The influence of the non-motor vehicles for the car-following model considering traffic jerk

• We consider the influence of the non-motor vehicles and traffic jerk for the car-following model.
• We use the control method to analyze the stability of the improved model and obtain some results.
• The feedback control signal is added into the improved model and the stability condition is obtained.
• Numerical simulations are conducted to show the results for the stability of the model with and without control signal.

The influence of the non-motor vehicles and traffic jerk is considered for the car-following model in this paper. The control method is used to analyze the stability of the model. A control signal which is the velocity difference between the target vehicle and the following vehicle is added into the model and the stability condition is obtained. Numerical simulation is used to display the results for the stability of the model with and without control signal.