structure preserving and direct Monte Carlo schemes, we use this equation to compute theoretical speed-density diagrams of traffic both along and across the lanes, including estimates of the data dispersion, and validate them against real data.