# Analysis of Cascading Failures and Recovery in Freeway Network Under the Impact of Incidents
## 4 Case Study
### Recovery of Cascading Failure  
During the network recovery process, determining an effective restoration sequence is essential, and should be guided by the relative significance of individual edges. Metrics such as edge betweenness and link load have been extensively applied in prior research to evaluate the impact of nodes within network structures. For comparative analysis, several sequential recovery strategies were evaluated, each based on a distinct metric among four selected indicators. (1) High-Edge Betweenness-Based Strategy (HBS): In the residual freeway network following cascading failures, this recovery strategy selects the top \(m\) edges with the highest betweenness centrality from the candidate set, ordered in descending magnitude. (2) High-Load-Based Strategy (HLS): This recovery sequence consists of the top \(m\) edges with the highest traffic demand, selected from the candidate set and ordered in descending demand. (3) Random Strategy (RS): Edges are randomly selected to form the recovery sequence. (4) Critical-Edges Strategy (CES): This recovery strategy is based on critical-edge prioritization.  
The recovery outcomes using the importance-based strategy demonstrate notable effectiveness compared to the other methods, as shown in Figure 9. In the assessment, the importance-based recovery strategy consistently outperforms the alternatives--the random, betweenness centrality, and degree centrality strategies. This approach strategically prioritizes the restoration of network components based on their criticality, thereby  
Figure 8: Results of cascading failure evolution. (**a**) SCC; (**b**) NR; (**c**) EFF; (**d**) CR.  
ensuring a more targeted and efficient recovery process. By focusing on vital nodes and edges first, the importance-based strategy minimizes the overall downtime and enhances the network's resilience. The empirical results indicate that this method not only accelerates recovery times, but also significantly reduces the impact of cascading failures, making it a superior choice for managing complex network disruptions. When using the HLS and CES, the results for network connectivity recovery are improved, as demonstrated in Figure 9a. The recovery of network efficiency and connectivity reliability is better under the CES, as shown in Figure 9c,d.  
In examining the results of cascading failures, we observe the impact of different attack strategies, initial loads, and capacity models on network stability. Under different attack strategies, targeted attacks on critical road segments often lead to more severe failures, highlighting the network's vulnerability, whereas random attacks demonstrate the network's resilience to random incidents. Variations in initial loads also significantly affect the results of cascading failures; higher initial loads lead to more frequent cascading failures, indicating the network's fragility under high-load conditions. Regarding different capacity models, increasing the capacity of road segments can alleviate cascading failures to some extent, but excessive capacity settings may result in resource wastage and other potential issues. Therefore, reasonable capacity allocation is crucial for enhancing network stability. These results indicate that in traffic network design and management, it is essential to  
Figure 9: Results of cascading failure recovery. (**a**) SCC; (**b**) NR; (**c**) EFF; (**d**) CR.  
comprehensively consider attack strategies, initial loads, and capacity models to improve overall risk resistance.