## 4 Case Analysis
### Optimal Subsidy and Penalty Scheme  
Utilizing the previously established AMO model, the optimal incentives and penalty scheme were calculated to explore the effects of implementing the TRS and its comprehensive impact on society. Three scenarios were assumed: Scenario 1 represents the road network's initial state before the TRS's implementation. Scenario 2 involves selecting extremely congested roads for the implementation of the TRS. Scenario 3 builds upon Scenario 2 by implementing the TRS with the optimal incentives and penalty scheme.  
The optimal subsidy and penalty combination includes: \(u_{re\_car}=2.43\) yuan; \(u_{bus}=0.65\) yuan; \(u_{metro}=1.52\) yuan; \(u_{p+R}=7.56\) yuan; and \(f=67.55\) yuan. The income and travel cost calculations for the road transportation system under different scenarios are shown in Table 8. The composite indicator is calculated based on Eq 3. The results indicate  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Class** & **Age** & \(v_{e}\) & \(v_{I}\) & \(v_{t}\) \\ \hline Class 1 & (0, 35) & 1 & 6 & 5 \\ Class 2 & [35; 45)\textless{}[65; 95] & 2 & 18 & 15 \\ Class 3 & [45; 65] & 3 & 30 & 25 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Travel time value classification.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c c} \hline \hline
**Line 1** & **1** & **3** & **4** & **5** & **9** & **10** & **15** & **14** & **23** & **24** & **13** & **Line 2** & **2** & **6** & **8** & **16** & **17** & **19** & **20** & **21** \\ \hline
4 & 3 & 2 & 0 & 2 & 3 & 3 & 5 & 6 & 6 & 7 & 7 & 8 & 3 & 2 & 0 & 2 & 3 & 3 & 4 & 5 \\
5 & 3 & 2 & 2 & 0 & 2 & 3 & 4 & 5 & 6 & 6 & 7 & 16 & 4 & 3 & 2 & 0 & 2 & 2 & 3 & 4 \\
9 & 5 & 4 & 3 & 2 & 0 & 2 & 3 & 4 & 5 & 5 & 6 & 17 & 4 & 3 & 3 & 2 & 0 & 2 & 2 & 4 \\
10 & 5 & 4 & 3 & 3 & 2 & 0 & 2 & 4 & 5 & 5 & 6 & 19 & 5 & 4 & 3 & 2 & 2 & 0 & 2 & 3 \\
15 & 6 & 5 & 5 & 4 & 3 & 2 & 0 & 2 & 3 & 4 & 5 & 20 & 5 & 5 & 4 & 3 & 2 & 2 & 0 & 2 \\
14 & 7 & 6 & 6 & 5 & 4 & 4 & 2 & 0 & 2 & 2 & 3 & 21 & 6 & 6 & 5 & 4 & 4 & 3 & 2 & 0 \\
23 & 7 & 7 & 6 & 6 & 5 & 5 & 3 & 2 & 0 & 2 & 2 & & & & & & & & & & \\
24 & 8 & 7 & 7 & 6 & 5 & 5 & 4 & 2 & 2 & 0 & 2 & & & & & & & & & & \\
13 & 8 & 8 & 7 & 7 & 6 & 6 & 5 & 3 & 2 & 2 & 0 & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 7: The fare structure of metro lines (yuan).  
that compared to Scenario 1, in Scenarios 2 and 3, the income of the transportation system increased by 5.07% and 17.26%, respectively, while travel costs decreased by 0.83% and 2.67%. This demonstrates the effectiveness of the TRS in encouraging residents to shift to public transportation, thereby increasing revenue, reducing residents' travel costs, and alleviating road congestion.  
The study investigates the impact of introducing incentives and penalty mechanisms on the road transportation system. Compared to Scenario 2, Scenario 3 showed an 11.60% increase in system income and a 1.85% decrease in travel costs, indicating a more positive impact by introducing incentives and penalty mechanisms. Specifically, the core idea of the TRS is to manage the spatial-temporal rights of vehicles, regulate residents' departure times and travel modes, and balance the supply and demand of the road network, ultimately easing traffic congestion. Although introducing incentives and penalty mechanisms in Scenario 3 led to a 3.17% decrease in public transport income, there was a 2.51% increase in parking revenue. This suggests that more travelers shifted to the \"P + R\" travel mode despite certain subsidy costs, yet overall revenue slightly increased. Moreover, simulation results show that, despite facing high penalties, some travelers still chose to violate reserved roads to save travel time, indicating that reliance solely on monetary penalties is insufficient to ensure the effective operation of the reserved mode. Therefore, additional punitive measures, such as deducting driving points, are necessary to increase the cost of non-compliance and ensure the long-term effectiveness of the strategy.