## 2 Digital Traffic Environment
### Digitization of TSS
#### 2.3.1 Static Environment  
The static data of TSS is the static environment information that can be obtained from the chart and will not change in a short time. The Chengshantou ship's routing includes three TSSs, two precautionary areas, and five traffic separation zones, as displayed in Figure 3.  
In Figure 3, each TSS features two traffic lanes and four boundary lines (numbered from east to west as 1, 2, 3...), with \(n\) points (numbered from north to south as 1, 2, 3...) on each boundary line. \(T_{sn}^{sn}\) denotes the \(n\)-th point on the \(m\)-th boundary line of the \(s\)-th TSS in this study. The traffic lanes are further divided into 16 segments based on distinct traffic flow directions and the places from where they occupy. The TSS does not prescribe a course in the precautionary area. According to COLREGs, when a vessel joins or leaves from  
Figure 3: Digitalization traffic environment of Chengshantou TSS. either side, it must do so at the smallest possible angle to the general direction of traffic flow. In this study, we set up a virtual traffic lane in the precautionary area \(A_{1}\), and set the centerline of the traffic lane as the planned route based on the author's real navigation experience and cluster analysis of the historical trajectories of ships in the study area [35]. 1. Traffic Lane The \(i\)-th traffic lane of the \(s\)-th TSS is represented by \(L_{si}\). \[L_{si}=\left\{ \begin{aligned} \left[area\big{|}T_{1}^{2i-1},T_{ 8}^{2i-1},T_{8}^{2i},T_{8}^{2i}\big{]}& s=1\\ \left[area\big{|}T_{1}^{2i-1},T_{8}^{2i-1},T_{8}^{2i-1},T_{8}^{2i },T_{8}^{2i},T_{8}^{2i}\big{]}& s=2\\ \left[area\big{|}T_{1}^{2i-1},T_{8}^{2i-1},T_{8}^{2i-1},T_{8}^{2i },T_{8}^{2i},T_{8}^{2i}\big{]}& s=3\end{aligned} \right.\right.\] (5)
2. Planned Route \(R_{si}\) shows the planned route on the \(s\)-th TSS's \(i\)-th traffic lane. The midpoint of the line between points \(T_{n}^{m}\) and \(T_{n}^{m-1}\) is represented by \(\left(T_{n}^{m}+T_{n}^{m-1}\right)/2\). \[R_{si}=\left\{ \begin{aligned} \left[line\big{|}\left(T_{1}^{2i-1}+T_{ 1}^{2i}\right)/2,\,\left(T_{8}^{2i-1}+T_{8}^{2i}\right)/2\right],& s=1\\ \left[line\big{|}\left(T_{1}^{2i-1}+T_{1}^{2i}\right)/2,\left(T_{ 3}^{2i-1}+T_{3}^{2i}\right)/2,\left(T_{5}^{2i-1}+T_{5}^{2i}\right)/2\right],& s=2\\ \left[line\big{|}\left(T_{1}^{2i-1}+T_{1}^{2i}\right)/2,\left(T_{ 3}^{2i-1}+T_{3}^{2i}\right)/2,\left(T_{5}^{2i-1}+T_{5}^{2i}\right)/2\right],& s=3\end{aligned} \right.\] (6)
3. Segment Equation (7) can be used to represent the segment \(\mathcal{O}_{s}\). \[\mathcal{O}_{s}=\mathcal{O}_{T_{n}^{m}}=\left[area\big{|}T_{n}^{m},T_{n+1}^{ m},T_{n+1}^{m+1},T_{n}^{m+1}\right]\] (7)  
Table 1 shows the main traffic flow direction of each segment as well as the segment area corresponding to \(O_{s}\). 4. Precautionary Area Equation (8) can be used to represent the precautionary area \(A_{s}\). \[A_{s}=\left\{ \begin{aligned} \left[area\big{|}T_{1}^{1},T_{ 1}^{1},T_{1}^{1},T_{\mathcal{V}}^{1},\,T_{2}^{2},T_{1}^{1}\big{]},& s=1\\ \left[area\big{|}(X_{1}+cosa,Y_{1}+R^{\prime}sina)\right],& s=2 \end{aligned} \right. \tag{8}\]  
where \(\alpha\in[0,\theta_{1}]\cup[2\pi-\theta_{2},2\pi]\), \((X_{1},Y_{1}),\,\,R^{\prime}\) represent the center and radius of the precautionary area, respectively. 5. Traffic Separation Zone  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline Segment Number & O\({}_{1}\) & O\({}_{2}\) & O\({}_{3}\) & O\({}_{4}\) & O\({}_{5}\) & O\({}_{6}\) & O\({}_{7}\) & O\({}_{8}\) \\ \hline Segment Area & \(O_{T_{1}^{3}}\) & \(O_{T_{2}^{3}}\) & \(O_{T_{1}^{3}}\) & \(O_{T_{2}^{3}}\) & \(O_{T_{1}^{3}}\) & \(O_{T_{2}^{3}}\) & \(O_{T_{2}^{3}}\) & \(O_{T_{1}^{3}}\)Equation (9) can be used to represent the traffic separation zone \(Z_{s}\). \[Z_{s}=\left\{