Stabilization effect of multiple drivers' desired velocities in car-following theory

In order to reveal the influence of driver's individual behavior on traffic flow more accurately, a new car-following model is proposed with consideration of multiple drives' desired velocities. The stability criterion of the new model is derived through linear stability theory and the results show that the current driver's desired velocity can stabilize traffic flow but the preceding driver's desired velocity can damage traffic stability. Through nonlinear analysis, the traffic jamming transition characteristics near the critical point can be described by the kink-antikink soliton of the mKdV equation. Numerical simulation confirms the analytical results, which shows that the multiple drivers' desired velocities play an important role in traffic evolution.