## 4 Simulation Results and Case Study
### Case Study
\begin{table}
\begin{tabular}{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)**} \\ \cline{3-13}  & & **800** & **1200** & **1600** & **2000** & **800** & **1200** & **1600** & **2000** & **800** & **1200** & **1600** & **2000** \\ \hline \multirow{3}{*}{1.0} & Case 0 & 0 & 5 & 6 & 26 & 4.93 & 21.56 & 24.92 & 34.90 & 81.2 & 52.4 & 47.3 & 41.2 \\  & Case 1 & 0 & 0 & 0 & 2 & 3.03 & 4.35 & 5.59 & 6.79 & 87.9 & 86.8 & 85.5 & 84.3 \\  & Case 2 & 0 & 0 & 0 & 0 & 2.12 & 2.96 & 3.02 & 3.74 & 89.0 & 88.6 & 87.9 & 87.1 \\ \hline \multirow{3}{*}{1.2} & Case 0 & 0 & 4 & 10 & 30 & 4.73 & 20.67 & 25.40 & 43.30 & 79.6 & 52.5 & 46.6 & 32.2 \\  & Case 1 & 0 & 0 & 1 & 4 & 3.02 & 4.35 & 5.59 & 7.66 & 87.4 & 84.9 & 82.6 & 79.4 \\  & Case 2 & 0 & 0 & 0 & 2 & 2.13 & 2.97 & 3.05 & 4.10 & 88.8 & 88.3 & 87.5 & 86.2 \\ \hline \multirow{3}{*}{1.5} & Case 0 & 0 & 7 & 53 & 99 & 7.42 & 22.06 & 27.23 & 44.12 & 74.0 & 51.7 & 43.5 & 33.1 \\  & Case 1 & 0 & 3 & 4 & 27 & 3.03 & 4.36 & 5.69 & 21.86 & 85.6 & 80.8 & 79.3 & 49.7 \\ \cline{1-1}  & Case 2 & 0 & 0 & 0 & 2 & 2.39 & 3.45 & 4.93 & 5.94 & 87.0 & 83.0 & 80.4 & 78.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation results under the 50–50 demand. Let us take the 50-50 demand split as an example; see Figure 10. As shown in Figure 10a, vehicles may have stopped because they adjust their speed to ensure a safe gap between vehicles. Unlike Case 0 and Case 1, the cars of Case 2 would basically not stop when the safety time gap was 1.0 s during the simulation. This advantage of Case 2 became more evident as the safety time gap and traffic volume increased. At 800 veh/h, there was no apparent difference between the three cases in terms of average delay and average speed. With the increase of freeway and ramp traffic flow, the difference in performance indicators was gradually significant. Significantly, at 2000 veh/h, the average delay of Case 1 was reduced by about 70.3%, and the average speed was approximately doubled compared to Case 0. The average delay of Case 2 was reduced by about 38.3%, and the average speed was increased by about 18.2% compared with Case 1. Additionally, the average speed and average delay of Case 0 were not stable. With the change of mainline traffic flow and ramp traffic flow, the average speed and average delay significantly changed, and the average speed and delay changes of Case 1 and 2 were relatively stable due to the vehicle's trajectory optimization. Furthermore, due to the addition of the lane-changing strategy, the average delay of Case 2 was lower, and traffic flow and safety time gaps had little impact on the average speed. Therefore, compared with Case 1 and Case 0, the merging model based on the lane-changing strategy improved efficiency. As with the 50-50 demand, the number of stops, average delay, and average speed, split of Case 2 always outperformed those of Case 1 and Case 0, as shown in Tables 4 and 5. As the demand increased, the performance difference became greater and more obvious. In addition, in the 80-20 demand split, the performance of the three cases was greatly improved when compared to the 50-50 and 65-35 splits. The ramp traffic decreased and vehicles experienced less merging interactions, resulting in lower travel delays and smaller numbers of stops when compared to the more even demand splits.