An extended car-following model considering the low visibility in fog on a highway with slopes

To depict the effect of low-visibility foggy weather upon traffic flow on a highway with slopes, this paper proposes an extended car-following model taking into consideration the drivers' misjudgment of the following distance and their active reduction of the velocity. By linear stability analysis, the neutral stability curves are obtained. It is shown that under all the three road conditions: uphill, flat road and downhill, drivers' misjudgment of the following distance will change the stable regions, while having little effect on the sizes of the stable regions. Correspondingly, drivers' active reduction of the velocity will increase the stability. The numerical simulations agree well with the analytical results. It indicates that drivers' misjudgment contributes to a higher velocity. Meanwhile, their active reduction of the velocity helps mitigate the influences of small perturbation. Furthermore, drivers' misjudgment of the following distance has the greatest effect on downhill and the smallest effect on uphill, so does drivers' active reduction of the velocity.