An extended visual angle model for car-following theory

Considering human drivers' visual angle, an improved full velocity difference model for car-following theory is proposed in this paper. The visual angle and its rate of change are used as stimulus in the proposed model based on the stimulus-response framework. The stability condition is obtained by the use of linear stability analysis. It is shown that the neutral stability line is asymmetry, and the stability of traffic flow varies with the length between the driver and the head of the following vehicle, the height difference between the driver and the head of the following vehicle and the width of the leading vehicle. The numerical simulations show a good agreement with the theoretical results such as asymmetry, density wave, hysteresis loop, acceleration, deceleration and so on. By introducing the visual angle and related variables, the proposed model can explain some complex nature of traffic phenomena and make the car-following models more realistic.