# Analysis of Cascading Failures and Recovery in Freeway Network Under the Impact of Incidents
## 5 Conclusions  
This study addressed the vulnerability and low recovery efficiency of freeway networks under the scenario of cascading failures by proposing and validating a systematic solution. Specifically, an improved edge-based CML model was developed to realistically simulate cascading failure phenomena in transportation networks, thereby overcoming the limitations of traditional models that insufficiently capture real-world operational characteristics. The primary contributions of this study are summarized as follows: (1) To simulate cascading failure phenomena in transportation networks, we developed an edge-based model that incorporates the operational characteristics of real-world traffic systems, and conducted simulations on a specific freeway network to capture the cascading failure process. (2) We propose a method to identify and rank important edges within the network. By evaluating the relative importance of edges, this method identifies critical edge combinations and determines an optimal recovery sequence to enhance network performance during the restoration process. (3) A recovery strategy was developed based on the identification of critical edges, taking into account the possibility of cascading failures occurring during the restoration process. The simulation results verify the effectiveness of the proposed scheme in enhancing the performance of the network against disruptions and accelerating system recovery. These findings provide a theoretical foundation and technical support for risk prevention, control, and emergency management in real-world transportation networks.  
Directions for further research on cascading failure and recovery models include improving existing models and expanding their application scope. Future research can also investigate cascading failure phenomena under more complex traffic operating conditions and gradually incorporate more realistic mechanisms, such as edge recovery and probabilistic failures. Additionally, we will consider conducting further tests using datasets from different regions and time periods to more comprehensively validate the robustness and applicability of the proposed method. Finally, we aim to consider the trade-off between network efficiency and functionality by establishing a comprehensive network quantification index system to evaluate various traffic recovery strategies, thereby enhancing the overall resilience and operational efficiency of the network following incidents.  
Conceptualization, X.Z.; methodology, X.Z. and S.Z.; software, X.Z.; validation, S.Z. and W.L.; resources, J.T.; writing--original draft, X.Z.; writing--review and editing, S.Z., W.L., and J.T.; project administration, J.T. All authors have read and agreed to the published version of the manuscript.  
This research was funded in part by the Key R&D Program of Hunan Province (No. 2023 GK2014), the National Natural Science Foundation of China (No. 52172310), the Science Research Foundation of Hunan Provincial Department of Education (No. 22B0010), the Natural Science Foundation of Hunan Province (No. 2022 JJ30763), and the Central South University Graduate Student Independent Exploration and Innovation Project (No. 2023 ZZTS0340).  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.