# The Car-Following Model and Its Applications in the V2X Environment: A Historical Review
## 3 Research on Car-Following Behavior in the V2X Environment
### Modelling the Car-Following Behavior
#### 3.2.2 Information of Multiple Preceding Vehicles  
In the previous traffic environment without V2X technology, the drivers could only rely on themselves to obtain parts of the microscopic traffic information (position, velocity, vehicle type, etc.). The obtained information is usually qualitative or inaccurate. For example, the preceding vehicle is \"close\" and its velocity is \"slow\". Furthermore, limited by the ability of human perception organs, the drivers can only obtain information of vehicles within their field of vision. However, in the new environment with V2X technology, the drivers can obtain quantitative, accurate, abundant information of all units in the system under ideal conditions. For example, the values of the position, velocity, and acceleration of the arbitrary number of preceding vehicles. In particular, the driver-vehicle unit can obtain the aforementioned information with very low delay, utilizing V2X technology based on 5G-LTE, which has been applied, and the 6G-LTE, which is to be applied. In fact, a kind of interaction relationship is formed between the vehicles that are connected and exchange information with others. As mentioned above, information is the basis of decision making. Thus, there will be new characteristics of car-following behavior affected by various pieces of information in the V2X environment, which requires new models to describe. [PERSON] et al. first extended the car-following model from dual-vehicle interaction to multi-vehicle interaction [34]. Considering the position of the arbitrary number of preceding vehicles in the current lane, [PERSON] et al. proposed an extended OV model by calculating the headway between each preceding vehicle and the object vehicle and, respectively, substituting the headways into optimal velocity functions. [PERSON] et al. pioneered the research on the multi-vehicle interaction car-following model. Since then, researchers have been extending and improving the traditional car-following models by considering various pieces of motion state information from multiple preceding vehicles in the current lane from different perspectives. [PERSON] et al. also proposed an extended OV model with consideration of the position of the arbitrary number of preceding vehicles in the current lane [35]. Unlike [PERSON]'s approach, [PERSON] et al. introduced the weighted sum of calculated headway into one optimal velocity function. The difference between these two kinds of optimal-function-based approaches to process the information is that in the corresponding model; it is assumed that the driver determines the car-following behavior according to multiple pieces of information, or determines that according to the overall situation represented by multiple pieces of information. Two extended OV models [34; 36] considering the motion state information of multiple preceding vehicles were compared and analyzed by [PERSON] et al. [37]. The results reveal that the information can effectively enhance the stability of traffic flow and improve the performance of the OV model through solving the problem that the model will output unrealistic acceleration and deceleration under some conditions. Later, [PERSON] et al. replaced the velocity difference item with the relative velocity of the arbitrary number of preceding vehicles to form an extended model, i.e., the Forward Looking Relative Velocity (FLRV) model [38]. In the same period, [PERSON] et al. proposed a similar FVD-based model [39]. After them, [PERSON] et al. constructed an extended FVD model [40]. In [PERSON]'s model, the weighted sum of the headway between the arbitrary number of preceding vehicles and their preceding vehicle was calculated and imputedinto one optimal velocity function. Based on the above models with consideration of relative velocity or headway, [PERSON] et al. proposed an extended OV model, i.e., the Multiple Headway and Velocity Difference (MHVD) model, which contains the relative velocity and headway mentioned above [41]. Then, [PERSON] et al.