An extended car-following model considering driver’s desire for smooth driving on the curved road

In real traffic, many driver’s desire to lower the fuel consumption by driving smoothly. In this paper, an extended car-following model considering the driver’s desire for smooth driving on a curved road is proposed. The desire for smooth driving can be considered as a control signal including the velocity difference between the steady and history velocity. The stability conditions are obtained by the control theory, and the modified Korteweg–de Vries (mKdV) equation is derived via the non-linear analysis method. The numerical simulations are carried out to analyze the control signal, the friction coefficient and radius of curved road effects on traffic flow. The results show that the control signal has a positive effect on improving traffic flow stability, while the stability decreases with the increase of the two other parameters.