A new nonlocal traffic flow model with anticipation-dependent relaxation time, equilibrium velocity and variance

We derived a nonlocal kinetic traffic model from a generalized carfollowing model with multiple look-ahead through the BBGKY hierarchy.A nonlocal hydrodynamical model was obtained consistently by the method of kinetic theory.The novel feature of nonlocality in equilibrium velocity and variance as well as in relaxation time was discovered.Simulation results showed that traffic hysteresis was induced by anticipation-dependent equilibrium velocity, relaxation time and equilibrium variance, indicating a 2D-region of synchronized flow.When drivers looked farther ahead, the amplitude of stop-and-go traffic reduced, and the resulting equilibrium velocity and flow increased, thus traffic stabilized as expected.Numerical results also indicated the existence of optimum anticipation vision.Finally, the model could also capture the physical nonlinear dynamic characteristics of metastability and the stop-and-go phenomenon in traffic flow.