Objective: The development of modern urban agglomerations requires cultivating integrated transportation networks, advancing transportation integration, and building resilient, comprehensive three-dimensional systems. Building a highly efficient and stable transportation network is fundamental to promoting the growth of modern metropolitan areas. Methods: This paper focuses on the metropolitan area multimodal transportation network (MA-MTN) and uses complex network methodologies to model different transportation network construction processes. By applying a load capacity model, it defines the load and capacity levels of the MA-MTN and develops a load redistribution model to facilitate network operations; then, different dimensions of network resilience evaluation indicators were developed, focusing on three levels: overall network, network structure, and network function. From an integrated perspective, a comprehensive resilience indicator for multimodal transportation networks in urban agglomerations was established. The Xi'an metropolitan area was selected as the research subject to conduct simulation analyses of the multimodal transportation network's integrated resilience. The sensitivity levels of different traffic subnetworks in the multimodal transportation network of the metropolitan area were assessed through scenario simulation methods. Simulations examined the performance loss stage, the recovery stage following the implementation of recovery strategies, and the dynamic recovery stage during network failures caused by attacks on the multimodal transportation network. The effectiveness of strategies aimed at improving the integrated resilience of the metropolitan multimodal transportation network was also compared and analyzed. Results: The research results indicated that different transportation subnets play distinct roles in the multimodal transportation network of urban agglomerations. When MA-MTN is attacked, the sharpest decline in network performance occurs before the failure rate of network nodes reaches 60%. The node capacity adjustment parameter β in MA-MTN needs to be dynamically calibrated, with a value of 0.2 recommended for daily operations and 0.7 during extreme weather events or holiday peaks. Enhancing the resilience of urban multimodal transportation networks requires prioritizing transportation efficiency factors in the transfer of passenger flow transfer between nodes; this approach improves the comprehensiveness of the network resilience. Recovery strategies based on node load capacity levels are the most effective in improving the integrated resilience level of these networks. Such strategies enhance resistance to attacks and significantly improve recovery capabilities during cascading failures, ensuring robust network performance even under dynamic recovery conditions. Conclusions: This paper measures the integrated resilience level of transportation networks against external disturbances using a multidimensional integrated perspective; moreover, it identifies effective strategies to improve the structural and functional resilience of multimodal transportation networks in urban areas. Based on the research results, this study emphasizes the importance of determining critical thresholds for network node failures. It recommends dynamically adjusting the node capacity parameter β according to the operational conditions of the MA-MTN and external factors. Furthermore, it advocates optimizing the transfer process of node passenger flow load by prioritizing transportation efficiency during network operations. The study also highlights the significance of prioritizing node load capacity and developing effective recovery strategies based on the comprehensive importance of nodes. These approaches are crucial for promoting the construction of efficient, stable, and multimodal transportation networks in urban areas.

Objective: The metro system, as a crucial component of modern urban transportation, relies heavily on the reliability of its traction power network to maintain stable operations. However, existing research on metro system resilience assessment often overlooks the complex coupling characteristics between the traction power network and the metro network. In particular, the many-to-one and one-to-many coupling characteristics of the traction power network significantly influence metro system resilience but remain underexplored. This study proposes a resilience assessment method for metro networks based on the network coupling characteristics, focusing on quantitatively evaluating the dynamic impact of traction power network failures on metro network operational performance under both partial and complete failure scenarios. Methods: This research constructs separate models for the traction power network and the metro network. Building on these foundational models, it incorporates the many-to-one and one-to-many power supply characteristics of the traction power network, establishing a coupling model that integrates both systems. Network efficiency, which considers passenger flow weighting and travel time impedance, forms the basis for assessing resilience. The Monte Carlo method is used to model the recovery process of the metro traction power network. Using the Xi'an metro network as a case study, different failure scenarios are simulated, enabling a comprehensive evaluation of the metro system's service capacity and resilience changes under various fault conditions. Results: The results of this study are as follows: (1) The many-to-one redundancy characteristic of the traction power network enhances metro network resilience by 6.8%-14.4%. However, ignoring the one-to-many characteristics of the traction power network may lead to an overestimation of resilience, as cascading failure effects are inadequately accounted for. (2) Traction power network failures in high passenger flow areas can cause efficiency losses of up to 50.2%, with corresponding resilience losses reaching 36.1%. (3) Resilience performance varies across metro stations and the overall network depending on the complexity of failure scenarios. More complex scenarios involve a greater number and broader distribution of repair targets, increasing the intricacy and time demand of recovery processes. Conclusions: The proposed metro network resilience assessment method based on network coupling characteristics provides a more accurate evaluation of the impact of traction power network failures. By accounting for both many-to-one and one-to-many coupling characteristics, the method realistically reflects the redundancy supply effect of the system and the cascading failure process. The study emphasizes that while adopting a decentralized layout, metro system operation and planning need to strengthen the redundancy design of traction substations and supply section networks. Furthermore, a coordinated emergency response across multiple departments is recommended to ensure rapid mobilization of repair resources and shuttle capacity, minimizing disruptions to passenger travel during emergencies. The findings of this study provide theoretical guidance for developing emergency response and recovery strategies in metro systems under power facility failure scenarios. Future research will expand the resilience assessment framework to multi-modal transportation systems, further improving the universality and practicality of the model.

