## 4 Case Analysis
### Traffic Network State Analysis  
Figure 4 presents heat maps of the saturation of each road in different scenarios. As shown in Figure 4a, in Scenario 1, roads 17, 22, 36, 39, 55, 58, and 76 all had average saturation levels exceeding 0.8, indicating significant traffic pressure and severe congestion, especially on road 55, where the average saturation level reached 1.53, marking it as an area of extreme congestion. Therefore, the implementation of the TRS was considered for these roads. Figure 4b,c show that after introducing the TRS, the saturation levels in the roads above were alleviated, and areas of extreme congestion throughout the network were significantly reduced. It is crucial to recognize that due to severe imbalances in the spatial distribution of traffic flows during peak hours, primary commuting corridors shoulder most of the commuting demand, leaving surrounding road resources underutilized. Thus, post-implementation, saturation in major commuting corridors decreased, while that in secondary roads increased (e.g., roads 6, 62, and 63), indicating the strategy's ability to alleviate congestion in primary corridors and enhance the utilization of secondary roads. This further validates the strategy's efficacy in enhancing network traffic flow equilibrium. \begin{table}
\begin{tabular}{l c c c} \hline  & **Scenario 1** & **Scenario 2** & **Scenario 3** \\ \hline
**Transportation system revenue (yuan)** & 126,924 & 133,356 & 148,829 \\ Public transport revenue & 78,214 & 85,106 & 82,410 \\ Parking revenue & 48,710 & 48,250 & 49,460 \\ Fine & — & — & 36,079 \\ Subsidy & — & — & 19,120 \\
**Travel costs (yuan)** & 6,076,896 & 6,026,463 & 5,914,846 \\
**Composite indicator** & \(-\)3,595,368 & \(-\)3,562,536 & \(-\)3,486,785 \\ \hline \end{tabular}
\end{table} 
Table 8: Revenue and cost calculation results of road transportation systems under different scenarios. Additionally, in Scenario 2, peak congestion in the reserved roads remained concentrated between 07:10 and 08:10. At other times, the saturation levels were lower, indicating underutilization of road resources and unclaimed reservation slots during certain time windows. Thus, in Scenario 3, introducing the incentives mechanism led to adjusting travel demand, effectively \"smoothing out\" peak periods and improving resource utilization during off-peak times. Closer observation revealed that in Scenario 3, the saturation levels in the reserved roads reached an ideal state during almost every time window. This indicates that the incentive mechanism enhanced travelers' willingness to adjust their travel times, leading to the full utilization of reservation slots. Travelers enjoyed the convenience of private vehicle travel while experiencing the efficiency of the reserved mode, effectively enhancing the utilization of road resources and overall traffic efficiency. Table 9 provides a detailed comparative analysis of the traffic network performance under various scenarios, illustrating the impact of the TRS on network efficiency. The results highlight the effectiveness of TRS in enhancing the overall traffic conditions, improving the average speed by 6.7%, reducing road saturation by 9.3%, and decreasing network traffic volume by 3.7%. In Scenario 3, a significant observation is the 4.74% increase in network traffic flow compared to Scenario 2. This rise is attributed to the constraints imposed by the reservation system. Some travelers, unable to find available slots in their desired time windows, were compelled to modify their travel plans. The introduction of incentives and penalties nudged travelers to adjust their travel times rather than switch modes. While potentially counterintuitive, this slight increase in traffic volume reduced opposition to the new policy, enhancing the strategy's sustainability. Additionally, Scenario 3 showed a 2.37% increase in overall network saturation and a 17.73% rise in saturation on reserved roads compared to Scenario 2.