# The Car-Following Model and Its Applications in the V2X Environment: A Historical Review
## 3 Research on Car-Following Behavior in the V2X Environment
### Applications of the Car-Following Models
#### 3.3.2 Analyzing the Characteristics of Traffic Flow  
Generally, traffic flow characteristics include all features of the traffic flow when operating. In traffic flow theory, the traffic flow characteristics usually refer to the stability characteristics and operation characteristics. Among them are described the stability characteristics and the resistance characteristics of traffic flow to disturbance, which are usually represented by the neutral stability condition and density wave equations. The operating performance of traffic flow is described with the operation characteristics, which is usually represented by the traffic flow three-parameter (i.e., volume, velocity, and density) and the space-time graph. The traffic flow characteristics are essentially the macroscopic aggregation of microscopic characteristics of units in the system. In the V2X environment, the changes in car-following behavior will cause the traffic flow characteristics to be different from the past. The traffic flow characteristics in the V2X environment were analyzed in parts of the aforementioned studies based on approaches such as stability analysis and numerical simulation. Among these works, the optimal velocity models and the intelligent driving models were widely employed, which is because of their unique advantages in performance and, more importantly, the convenience to analyze stability characteristics using (non)linear analysis methods based on these two types of models. In [43; 48; 56; 65; 70; 71; 72; 73; 74; 127; 75; 76; 77; 78; 79; 80; 81; 82; 83; 84; 85; 86; 87; 88; 89; 90; 91; 92; 93; 94; 95; 96; 97; 98; 99; 100; 101; 102; 103; 104; 105; 106; 107; 108; 109; 110; 111; 112; 113; 114; 115; 116; 117; 118; 119; 120; 121; 122; 123; 124; 125; 126; 127; 128; 129; 130; 131; 132; 133], the researchers derived the neutral stability condition and nonlinear characteristics of traffic flow and analytical solutions of traffic flow stability affected by various kinds of information in the V2X environment, utilizing the (non)linear analysis methods based on the car-following models proposed by themselves. The analytical solutions of traffic flow stability are the vital theoretical basis for preventing or alleviating traffic congestion. As the quantitative expression of traffic flow, the operation characteristics also should be given importance. In the previous studies on car-following behavior in the V2X environment, the operation characteristics of traffic flow were explored by constructing virtual scenarios and employing numerical simulation based on the proposed car-following models. [PERSON] et al. analyzed the operation characteristics of traffic flow with different penetrations of connected vehicles in the system based on the extended CM model, which is incorporated with the velocity fluctuation information of multiple preceding vehicles, proposed by themselves [110]. [PERSON] et al. employed the OV model and the extended OV model, which incorporated the headway of two preceding vehicles, to, respectively, describe the car-following behavior of traditional and connected vehicles, and explored the operation characteristics with different penetrations [51]. Based on the extended FVD model with consideration of the ETOA information of multiple preceding vehicles and the Back Looking Effect, [PERSON] et al. explored the characteristics of traffic flow when operation was affected by the information in the V2X environment [67]. In the same period, [PERSON] et al. analyzed the characteristics of traffic flow when operation was affected by various sources of motion state information, including the ETOA, of multiple preceding vehicles based on the extended FVD model [68]. In traffic flow theory, there is a mathematical relationship between aspects of the microscopic motion state, such as velocity and position described by the car-following models, and the macroscopic operating indexes of traffic flow.