# 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
#### 3.2.3 Information of Multiple Following Vehicles
further introduced the headway between the two successive ones of the arbitrary number of vehicles in the front and back of the object vehicle into one optimal velocity function and proposed an extended OV model [54]. Then, [PERSON] et al. constructed a Heavyside function to describe the drivers' behavior of tending to accelerate to avoid the possible collision caused by the too-small headway between them and the following vehicle, and, based on this, established an extended OV model with consideration of the headway between the arbitrary number of preceding vehicles and the Back Looking Effect [55]. [PERSON] et al. extended the FLRV model into a new one that incorporated the relative velocity between the two successive vehicles of the arbitrary number of vehicles in the front and back of the object vehicle [56]. [PERSON] et al. extended their previous research [42] with consideration of the Back Looking Effect and proposed a new extended OV model that incorporated the headway and relative velocity of the two successive ones in the arbitrary number of preceding vehicles and the headway between the object vehicle and its following vehicle [57]. Soon after, [PERSON] et al. introduced the Back Looking Effect into the FVD model to form an extended model, the Black Looking Full Velocity Difference (BLFVD) model [58].The Back Looking Effect was introduced into [PERSON]'s extended OV model [42] by [PERSON] et al. with consideration of the headway and relative velocity between the object vehicle and its following vehicle [59]. Like [PERSON]'s approach, [PERSON] et al. further introduced the relative velocity into the BLFVD model and formed a new extended model [60]. Based on this model, they discussed the impacts of the following vehicle information on traffic flow, and the results show that the headway information or the relative velocity information along with the headway can effectively enhance the stability of traffic flow. However, single relative velocity information will produce negative effects on the stability of traffic flow. Considering the marginal effect discussed in the previous section, [PERSON] et al. proposed a three cooperated vehicles extended FVD model [61]. In this model, the car-following behavior of the object vehicle is determined by the difference between the velocity of itself and the re-defined optimal velocity of all three vehicles. The re-defined optimal velocity is the output of optimal velocity function about the headway between the vehicle and the other two vehicles. Recently, [PERSON] et al. extended the BLFVD model by introducing the relative velocity of two preceding vehicles [62], and [PERSON] et al. proposed an extended ID model with consideration of the velocity and acceleration of multiple vehicles in the front and back of the object vehicle, as well as the headway and relative velocity between these vehicles and the object vehicle [63]. The incorporated information and the expressions of the above models considering the motion state of following vehicles in the current lane are as shown in Table 2.  
The results of the above studies confirm that the drivers will pay attention to their following vehicle(s) in the car-following process. With the results of this and the previous section, one can obtain that among all preceding and following vehicles in the current lane, the driver's primary concern is the motion state of the vehicles in the front, especially the preceding vehicle and its preceding vehicle. Based on this, the driver will take into account the motion state of vehicles in the back. The results also suggest that there are positive effects exerted by the information of vehicles in the back on the object vehicle's car-following behavior. Among various kinds of information on the vehicles in the back, the headway between the object vehicle and its following vehicle produces the most intense positive influence on the car-following behavior.