# 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
Thus, the corresponding macro traffic flow model can be derived based on this mathematical relationship and the corresponding car-following model. Considering this, [PERSON] derived a second-order continuous medium model based on the improved car-following model with consideration of drivers' memory effect to explore the macro characteristics of traffic flow [134]. The results reveal that there is a direct relationship between the macro viscosity effect in traffic flow and the micro memory effect in car-following behavior. [PERSON] et al. constructed a macro traffic flow model considering the drivers' forecast effect based on the micro-macro relationship and a car-following model with consideration of this effect [135]. Later, [PERSON] et al. further derived a macro model based on the extended car-following model incorporating drivers' reaction delay to explore the traffic flow characteristics analytically [136]. It is also confirmed with these studies that it is necessary to introduce the drivers' memory effect, forecast effect, and reaction delay in modeling their car-following behavior from the macro perspective of the system level, which is consistent with the conclusion given in the previous reviews. After the above works, more studies were carried out. [PERSON] et al. derived a macro model utilizing the micro-macro relation based on [PERSON]'s model [137] to explore the traffic flow characteristic affected by information about the average velocity of multiple preceding vehicles in the current lane [70]. [PERSON] et al. derived a macro model for describing characteristics of traffic flow with slope based on the extended car-following model with consideration of the ETOA information [138]. [PERSON] et al. derived a macro model to analyze how the traffic flow affected the information of two preceding vehicles based on the extended model incorporating the same information [139]. [PERSON] constructed a continuous medium macro model based on the car-following model with consideration of the drivers' reaction delay, using the headway and relative velocity information [140]. Different from the above works, [PERSON] et al. proposed a simulation framework to combine the car-following model into the cellular automata model, and analyzed the traffic flow affected by information about the average velocity of the GPV based on the framework [141]. The results of the studies on traffic flow stability along with their meaning are summarized in Section 3.2.5. As another core content of traffic flow characteristics, the operation characteristics were discussed from various perspectives based on numerical simulation or theoretical analysis in the aforementioned works. Generally speaking, the various sources of information mentioned above in the V2X environment can exert positive effects on traffic flow with different degrees in the operation and stability characteristics. On the one hand, the traffic flow can maintain a steady state in resisting larger disturbance. On the other hand, as the representation of better stability characteristics in the operation characteristics, the efficiency of traffic flow can be improved, which means an increase in volume, velocity, and critical density. It is also pointed out that with the increase in the penetration of connected vehicles in the system, the optimization effects caused by these vehicles on traffic flow will increase. Noteworthy is that the positive effects caused by each increase in the penetration are not all increasing linearly. There are some results we would like to further discuss, which are that the connected vehicles may exert negative effects on traffic flow when their penetration is low. When the penetration of connected vehicles is low, only a small proportion of the vehicles in the system can obtain V2X information and adjust their car-following behavior according to the information.