# 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  
In the V2X environment, the impacts of various kinds of information on car-following behavior and traffic flow have been widely discussed. The positive effects of the information have been acknowledged. However, the assumptions about the affecting mode of information on car-following behavior are usually too ideal, which is reflected in that the characteristics of the driver applying the information were not considered. On the one hand, there is a certain amount of time for drivers to react according to the information after they received it, which is defined as the \"reaction delay\". On the other hand, drivers determine their car-following behavior according to not only the information of the current  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Research** & **Information** & **Expression** \\ \hline
[70] & velocity & \(\frac{d^{2}x_{n}(t)}{dt^{2}}=\alpha[V(\Delta x_{n}(t))-v_{n}(t)]+\lambda[\overline {v}_{n}(t)-v_{n}(t)]\) \\ \hline
[71] & position & \(\frac{d^{2}x_{n}(t)}{dt^{2}}=\alpha\big{[}V\big{(}\Delta x_{n}(t),\overline{ \Delta x_{n}}(t)\big{)}-v_{n}(t)\big{]}+\lambda\Delta\varpi_{n}(t)\) \\ \hline
[72] & velocity & \(\frac{d^{2}x_{n}(t)}{dt^{2}}=\alpha(V_{e}(\Delta x_{n}(t))-v_{n}(t))+\alpha \kappa\Big{(}\frac{1}{n}\  
time \(t\) but also the historical information in the past period \([t-\tau,t]\), which is defined as the \"memory effect\". In the previous sections, the car-following models with consideration of the information of preceding and following vehicles in the current and adjacent lanes were comprehensively reviewed. In these models, the drivers will instantly adjust their car-following behavior when they receive the information, which is inconsistent with the actual characteristics of the drivers' behavior. For the drivers, they need some time to determine and then conduct the adjustment according to the received information. In other words, there is a certain \"reaction delay\" in the adjusting process of car-following behavior. To explore the delay in detail, some researchers re-defined the delay as the \"reaction delay\", which is the delay due to drivers' decision-making process, and the \"action delay\" which is the acting time for drivers to carry out the decision. In most scenarios, it is difficult to accurately classify these two kinds of delay, and the impacts of regarding the two kinds of delay as one when modeling car-following behavior are small. Thus, we apply the first definition, that the time for drivers to finish the adjustment of their car-following behavior after they received the information is the reaction delay (RD). Based on this definition, we review and discuss the corresponding studies in the following contents. [PERSON] et al. extended [PERSON]'s model [37] by introducing the RD corresponding to the information of preceding vehicles considered in [PERSON]'s model [81]. [PERSON] et al. extended [PERSON]'s model [34] by incorporating the relative velocity and the RD corresponding to it, as well as the headway [82]. Soon after, [PERSON] et al. extended the OV and ID model with consideration of the information of preceding vehicles and their RD [83]. In the same period, [PERSON] et al. introduced the RD into the extended FVD model, which incorporated the relative velocity of the two preceding vehicles [49]. Then, [PERSON] et al. proposed an extended OV model with consideration of the optimal velocity, desired following headway, and the RD [84]. [PERSON] et al. established an extended FVD model with consideration of the RD corresponding to velocity, headway, and relative velocity and discussed the impacts of various kinds of RD on car-following behavior and traffic flow stability [85]. In the above studies incorporated in the RD, drivers' RD was set as a constant, making these models unable describe the drivers' heterogeneity. According to this, [PERSON] et al.