# Modeling of Lane Changing Behavior of Connected Driving Based on Vehicle Interaction Potential
## 3 Acceptable Clearance for Lane Changing
### Research on Acceptable Clearance of Lane Changing  
#### 3.2.1 Acceptable Lane Changing Clearance between Vehicle \(M\) and Vehicle \(TL\)  
There is a risk of collision between lane changing vehicle \(M\) and target lane leading vehicle \(TL\) in the process of lane changing, so it is necessary to study their interaction state. As shown in Figure 5, in order to avoid collision accidents between vehicle \(M\) and vehicle \(TL\), the two vehicles should meet the conditions shown in the following formula, that is  
\[G_{a}^{M-TL}\geq S_{M}-S_{TL}+G_{\min}+w\sin(\theta) \tag{6}\]  
where, \(G_{a}^{M-TL}\): the acceptable lane changing gap between vehicle \(M\) and vehicle \(TL\); \(S_{M}\): the distance of lane changing vehicle \(M\) after the end of lane changing; \(S_{TL}\): the distance traveled by the leading vehicle \(TL\) in the target lane after the lane changing; \(G_{\min}\): the longitudinal critical distance between the two vehicles at the end of the lane changing; \(w\): the width of the lane changing vehicle; and \(\theta\): the angle between the lane changing vehicle \(M\) and the horizontal direction of the road. If a vehicle wants to implement lane changing in a network environment, it is necessary to calculate whether the acceptable gap of lane changing is satisfied on the premise of obtaining the operating parameters of surrounding vehicles, and the determination of  
Figure 4: Lane changing scene setting. \(G_{\text{min}}\) and \(\Delta S\) is particularly critical. The following studies are conducted on \(G_{\text{min}}\) and \(\Delta S\), respectively. (1) Longitudinal critical distance  
The longitudinal critical distance indicates that the vehicle can safely follow the vehicle in front after completing the lane changing behavior under the premise of meeting this distance. Therefore, it can also be explained by the distance required for following. [PERSON] [17] believes that the required safety distance is related to the speed and reaction time of the vehicle, and puts forward a formula:  
\[G_{\text{min}}=\eta v+\gamma v^{2} \tag{7}\]  
where: \(v\) represents the speed of the vehicle; \(\eta\) indicates the response time of the vehicle; and \(\gamma\) indicates the undetermined coefficients. In the VTH following strategy [18], the required safety distance is related to the current vehicle speed and the speed difference between the front and rear vehicles, and the expression is as follows:  
\[G_{\text{min}}=(t_{0}-c_{v}\Delta v)v \tag{8}\]  
where: \(v\) represents the speed of the vehicle; \(\Delta v\) represents the speed of the front car minus the speed of the rear car; and \(t_{0}\) and \(c_{v}\) are undetermined coefficients. In the intelligent network environment, the acquisition, processing, and transmission of information have been improved qualitatively, the vehicle reaction time is basically negligible, and the driving state parameters between vehicles can be obtained in real time. Therefore, the setting of the longitudinal critical distance should also introduce the influence of the acceleration difference between the front and rear vehicles, and the expression is:  
\[G_{\text{min}}=(t_{0}-c_{v}\Delta v-c_{a}\Delta a)v \tag{9}\]  
where: \(\Delta a\) is the acceleration difference between the front and rear vehicles, \(c_{a}\) is the undetermined coefficient, and other parameters are the same as above. According to the above analysis, the longitudinal critical distance between vehicle \(M\) and vehicle \(TL\) can be obtained as:  
\[G_{\text{min}}=[t_{0}-c_{v}(v_{TL}-v_{M})-c_{a}(a_{M}-a_{TL})]v_{M} \tag{10}\]  
(2) Safe critical time for lane changing  
The safe critical time for lane changing represents the time it takes for lane changing vehicles and interacting vehicles to reach the same speed during lane changing. When the two cars reach the same speed, if there is no collision risk, there will be no collision later.