# The Car-Following Model and Its Applications in the V2X Environment: A Historical Review
## 2 Development Process of the Traditional Car-Following Models  
As the most basic driving behavior, car following is the behavior of an object vehicle as it follows its preceding vehicle and maintains the current lane, which describes the longitudinal movement characteristics of the object vehicle. The research of car-following  
Figure 1: Framework of the review contents. behavior began with the car-following theory based on \"California Rules\" in the 1950s. In the \"California Rules\", it is assumed that the driver will maintain a prescribed safe distance between his/her vehicle and the preceding vehicle. To be specific, when the preceding vehicle accelerates per 4.47 m/s, the safe distance will enlarge by 4.57 m. After a nearly 70-year development, a large number of car-following models have been proposed. Among them, the representative ones can be classified into six types, which are the stimulus-response models, the safety distance models, the physiology-psychology models, the artificial intelligence models, the optimal velocity models, and the intelligent driving models, according to the modeling ideas. The GM model, which establishes the foundation for study on the car-following models, is the first model of the stimulus-response type [1,2]. In the GM model, the relative velocity of the object vehicle and its preceding vehicle was regarded as the stimulus, and the acceleration of the object vehicle was regarded as the response to the stimulus. Generally, in the stimulus-response models, the car-following behavior is modeled as the response to external changes that usually refer to the movement changes in (multi-)preceding vehicle(s). After the first stimulus-response model proposed by [PERSON] et al., [PERSON] et al. established the first safety distance model [3]. Then, the classical safety distance model that is the Gipps model was proposed by [PERSON] [4]. In the safety distance models, the car-following behavior is modeled as a process that the driver tries to reach and to maintain the desired headway, i.e., the safety distance. There are some unique advantages in the safety distance models, including [PERSON]'s laws of motion-based, concise structure and collision avoidance, making these models widely used to control vehicle longitudinal movement in the microcosmic traffic flow simulation software [5]. With the development of cognitive psychology, the researchers realized that the car-following behavior was not just a kinetic process, but also the results of the driver's physiology and psychology characteristics. Considering this, [PERSON] proposed the first physiology-psychology model [6]. Later, the most well-known physiology-psychology model, the Wiedemann 74 model, was established by [PERSON] [7] and then developed as the core of Vissim, which is one of the most famous traffic flow simulation programs. In the Wiedemann 74 model, of which the major innovation is that the stimulus is modeled physiologically and psychologically, there are two psychology following distances. The driver will recognize the risk and decelerate when the headway is smaller than the first psychology following distance, and he/she will recognize the safety and accelerate when the headway is larger than the second psychology following distance. At the turn of the century, computing hardware and artificial intelligence technology were rapid developing, making possible the discovery of the laws of car-following behavior directly from the trajectory data and, based on this, the formation of a model. The first artificial intelligence model was proposed by [PERSON] [8]. Since then, many car-following models of the artificial intelligence type based on different methods have been constructed. Among them, the common artificial intelligence methods employed to establish the model are fuzzy logic [9] and artificial neural network [10]. The artificial intelligence models based on fuzzy logic can describe the fuzziness of drivers' decision-making processes in car-following behavior.