## 3 Results
### Association Analysis
#### 3.2.2 Grey Relational Analysis  
We used Equation (13) to form the comparison sequence \(X\) as follows:  
\[X= \begin{bmatrix}V\\ C\\ L\\ H\end{bmatrix} = \begin{bmatrix}40&45&50&55&60\\ 110&120&130&140&150\\ 12&16&20&24&28\\ 1&2&3&4&5\end{bmatrix} .\]  
We also used Equation (14) to form the reference sequence \(Y\) as follows:  
\[Y= \begin{bmatrix}E_{1}\\ E_{2}\\ E_{3}\\ E_{4}\end{bmatrix} = \begin{bmatrix}1.059&0.971&0.922&1.058&0.990\\ 1.004&0.931&0.947&1.023&1.094\\ 0.989&0.991&0.998&1.006&1.015\\ 0.978&0.992&0.997&1.012&1.020\end{bmatrix} .\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Intersection** \\ **Number** \\ \end{tabular} } & \multicolumn{2}{c}{**East**} & \multicolumn{2}{c}{**West**} & \multicolumn{2}{c}{**South**} & \multicolumn{2}{c}{**North**} \\ \cline{2-9}  & **Left-Turn** & **Straight** & **Left-Turn** & **Straight** & **Left-Turn** & **Straight** & **Left-Turn** & **Straight** \\ \cline{2-9}  & **✓** & **✓** & **✓** & **✓** & **✓** & **✓** & **✓** & **✓** & **✓** \\ \hline
1 & 392 & 608 & 432 & 622 & 206 & 264 & 156 & 205 \\
2 & 184 & 919 & 335 & 403 & 126 & 235 & 164 & 165 \\
3 & / & 423 & 300 & 1082 & / & / & 345 & / \\
4 & 398 & 1285 & 286 & 1038 & 153 & 203 & 105 & 165 \\
5 & 429 & 1502 & 91 & 1058 & 111 & 219 & 132 & 405 \\
6 & 1147 & 1220 & 187 & 1161 & 154 & 109 & 176 & 237 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Flow-related data (Unit: pcu/h). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Schemes** & \(V\) **(km/h)** & \(C\) **(s)** & \(L\) **(times)** & \(H\) **(\%)** & \(S\) & \(T\) & \(D\) & \(E\) \\ \hline A1 & 40 & 130 & 20 & 3 & 0.72 & 520.65 & 49.52 & 1.059 \\ A2 & 45 & 130 & 20 & 3 & 0.58 & 487.13 & 50.22 & 0.971 \\ A3 & 50 & 130 & 20 & 3 & 0.53 & 486.39 & 46.97 & 0.922 \\ A4 & 55 & 130 & 20 & 3 & 0.74 & 524.16 & 47.51 & 1.058 \\ A5 & 60 & 130 & 20 & 3 & 0.68 & 513.54 & 43.28 & 0.990 \\ \hline B1 & 50 & 110 & 20 & 3 & 0.73 & 525.69 & 36.07 & 1.002 \\ B2 & 50 & 120 & 20 & 3 & 0.58 & 487.89 & 40.84 & 0.929 \\ B3 & 50 & 130 & 20 & 3 & 0.53 & 486.39 & 46.97 & 0.945 \\ B4 & 50 & 140 & 20 & 3 & 0.60 & 490.87 & 51.91 & 1.023 \\ B5 & 50 & 150 & 20 & 3 & 0.62 & 517.77 & 57.86 & 1.092 \\ \hline C1 & 50 & 130 & 12 & 3 & 0.53 & 482.89 & 46.06 & 0.989 \\ C2 & 50 & 130 & 16 & 3 & 0.53 & 485.20 & 46.09 & 0.991 \\ C3 & 50 & 130 & 20 & 3 & 0.53 & 486.39 & 46.97 & 0.998 \\ C4 & 50 & 130 & 24 & 3 & 0.54 & 488.26 & 47.02 & 1.006 \\ C5 & 50 & 130 & 28 & 3 & 0.55 & 488.70 & 47.33 & 1.015 \\ \hline D1 & 50 & 130 & 20 & 1 & 0.52 & 481.60 & 45.60 & 0.978 \\ D2 & 50 & 130 & 20 & 2 & 0.53 & 485.17 & 46.39 & 0.992 \\ D3 & 50 & 130 & 20 & 3 & 0.53 & 486.39 & 46.97 & 0.997 \\ D4 & 50 & 130 & 20 & 4 & 0.54 & 494.74 & 47.41 &Normalization was carried out through Equations (15) and (16), and the difference matrix was then obtained through Equation (17):  
\[\Delta= \begin{bmatrix}1.000&0.105&0.500&0.239&0.500\\ 0.446&0.250&0.405&0.187&0.000\\ 0.000&0.179&0.151&0.093&0.000\\ 0.000&0.089&0.043&0.065&0.000\end{bmatrix} .\]  
We also used Equations (18)-(21) to obtain the sequence of correlation coefficients \(L\) as follows:  
\[L= \begin{bmatrix}0.333&0.827&0.500&0.677&0.500\\ 0.528&0.667&0.553&0.728&1.000\\ 1.000&0.736&0.768&0.844&1.000\\ 1.000&0.848&0.921&0.885&1.000\end{bmatrix} .\]  
Finally, we used Equation (22) to calculate the degrees of correlation as \(Q_{V}=0.567\), \(Q_{C}=0.695\), \(Q_{L}=0.870\), and \(Q_{H}=0.931\). They were thus ranked as \(Q_{H}>Q_{L}>Q_{C}>Q_{V}\). The above results showed that \(Q_{L}\) and \(Q_{H}\) were higher than 0.7. They were thus important factors affecting the operational effect of the green wave that should be prioritized when formulating optimization measures. The \(Q_{V}\) and \(Q_{C}\) were 0.5-0.7, and thus they were relatively important factors in the optimization.