## 3 Results
### Model Comparison  
For convenience, the traditional model focusing on the through path for motor vehicles (cars and buses) is referred to as Model 1, while the model presented in this paper is referred to as Model 2.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Outbound** & **Outbound** & **Outbound** & **Outbound** & **Inbound** & **Inbound** & **Inbound** & **Inbound** & **Inbound** \\
**Band-** & **Path 1** & **Path 2** & **Path 3** & **Path 4** & **widths** & **Path 1** & **Path 2** & **Path 3** & **Path 4** \\ \hline \(b_{1,1,p}\) & 0.1944 & 0 & 0 & 0 & \(\overline{b}_{1,1,\overline{p}}\) & 0.1653 & 0 & 0 & 0 \\ \(b_{1,2,p}\) & 0 & 0.232 & 0.276 & 0 & \(\overline{b}_{1,2,\overline{p}}\) & 0 & 0.217 & 0.195 & 0.046 \\ \(b_{1,3,p}\) & 0 & 0.1915 & 0.2345 & 0.0495 & \(\overline{b}_{1,3,\overline{p}}\) & 0 & 0.1746 & 0.1316 & 0.1094 \\ \(b_{2,1,p}\) & 0.0687 & 0.1483 & 0 & 0.1087 & \(\overline{b}_{2,1,\overline{p}}\) & 0.1654 & 0 & 0.1106 & 0.1464 \\ \(b_{2,2,p}\) & 0.1633 & 0.0537 & 0 & 0.2033 & \(\overline{b}_{2,2,\overline{p}}\) & 0.257 & 0 & 0 & 0.241 \\ \(b_{2,3,p}\) & 0.0575 & 0 & 0.1545 & 0.0865 & \(\overline{b}_{2,3,\overline{p}}\) & 0.0648 & 0.1922 & 0 & 0.0488 \\ \(b_{3,1,p}\) & 0 & 0 & 0 & 0.1852 & \(\overline{b}_{3,1,\overline{p}}\) & 0 & 0 & 0 & 0.1932 \\ \(b_{3,2,p}\) & 0 & 0.2312 & 0.2132 & 0.0438 & \(\overline{b}_{3,2,\overline{p}}\) & 0 & 0.2102 & 0.212 & 0.0468 \\ \(b_{3,3,p}\) & 0 & 0.257 & 0.22 & 0 & \(\overline{b}_{3,3,\overline{p}}\) & 0 & 0.244 & 0.212 & 0 \\ \(b_{4,1,p}\) & 0 & 0 & 0.2285 & 0.0465 & \(\overline{b}_{4,1,\overline{p}}\) & 0.0438 & 0.2232 & 0 & 0.0518 \\ \(b_{4,2,p}\) & 0.0889 & 0 & 0.1571 & 0.1179 & \(\overline{b}_{4,2,\overline{p}}\) & 0.1152 & 0.1518 & 0 & 0.1232 \\ \(b_{4,3,p}\) & 0.244 & 0 & 0 & 0.252 & \(\overline{b}_{4,3,\overline{p}}\) & 0.2147 & 0 & 0 & 0.2467 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Green wave bandwidths for the test arterial generated by the presented model.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Road Segments** & **Outbound Dwell Time/s** & **Inbound Dwell Time/s** \\ \hline Between intersections 1 and 2 & 19 & 17 \\ Between intersections 3 and 4 & 18 & 17 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Average bus dwell time at each bus stop.  
Note that Model 1 can be obtained by modifying Model 2. The reason is that Model 1 solves the arterial green wave control problem for through cars and buses, while Model 2 considers the green wave demand of both cars and buses as well as electric bicycles and optimizes all paths as decision variables. The key modification of Model 2 is changing the range of the subscripts. \(m\) is changed from \(m=1,2,3\) to \(m=1,2\), \(p\) is changed from \(p=1,2,3,4\) to \(p=4\), and \(\overline{p}\) is changed from \(\overline{p}=1,2,3,4\) to \(\overline{p}=4\). Model 1 was used to generate a green wave control scheme for the test arterial, and the corresponding green wave control problem was solved by the optimization tool Gurobi 11. The green wave bandwidths for the test arterial generated by Model 1 are shown in Table 5. It is worth noting that although the traditional model targets the through paths of motor vehicles, other paths of motor vehicles and electric bicycles may also indirectly benefit from the green wave bands. We can identify these indirectly obtained green wave bands by the time-space diagram generated by Model 1. These indirectly obtained green wave bands are also shown in Table 5. In addition, green wave bandwidths that are too small are considered ineffective. Since the minimum green wave bandwidth is set to 4 s in this study, any green wave band, whether directly or indirectly obtained, with a bandwidth less than \(4\times z\) is considered ineffective. Ineffective green wave bandwidths are uniformly treated as zero. This principle applies to both Models 1 and 2.