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• QN-ACTR could model effect of limited sight distance on car-following performance. • Cognition modeling provides support for adverse fog traffic safety assessments. • Frequent eye movement led to increasing of cognitive time when driving in fog. • Driver's perception, decision-making and control behavior were more complex in fog. • Reduction of cognitive capacity led to an impairment of the overall driver behavior. This study explored human error risk factors in car-following behaviors, cognitive resource bottlenecks and performance impairment mechanisms in the context of cognitive capacity while driving on foggy roads. Firstly, a hierarchical driving behavior assessment was used to observe risky driving behavior in a foggy area. A driver's dynamic speed adjustment analog experiment was carried out in foggy conditions. Unique parameters were substituted into the traditional QN-ACTR driver behavior model. The visual far-time of the traditional model and the latitude-longitude control sensitivity parameters were estimated. Foggy conditions were modeled based on the QN-ACTR cognitive architecture to observe the effect of limited sight distance through fog on car-following performance. Jsim in the Eclipse environment and TORCS were applied in co-simulation and verified. The results show that (1) the proposed cognitive modeling approach effectively simulates a foggy driving environment and allows researchers to study affected and related driver behavior; and (2) the car-following performance in low visibility is significantly worse than in high visibility. These findings provide theoretical support and a scientific basis for the study of speed, safe distance, standard of limited speed and design methods for engineering safety mechanisms to counter the negative effects of driving on foggy roads. This study can inform actions to increase road safety during fog. [ABSTRACT FROM AUTHOR]