[Objective] The resilience of transportation networks is a prominent research area in transportation safety. However, current studies on transportation network resilience often inadequately measure the changes in spatiotemporal travel costs for passengers, primarily focusing on the recovery phase rather than the resistance phase in two-stage resilience. There is also insufficient identification and analysis of critical segments, and a lack of suitable resilience simulation and evaluation methods for urban agglomeration railway passenger transport networks. This paper proposes a resistance resilience assessment model and a resistance resilience simulation evaluation process for urban agglomeration railway passenger transport networks centered on spatiotemporal accessibility for passengers. The aim is to evaluate the resistance resilience of these networks and identify critical segments. [Methods] This paper explores the concepts of resistance resilience and recovery resilience within transportation networks. Utilizing the complex network Space L modeling method, this paper develops a spatiotemporal weighted urban agglomeration railway passenger transport network model that considers actual railway passenger stations as network nodes. Segment interruption scenarios were simulated using attack modes involving single segment deletion and multiple segment continuous deletion. A dynamic resistance resilience evaluation index termed the network performance retention rate, was introduced based on the performance response function and spatiotemporal accessibility of passengers. This paper devises a resistance resilience assessment model and simulation evaluation process to evaluate the substitutability of segments and the overall network resistance resilience. The Chengdu—Chongqing urban agglomeration was selected as a case study to identify and compare critical segments and resistance resilience across unweighted, spatially weighted, and temporally weighted railway networks. [Results] The results of this paper were as follows: (1) The interruption of critical segments near railway hub cities could lead to a maximum network performance loss of 12.23%. It was necessary to identify critical segments through predisaster simulations. (2) Significant differences were found in the critical segments identified through resistance resilience simulations across unweighted, spatially weighted, and temporally weighted railway networks. The Spearman correlation coefficient indicated a relatively poor correlation between the critical segment rankings of unweighted and weighted railway networks. (3) The resistance resilience indices of the three railway networks highlighted that single segment interruptions significantly affected travel time. (4) Continuous interruption of identified critical segments severely affected network performance, with temporally weighted railway networks experiencing a stronger impact than spatially weighted and unweighted railway networks. Predisaster simulations solely based on topological structure or spatial distance might underestimate the consequences of risk interference. [Conclusions] The methods proposed in this paper address the gap in targeted research on the resistance resilience of railway passenger transport networks in urban agglomerations. Simulations of single segment interruption and multiple segment continuous interruption enable the identification and verification of key network segments. Additionally, analyzing the network resistance to interruptions provides a scientific foundation for transportation network planning and decision-making. Furthermore, analyzing the network's resilience evaluation index of the network performance retention rate proposed in this paper offsets the impact of disturbance time uncertainty, providing a scientific foundation for transportation network resilience research.

[Objective] Despite unbalanced large passenger flows, urban rail transit network (URTN) frequently encounter the dual pressures of structural and functional resistance. This can result in cascade failure, potentially leading to partial or even total collapse of the URTN. To ensure the normal operation of these networks and understand the characteristics of their disaster resistance evolution, this study explores how an unbalanced large passenger flow affects the disaster resistance of URTN. [Methods] This study initially examines the effect of unbalanced large passenger flows on the URTN cascade failure from two perspectives: transport efficiency and passenger service. Subsequently, a passenger-flow weighting network is constructed to calculate the passenger-flow intensity. Herein, the weights of different nodes represent the proportion of the passenger flow per unit of time at different track stations during periods of unbalanced large passenger flows. This allows the measurement of a track station's importance level based on node number, node betweenness, and passenger flow intensity. Moreover, this study adapts the coupled map lattice (CML) model, building upon cascade failure theory and chaos dynamics, to obtain more accurate values for the failure node ratio and network strength entropy. In the modified CML model, the sudden disturbance level is defined according to the breakdown degree and influence range. The initial state value is determined by the saturation degree of the passenger flow at the track station, thus addressing the sensitive dependence of the spatiotemporal chaotic system on the initial state value. Subsequently, the dynamic evolution characteristics of the URTN structural and functional resilience levels are explored under different conditions of fault propagation and passenger flow strength. These analyses were based on failure node ratio and network strength entropy metrics. Finally, a case study was conducted using the Xi'an subway as an example. [Results] The results showed the following: (1) During a URTN cascade failure, the disaster resistance evolution trends of structure and function aligned, changed, and failed simultaneously. (2) Critical values existed for the inter-station coupling coefficient ε and sudden event disturbance R, which were ε=0.3 and R=1, respectively. Below these thresholds, the URTN cascade failure effect did not occur. However, when ε＞0.3 and R＞1, the failure time of the URTN's structural and functional disaster resistance decreased as ε and R increased. (3) The intensity of the passenger flow negatively affected the structural and functional resilience of the URTN. When disturbed, stations with high passenger flow intensity were more likely to trigger a URTN cascade failure. (4) Stations with large interconnectors and high passenger flow intensity exhibited lower structural and functional vulnerability after a sudden disturbance than stations with larger degrees. [Conclusions] This study has important theoretical and practical implications. Theoretically, it helps uncover the factors affecting cascade failure and the evolution characteristics of the URTN's disaster resistance under the impact of an unbalanced large passenger flows. In practice, this study provides a crucial foundation for decision-making regarding the enhancement of safety management in rail transit when faced with challenges posed by unbalanced large passenger flows.

