## 4 Simulation Results and Case Study
### Case Study  
To further verify the model proposed above, we considered three different cases and tested four different demand levels of 800, 1200, 1600, and 2000 veh/h; three different demand splits of 50-50, 65-35, and 80-20; and three different safety time gaps of 1.0, 1.2, and 1.5 s according to [25]. The simulation time for each scenario was 3600 s. Additionally, we evaluated the model's effectiveness through three indicators: number of stops (if the speed was less than 1 m/s, it was regarded as stopping), average delay time, and average speed. Three different control cases are as follows:  
* Case 0: do nothing. The vehicles travelled freely without any optimization control. This case adopted SUMO's default driving model. * Case 1: only trajectory optimization. Only the trajectory optimization and adjustment zones were set, and the vehicles were optimized after entering the trajectory optimization zone. * Case 2: lane-changing strategy and trajectory optimization. With the addition of lane-changing strategy, the vehicle can change lanes in the lane-changing zone, and then enter the trajectory optimization zone for trajectory optimization. The simulation results under different demands are shown in Tables 3-5. Overall, for the three different demand splits, Case 1 was better than Case 0 on the whole, and Case 2 outperformed Case 1. Figure 9: Schematic diagram of vehicle trajectory. The left side is the scenario without lane changing, and the right side is the lane-changing scenario. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Number of Stops**} & \multicolumn{6}{c}{**Average Delay (s)**} & \multicolumn{6}{c}{**Average Speed (km/h)**} \\ \cline{3-13}  & & \multicolumn{6}{c}{**Demand (ve/h)**} & \multicolumn{6}{c}{**Demand (ve/h)**} & \multicolumn{6}{c}{**Demand (ve/h)**} & \multicolumn{6}{c}{**Demand (ve/h)**} \\ \cline{3-13}  & & \multicolumn{6}{c}{**Demand (ve/h)**} & \multicolumn{6}{c}{**Demand (ve/h)**} & \multicolumn{6}{c}{**Demand (ve/h)**} & \multicolumn{6}{c}{**Demand (ve/h)**} \\ \cline{3-13}  & & \multicolumn{6}{c}{**800**} & **1200** & **1600** & **2000** & **800** & **1200** & **1600** & **2000** & **800** & **1200** & **1600** & **2000** \\ \hline \multirow{3}{*}{1.0} & Case 0 & 0 & 0 & 1 & 24 & 3.02 & 4.72 & 7.32 & 32.09 & 84.6 & 81.9 & 72.3 & 40.6 \\  & Case 1 & 0 & 0 & 0 & 0 & 3.07 & 3.55 & 4.46 & 5.24 & 88.8 & 88.4 & 87.9 & 87.2 \\  & Case 2 & 0 & 0 & 0 & 0 & 2.61 & 2.82 & 3.18 & 3.37 & 89.3 & 89.0 & 88.5 & 88.0 \\ \hline \multirow{3}{*}{1.2} & Case 0 & 0 & 0 & 9 & 16 & 2.51 & 5.28 & 25.26 & 45.72 & 84.3 & 77.4 & 47.0 & 32.5 \\  & Case 1 & 0 & 0 & 0 & 2 & 3.07 & 3.55 & 4.31 & 7.24 & 88.6 & 88.1 & 87.4 & 86.4 \\  & Case 2 & 0 & 0 & 0 & 0 & 2.61 & 2.83 & 3.19 & 3.39 & 89.2 & 88.7 & 88.2 & 87.5 \\ \hline \multirow{3}{*}{1.5} & Case 0 & 1 & 3 & 9 & 31 & 2.71 & 5.23 & 27.48 & 43.62 & 83.9 & 74.1 & 44.3 & 33.1 \\  & Case 1 & 0 & 0 & 0 & 8 & 3.08 & 3.55 & 5.47 & 10.17 & 88.2 & 87.1 & 85.3 & 76.2 \\ \cline{1-1}  & Case 2 & 0 & 0 & 0 & 0 & 2.61 & 2.84 & 3.28 & 3.50 & 89.1 & 88.2 & 86.1 & 83.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation results under the 65–35 demand.