## 2 Methodology  
### Length of Median Opening and Its Influencing Factors  
The median opening length in the crossover work zone should ensure that vehicles safely cross through the opening at a moderate running speed. The vehicles need to change lanes at the opening, turn left to reach the midpoint of the opening and then drive right into the opposite lane. According to the vehicle driving track in the median opening, it can be simplified to a model, as shown in Figure 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Research Methods** & **Applicability** & **Advantage** & **Disadvantage** \\ \hline \multirow{4}{*}{Traffic simulation} & Traffic flow theory & Risk-free & \\  & Road design & Flexible & Difficulty in model \\  & Traffic safety & Repeatable & calibration \\  & Intelligent transportation & Comparable & Results differ greatly \\  & & Cost-efficient & \\  & Driving behavior & Risk-free & Low degree of simulation \\  & Traffic safety & Cost-efficient & Relative validity \\  & Vehicle research & Ease of data collection & Simulator sickness \\  & Driving behavior & & \\  & Traffic safety & Real & Expensive \\  & Vehicle research & Reliable data & Harsh test conditions \\  & Driver’s psychophysiological indicators & Long-term observation & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the advantages and disadvantages of research methods in the work zone. The track of the vehicle crossing through the opening is S-shaped, forming two circular curves with the same radius connected in reverse. According to the equilibrium of the forces when a vehicle crosses through the median opening, we obtained the vehicle driving radius as follows [29]:  
\[R=\frac{V^{2}}{127(\varphi+i)} \tag{1}\]  
where \(R\) is the vehicle driving radius at the median opening, m; \(V\) is the vehicle speed at the median opening, km/h; \(\varphi\) is the sideway force coefficient; and \(i\) is the cross slope. From Figure 1, Equations (2) and (3) are derived as follows:  
\[R^{2}=l_{t}^{2}+\left(R-\frac{D_{x}+D_{z}}{2}\right)^{2} \tag{2}\]  
\[l_{t}=\frac{\sqrt{4R(D_{x}+D_{z})-\left(D_{x}+D_{z}\right)^{2}}}{2} \tag{3}\]  
where \(D_{z}\) is the median width, m; \(D_{x}\) is the inside-lane width, m; and \(l_{t}\) is the projection length of the vehicle track line. Equations (4) and (5) can be derived as follows:  
\[l_{a}=(R-\frac{D_{x}}{2})\tan\alpha \tag{4}\]  
\[\cos\alpha=\frac{R-\frac{D_{x}}{2}}{R-\left(D_{x}-D_{a}\right)} \tag{5}\]  
The calculation model of the median opening length is as follows:  
\[l=2[l_{t}-(R-\frac{D_{x}}{2})\tan\alpha] \tag{6}\]  
where \(\alpha\) is the deflection angle corresponding to the circular curve of the vehicle driving track; \(l_{a}\) is the deflection angle corresponding to the track projection; and \(D_{a}\) is the safety distance between the vehicle and median, taken as 0.5 m.  
According to the calculation model, the length of the median opening is related to the median width, lane width and vehicle turning radius; the turning radius of the vehicle is determined by the vehicle running speed, sideway force coefficient and cross slope. When the opening length is fixed and the vehicle crosses through the median opening, the wider the median, the greater the vehicle's lateral displacement and the smaller the turning radius, resulting in decreases in the vehicle's running speed and road capacity. According to a survey, median widths of 2 m, 3 m, 3.5 m and 4.5 m are generally used on freeways. The lane width also affects the lateral displacement and running speed of vehicles crossing through the opening, thus affecting the length of the median opening. Most of  
Figure 1: Schematic diagram of the median opening length calculation model. the openings are one lane, making it difficult to meet the turning requirements of large vehicles. In work zones, the lane width is widened according to the most unfavorable vehicle crossing through the opening.