[Objective] Seismic damage and destruction of the stations, tunnels, and other structures considerably impair the functionality of the urban rail transit system. Current research on the system performance of the rail transit network primarily focuses on the scenarios of intentional attack and stochastic damage, which is dramatically different from the earthquake disaster scenarios. This paper proposed a quantitative framework to evaluate the seismic performance and resilience of rail transit networks. [Methods] The seismic fragility model was used to calculate the failure probability of the primary structural elements, including stations, tunnels, and bridges of the rail transit system. The graphical model of the network was established using the Space L modeling method. This approach was used to depict the interdependency of system elements. The network performance was expressed by the network efficiency weighted by passenger flow between rail transit stations. The Monte Carlo simulation was used to assess the uncertainty of the earthquake damage state of structures and the post-earthquake recovery of the damaged elements. According to the network performance curves during the post-earthquake recovery process, the seismic resilience index and resilience loss of the rail transit network were quantitatively evaluated using the concept of resilience triangle. Considering the Beijing rail transit network, the effects of earthquake intensity, recovery strategy on network performance, and resilience indexes were investigated. [Results] The results of the present analysis were as follows. (1) The resilience characteristics of rail transit networks under earthquakes, intentional attacks, and stochastic damage were different. The resilience index under earthquake damage was 0.936 3, whereas the resilience index under stochastic damage was 0.934 0. The resilience index under intentional attack was 0.863 4. (2) In the damage scenario corresponding to different earthquake intensities, the system resilience index calculated by the recovery sequence sorted by the dynamic importance of damaged elements were larger than that sorted by the static importance of damaged elements. Moreover, the damage scenario involving several damaged elements typically results in a larger difference between the resilience index calculated by the two recovery strategies. (3) Pre-earthquake enhancement measures to reduce the failure probability of crucial elements could effectively enhance the disaster resistance capacity of the network; however, their influence on improving the post-earthquake recovery capacity remained unclear. [Conclusions] Based on the seismic fragility models of the primary structure of the rail transit network, the graphical model of the network, and the importance of ranking-based post-earthquake recovery of the damaged elements, this paper establishes a framework to quantitatively evaluate the seismic resilience of rail transit network by the passenger-weighted network efficiency. When evaluating network resilience and comparing antiseismic improvement measures, multiple indicators such as resilience index, resilience loss, and recovery duration should be comprehensively analyzed. This framework can provide a reference for the seismic performance evaluation of the urban rail transit network and help decision-makers in allocating maintenance resources to restore the operation function of the urban rail transit system in a timely and cost-effective manner during the recovery process.

The resilience of multimodal transportation networks in urban agglomerations to attacks was analyzed using a network structural resilience assessment model based on complex network theory and resilient city theory which considered the absorbing capacity, buffering ability and recovery ability of the networks. The network resilience was calculated by a space vector modulus. Data for road and railway passenger transport between cities in the Guanzhong Plain urban agglomeration (GZP agglomeration) was used to construct the regional transportation network. The topological characteristics of the multimodal transportation network were then analyzed using the ArcGis and Ucinet tools. Each node's geographical location and transport connections with the surrounding area were used to identify key nodes based on the node importance. Analyses of the effects of attacks on these key nodes in the multimodal transportation network showed that the network had poor buffering ability, especially after failure of the Caijiapo station when the buffer value decreased to 0.388 9. The system had very weak ability to return to the normal state after a site with a large node degree failed. Failures of the general railway station and the high-speed rail station had far greater impacts on the structural resilience than failure of the highway terminals. Analysis of the characteristics of the key nodes led to suggestions for improving the network structure resilience.

The resilience of the urban public transport systems was evaluated using a system function curve model to quantify the urban public transport system resilience. The model included the bus and taxi systems with the bus service rate and the taxi online rate used as the system function to evaluate the urban public transport system resilience. This method was then used to evaluate the resilience of the public transport system during the Zhengzhou storm and flooding in 2021. The results show that the Zhengzhou public transport system is moderately resilient and various recovery schemes could affect the recovery capacity and adaptability of the system. The model describes the system functions in stages from the initial disturbance to a new equilibrium state to calculate the urban public transport system resilience. This method is suitable for single disasters and multiple, coupled disasters and can provide guidance for improving the ability of urban public transport systems to deal with unknown disruptions.