# Analysis of Cascading Failures and Recovery in Freeway Network Under the Impact of Incidents
## 2 Literature Review
### Cascading Failure of Transportation Networks  
Due to the complexity of their internal topological structure, traffic networks have been proven to exhibit complex network characteristics [30; 31]. These structural properties make the system inherently vulnerable to localized disruptions. Road traffic incidents, which have increased significantly with the rapid expansion of freeway infrastructure [32; 33; 34], are not randomly distributed, but tend to cluster in specific spatial areas, exhibiting significant spatial dependence [35]. When components of the traffic network are damaged, the failure of nodes and edges can redistribute and amplify the traffic load to neighboring components. This process often triggers cascading failures that further propagate through the network, ultimately disrupting transportation functionality on a larger scale [36]. [PERSON] and [PERSON] et al. improved the cascading failure model to closely match real traffic conditions, illustrating the fault propagation process in traffic networks [2; 3]. [PERSON] et al. proposed a trust value model to assess road congestion, which was then used as a basis for reallocating the load of congested intersections [4]. [PERSON] et al. investigated cascading failures in dynamic urban rail transit networks under various passenger-flow fluctuation fault modes. Several studies have identified critical nodes or links and quantified influencing factors through the analysis of these cascading failures [5]. In addition, extreme weather significantly increases the probability of traffic incidents. [PERSON] et al. [37] and [PERSON] al. [38] conducted separate studies under extreme weather conditions, both revealing the spatiotemporal evolution patterns of cascading failures in transportation networks. [PERSON] et al. [39] further considered fluctuations in passenger demand and response delays, investigating the dynamic evolution of cascading failures in urban rail transit systems. However, existing research does not sufficiently address route choice behavior in traffic networks within the cascading failure framework, potentially leading to inaccurate assessments of traffic network performance. In the study of traffic network recovery strategies, some research focuses on reducing the extent of failure diffusion and mitigating the adverse effects of cascading failures once they occur. [PERSON] et al. proposed four mitigation strategies to promptly protect critical nodes during the propagation of cascading failures [40]. [PERSON] et al. used the method of protecting critical nodes to prevent the propagation of cascading failures [41]. The above strategies help to control and mitigate cascading failures, but do not restore the damaged network. With regard to the study of restoring damaged components and functions, [PERSON] et al. proposed a prioritized recovery method that focuses on restoring the functions of components with the most connections to isolated nodes [42]. [PERSON] et al. established a cascading failure model for multilayer networks and proposed a recovery strategy that considers the recovery probability of failure clusters [43]. In reality, during the process of cascading recovery, failures and recoveries may occur within the same time step. Components that have been restored may fail again at each time step until the network reaches a stable state. Additionally, the priority of component restoration also affects the efficiency of the recovery process. Currently, there is still a lack of research on the combination of dynamic load fluctuations and restoration sequences. While recent research has advanced the modeling of cascading failures in transportation networks, important gaps persist in understanding and evaluation. Most existing models do not adequately address the effects of dynamic load fluctuations and realistic traveler route choice on the propagation of failures. In addition, current evaluation methods often ignore how restoration sequences interact with changing network conditions.