# Freeway Traffic Congestion Reduction and Environment Regulation via Model Predictive Control
## 6 Simulation Research
### Simulation Results
#### 6.2.4 Discussion about Traffic Conditions  
Then we will explore the effect of traffic variables, including average flow, density and speed, with three control methods in this paper. Since an on-ramp located in segment 2, bottleneck often occurs in that area, so we mainly analysis the variation of traffic variables on segment 2 (see Figure 12). Generally, MPC_SOO and MPC_CPDMO-NSGA-II perform better. They improve the situation of low efficiency resulted from fixed speed limit, proved by greatly enhanced flow and speed. From 1 h to 1.5 h, the density of segment 2 decreases a lot. It can be seen from Figure 12 that the results of MPC_CPDMO-NSGA-II algorithm and MPC_SOO method are too similar, therefore the results of traffic conditions on segment 1, 2, 3 are discussed in Table 4. It can be concluded from Table 4 that compared to fixed speed limit strategy, the results of traffic conditions perform better under the MPC_SOO method and MPC_CPDMO-NSGA-II algorithm. For example, in the aspect of traffic flow, the average flow on segment 2 is increased by 7.4% and 7.9% respectively under the MPC_SOO method and MPC_CPDMO-NSGA-II algorithm compared with the fixed speed limit strategy, in the aspect of average density, it is decreased by 40.6% and 40.7% respectively on segment 2 under the MPC_SOO method and MPC_CPDMO-NSGA-II algorithm compared with the fixed speed limit strategy, in the aspect of average speed, it is increased by 14.0% and 14.2% respectively on segment 3 under the MPC_SOO method and MPC_CPDMO-NSGA-II algorithm compared with the fixed speed limit strategy. Figure 13 displays the queue lengths of the on-ramp and its upstream mainline with three control methods. It can be seen from Figure 13 that in the period of high demand of the on-ramp, the RM adopted in MPC_SOO greatly reduces the queue length, and shortens time of severe congestion. It should be noted that the queue is formed naturally with fixed speed limit, while may be resulted actively by traffic lights with other two methods. Thus, in MPC_SOO, there are slight vehicles wating in the on-ramp after 1 h, indicating that it may put efficiency of the mainline first. However, the heavy congestion the on-ramp disappears by using MPC_CPDMO-NSGA-II, with a peak valued 11. Afterwards, there is almost no waiting vehicle of the on-ramp. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Indictors** & **TTS (h)** & **TTD (km)** & **TE (kg)** & **TF (0)** \\ \hline
**Fixed speed limit** & 554.217 & 29,228.58 & 99.554 & 5493.556 \\
**MPC\_SOO** & 465.8766(\(-\)15.9\%) & 30,564.134.6\% & 38.687(\(-\)61.1\%) & 1775.608(\(-\)67.7\%) \\
**MPC\_CPDMO-NSGA-II** & 459.8024(\(-\)17\%) & 30,653.244.9\% & 38.576(\(-\)61.3\%) & 1767.215(\(-\)67.8\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The performance of the freeway with three control methods. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Traffic Conditions**} & \multicolumn{2}{c}{**Methods**} & \multirow{2}{*}{**Fixed Speed Limit**} & \multirow{2}{*}{**MPC\_SOO**} & \multirow{2}{*}{**MPC\_CPDMO-NSGA-II**} \\ \cline{3-3} \cline{5-5}  & Segment 1 & 3942.02 & 4124.114.6\% & 4121.854.6\% \\
**(veh/h)** & Segment 2 & 4360.05 & 4682.847.4\% & 4704.817.9\% \\  & Segment 3 & 4489.31 & 4652.833.6\% & 4670.684.0\% \\ \hline \multirow{2}{*}{**Density**} & Segment 1 & 31.55 & 18.73(\(-\)40.6\%) & 18.72(\(-\)40.7\%) \\
**(veh/km/lane)** & Segment 2 & 24.70 & 22.56(\(-\)8.7\%) & 22.62(\(-\)8.4\%) \\  & Segment 3 & 23.60 & 21.35(\(-\)9.5\%) & 21.40(\(-\)9.3\%) \\ \hline \multirow{2}{*}{**Speed**} & Segment 1 & 52.37 & 73.4940.3\% & 73.5240.4\% \\ \cline{1-1}  & Segment 2 & 60.07 & 69.5515.8\% & 69.6315.9\% \\ \cline{1-1} \cline{2-5}  & Segment 3 & 63.67 & 72.6214.0\% & 72.7014.2\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The results of traffic conditions on segment 1, 2, 3 using three control methods. Figure 12: The traffic conditions of segment 2 using three control methods.