# 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
#### 3.2.6 Characteristics of Driver Applying Information
proposed an extended OV model by differentiating the RD to describe the characteristic of RD varying due to different conditions or various drivers [86]. Based on [PERSON]'s approach, [PERSON] et al. further incorporated the differentiated RD corresponding to the velocity of preceding vehicles to extend the OV model [87]. The results of the above achievements confirm that incorporating the RD is important to accurately model the car-following behavior and reproduce the complex traffic phenomenon in the simulation using the car-following model. As one of the most important behavioral characteristics, RD should be considered in modeling car-following behavior and analyzing traffic flow in the environment, with or without V2X technology, although the automatic controller, such as the ACC and CACC, can assist or even replace the driver in the car-following process. Limited by the vehicle dynamics and communication delay, the car-following behavior cannot alter instantly when the traffic situation changes. Thus, there will still be a \"reaction\" delay in the future, and it is of great significance to incorporate the delay for exploring the car-following behavior and traffic flow in the V2X environment. In the traditional car-following models, along with its most extended models, the motion state at the next time step \(t+1\), which is the model output, is determined by various kinds of information at the current time step \(t\). Nevertheless, drivers determine their car-following behavior at the next time step \(t+1\) not only based on the information at the current time step \(t\) but also considering the historical information in the past period \([t-\tau,t]\). This behavioral characteristic is the so-called \"memory effect\". The correlation between the historical information and car-following behavior was identified from the field data [88; 89; 90; 91]. [PERSON] et al. introduced a memory item about the headway into the OV model and formed the first extended model incorporating the memory effect [92]. Considering that drivers memorize the historical information over the past period rather than at a specific time, [PERSON] constructed a desired-velocity function based on an integral form to describe the drivers' continuous memory of the historical headway over the past period and proposed the first extended OV model that incorporated continuous memory [86]. Utilizing the Grey correlation analysis method, the correlation between the memory of the historical headway and the car-following behavior was identified by [PERSON] et al., and, based on this, they introduced a new item, the difference between the headway and its historical value into the FVD model to form an extended model [88]. Unlike [PERSON]'s approach, [PERSON] et al. introduced the difference between the optimal velocity calculated by the headway and the historical optimal velocity calculated by the historical headway into the FVD model [93]. Considering that drivers determine the optimal velocity based on short-term memory of the historical headway, [PERSON] et al. replaced the optimal velocity item in the FVD model with a new one based on short-term memory and the correction index [94]. Soon after, [PERSON] et al. also explored the correlation between the car-following behavior and the historical headway using the grey correlation analysis method based on a field data set and proposed an extended FVD model [90]. Unlike the previous research, [PERSON] et al. introduced an item describing the memory of headway and incorporated this kind of memory in the optimal velocity function. In the same period, [PERSON] et al. proposed an extended OV model with consideration of drivers' desire to maintain a steady state, which was represented by the difference between the optimal velocity and its historical value [95]. [PERSON] et al. further incorporated an integral item to represent the continuous memory of optimized velocity information over a period in the BLFVD model and constructed a new extended model [96]. [PERSON] et al.