## 4 Results and Discussion
### Freeway Lane Width Design Based on the Overtaking  
In engineering applications, the lane width design mainly concerns the Poliakoff model. As shown in Figure 15a, the control factors mainly include the vehicle width \(w\), the lateral safety distance \(d_{w}\) (wheel distance) and the lateral safety margin \(M\), where both \(d_{w}\) and \(M\) are considered to be related to the vehicle speed. [PERSON] et al. [19] proposed the lane width control factors from the perspective of vehicle lateral swing, as shown in Figure 15b, as the vehicle width \(w\), the lateral swing amplitude \(A\) and the safety margins \(M_{1}\) and \(M_{2}\) on the left and right sides of the lane. However, the model did not take into account the interactions between vehicles, and it is suitable for the lane width design for the free flow. From the above two models, it is evident that lane width design primarily considers vehicle width along with the safe spacing on both sides of the vehicle. The width of the vehicle is typically determined by referencing the dimensions of the most popular model in the local market. Drawing on the model proposed by [PERSON] et al., we assume that the safety distance on the left side of the overtaking vehicle remains unaffected by other vehicles and can therefore be set as a fixed value, whereas the safety distance on the right side is determined based on the findings presented in this study. Our work demonstrates  
Figure 14: Metrological heat maps of different speed indexes and wheel distance of cars. (**a**) Speed sum; (**b**) Speed difference; (**c**) Speed squared difference. Figure 15: Different methods to design lane width. (**a**) Polyakov model; (**b**) Model of [PERSON] et al. ; (**c**) This paper. that the wheel distance of vehicles in the freeway driving environment is insensitive to speed, but there is a significant negative correlation with body width. To avoid complex interaction effects, control factors should be independent of each other in the lane width design. Given that the geometric center distance exhibits low sensitivity to variations in vehicle width, this parameter is utilized as an evaluation metric to determine the safe lateral distance on the right side of the overtaking vehicle. In summary, as shown in Figure 15c, the vehicle width \(w\), the geometric center distance \(d_{gc}\) and the lateral safety margin \(M\) are taken as the control factors for freeway lane width design, and the relationship is given by Equation (7). \[lane\ width=M+w+d_{gc}/2 \tag{7}\]  
According to the survey results of the best-selling models in China's passenger car market, the body width of a car is generally around 1.9 m, while a truck is generally around 2.5 m. In the design specification of developed countries and the existing research, the lateral safety margin is taken as 0.25 m. Generally, the 50 th percentile or 85 th percentile driving parameters are the basis for design in road engineering. As shown in Table 6, the geometric center distance of TT in the 85 th percentile is 4.59 m, and if the width of the truck is taken as 2.5 m, the lateral margin of the outermost lane is 3.75 \(-\) (4.59 + 2.5)/2 = 0.205 m, which is close to the freeway lateral safety margin in developed countries. According to Equation (7), when the geometric center distance of CC in the 85 th percentile is 4.52 m, the width of the car is taken as 1.9 m, and when the lateral safety margin is taken as 0.25 m, the width of the passenger-dedicated lane is (4.52 + 1.9)/2 + 0.25 = 3.46 m, which is taken as 3.5 m according to Chinese design custom, and it can be taken as the general value of the passenger-dedicated lane. Similarly, when the geometric center distance of CC in the 50 th percentile is 4.07 m, the width of the passenger-dedicated lane is (4.07 + 1.9)/2 + 0.25 = 3.235 m, which is taken as 3.25 m according to Chinese design custom, and it can be taken as the limiting value of the passenger-dedicated lane.