## 5 Results and Discussions
### The Near-Optimal Trajectories  
We show two samples of near-optimal trajectories obtained from the simulations to verify that any point in the graph \(G\) is visited by different vehicles with the arrival time difference between any vehicles exceeds \(\mathrm{t_{occ}}\). Tables 6 and 7 show the optimal trajectories for \(t_{\mathrm{occ}}>10\) s and \(t_{\mathrm{occ}}>150\) s, respectively. To verify that the arrival time differences exceed \(t_{\mathrm{occ}}\), we provide Table 8. According to Table 8, for \(t_{\mathrm{occ}}>10\) s, the smallest arrival time difference is 11.7 s, i.e., between Vehicles 2 and 3 at Node 2. For \(t_{\mathrm{occ}}>150\) s, the smallest arrival time difference is 165.4 s, i.e., between Vehicles 2 and 3 at Node 2.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Vehicle**} & **Routes** & **4** & **10** & **2** & **6** & **7** & **9** & **1** & **5** & **3** & **8** \\ \cline{2-11}  & Arrival Time (s) & 0 & 365.6 & 446.9 & 511.5 & 584.0 & 659.5 & 767.8 & 874.4 & 998.3 & 1194.9 \\  & Applied Speed (m/s) & 0.1 & 1 & 1.5 & 1.5 & 1 & 1.5 & 1.5 & 1 & 1.5 \\ \hline \multirow{2}{*}{**Vehicle**} & **Routes** & **1** & **5** & **6** & **7** & **9** & **4** & **10** & **2** & **3** & **8** \\ \cline{2-11}  & Arrival Time (s) & 0 & 290.7 & 313.6 & 404.3 & 467.3 & 565.9 & 817.2 & 944.3 & 1174.1 & 1292.0 \\  & Applied Speed (m/s) & 1 & 1 & 0.5 & 1.5 & 1.5 & 0.1 & 1.5 & 0.1 & 1.5 & 1 \\ \hline \multirow{2}{*}{**Vehicle**} & **Routes** & **3** & **8** & **5** & **1** & **9** & **7** & **6** & **2** & **10** & **4** \\ \cline{2-11}  & Arrival Time (s) & 0 & 184.3 & 403.0 & 602.9 & 711.2 & 786.7 & 859.2 & 956.0 & 1091.5 & 1292.6 \\ \multirow{2}{*}{**Vehicle**} & Applied Speed (m/s) & 0.1 & 1.5 & 0.1 & 1.5 & 1.5 & 1 & 1.5 & 0.5 & 1 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Most near-optimal trajectories for \(\mathrm{t_{occ}}>10\) s.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Vehicle**} & **Routes** & **4** & **10** & **2** & **6** & **5** & **3** & **8** & **1** & **9** & **7** \\ \cline{2-11}  & Arrival Time (s) & 0 & 670.3 & 805.8 & 981.8 & 1003.3 & 1106.6 & 1290.9 & 1723.7 & 1886.1 & 1949.0 \\ \cline{2-11}  & Applied Speed (m/s) & 0.1 & 0.5 & 1 & 0.1 & 1.5 & 1.5 & 0.1 & 0.5 & 1.5 & 1.5 \\ \hline \multirow{2}{*}{**Vehicle**} & **Routes** & **1** & **8** & **5** & **3** & **2** & **10** & **4** & **9** & **7** & **6** \\ \cline{2-11}  & Arrival Time (s) & 0 & 432.8 & 666.2 & 872.8 & 1240.5 & 1342.2 & 1476.2 & 1539.3 & 1710.9 & 1875.8 \\ \multirow{2}{*}{**Vehicle**} & Applied Speed (m/s) & 0.1 & 0.5 & 1 & 0.5 & 0.5 & 1.5 & 1.5 & 1 & 0.1 & 1 \\ \hline \multirow{2}{*}{**Vehicle**} & **Routes** & **3** & **8** & **5** & **1** & **9** & **4** & **10** & **2** & **6** & **7** \\ \cline{2-11}  & Arrival Time (s) & 0 & 184.3 & 324.3 & 537.5 & 754.0 & 832.9 & 993.8 & 1075.1 & 1171.9 & 1262.6 \\ \multirow{2}{*}{**Vehicle**} & Applied Speed (m/s) & 0.1 & 1.5 & 1 & 0.5 & 1 & 1 & 1.5 & 1 & 1 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Most near-optimal trajectories for \(\mathrm{t_{occ}}>150\) s.  
Figure 7: The progression of searching the optimal solution for \(t_{\mathrm{occ}}>150\) s: (**a**) for \(\rho=0.1\); (**b**) \(\rho=0.5\).