# The Car-Following Model and Its Applications in the V2X Environment: A Historical Review
## 2 Development Process of the Traditional Car-Following Models
These models were usually established by fuzzifying one or multiple parameters in the previous car-following models. The artificial intelligence models based on the neural network can directly discover the laws of drivers' car-following behavior from the field data measured in various environments, such as the widely used Next-Generation Simulation (NGSIM) data. In the same period, the attention of researchers in the field of physics was attracted to the car-following behavior because of the unique movement characteristics of vehicles in the car-following process. Based on the theory and method of statistical physics, [PERSON] et al. established the first of the optimal velocity models, the optimal velocity (OV) model [11]. Subsequently, the negative velocity difference was introduced into the OV model to form the generalized force (GF) model by [PERSON] et al. [12]. [PERSON] et al. further integrated the positive velocity difference and proposed the full velocity difference (FVD) model [13]. These three models are the basic ones of optimal velocity models, and their core is the optimal velocity function. Due to the unique characteristics of this function, the optimal velocity models can describe the behavior of drivers pursuing higher speed but being unable to accelerate unlimitedly because of the constraints of vehicle and road. The last type of car-following model is intelligent driving, and the first model of this type, the intelligent driver (ID) model, was established by [PERSON] and [PERSON] and [PERSON] (2018). Later, [PERSON] et al. further considered the reaction delay and estimation error and formed an extended model, the human driver (HD) model [PERSON] and [PERSON] (2018). The intelligent driving models contains two vital items, which, respectively, represent the acceleration and deceleration trend. This kind of structure makes these models suitable to describe the car-following behavior of the vehicle(s) equipped the automatic controller such as the Adaptive Cruise Control (ACC) system and the Collaborative Adaptive Cruise Control (CACC) system. The above models constitute the main body of research on modeling car-following behavior. In this paper, they are collectively named as traditional car-following models, and their developing process is as shown in Figure 2.  
The traditional models have shown the ability to describe the driver's car-following behavior under different conditions. Different types of traditional car-following models have distinct performance characteristics. For example, the optimal velocity models can reproduce nonlinear and complex traffic phenomena such as phase transition, stop-and-go. However, as mentioned above, only the dual-vehicle interaction was considered in these models, and thus they cannot be directly employed to describe the car-following behavior or to be the basis for analyzing traffic flow characteristics, estimating vehicle(s) energy consumption and emission in the V2X environment. Nevertheless, considering their distinct performance characteristics, the traditional car-following models are suitable to be the basic model and to be extended or improved to form new models for the V2X environment.