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The purpose of this paper is to attempt to realize the optimization of cascading failure process of urban transit network based on Load‐Capacity model, for better evaluating and improving the operation of transit network.

Robustness is an essential index of stability performance for urban transit systems. In this paper, firstly, the static robustness of transit networks is analyzed based on the complex networks theory. Aiming at random and intentional attack, a concrete algorithm process is proposed on the basis of Dijstra algorithm. Then, the dynamic robustness of the networks, namely cascading failure, is analyzed, and the algorithm process is presented based on the Load‐Capacity model. Finally, the space‐of‐stations is adopted to build the network topology of Foshan transit network, and then the simulation analyses of static and dynamic robustness are realized.

Results show that transit network is robust to random attack when considering static robustness, but somewhat vulnerable to intentional attack. For dynamic robustness analysis, a large‐scale cascade of transit network may be triggered when the tolerance parameter α is less than a value, so that the robustness of transit network can be improved through some reasonable measures.

The results of this study provide useful information for urban transit network robustness optimization.

An effective method for analyzing the static and dynamic robustness of transit network is provided in this paper.

By aiming at defending cascade failures effectively, the purpose of this paper is to present a strategy of inserting modular topologies into urban road network through reducing the burdens of critical components with too much traffic flow.

Each module is considered as a small-world random network, which is inserted into the initial Barabási-Albert scale-free network. Based on the user-equilibrium assignment, the strategy searches for remote nodes with low betweeness and flow in the network, and sets these nodes to be connected with the modular topologies. In this sense, the inserted modules are supposed to attach to the nodes with lower intensity of shorter path, and avoid bringing more impact to the nodes with higher betweeness and traffic flow. By using efficiency as the measurement of cascading failures, the performance of the networks generated through the strategy is tested.

The results show that the performance of the strategy is sensitive to the average degree of the inserted modular, and the modular size with a better effect on reducing the size of cascading failures or delaying the time of breakdown, while the other factors (e.g. the rewired probability) present few differences among various values. Meanwhile, it is found that the importance-based attachment mechanism has a better effect on preventing the cascading failures, especially delaying the step time of the larger reduction.

The strategy aims at alleviating the burdens in critical components to prevent the cascading failures of the network, and provides practical guidance on the decision of the urban road network evolving process.

An effective strategy for cascade defense in urban road network is proposed in this paper.

The purpose of this paper is to explore the evolving mechanism of urban roadway network. With the consideration of self-organization effect and planning effect during evolution, the authors try to demonstrate the impact of preferential attachment, module scale and module structure on the evolving network model.

The roadway network is built in the form of abstract network by dual approach. By using the evolving model of modular growth, the authors analyze the effects and mechanism of the evolving process. Then through numerical analysis, the impact of evolving effects on urban roadway network topology structure is discussed from the aspects of preferential attachment, module scale and module structure.

The module structure property, small-world property and scale-free property of roadway network can be affected with various degrees by the change of preferential attachment and module scale. However, the impact of module structure on network properties is small, which can be ignored. Therefore, in practice, the self-organization effect and planning effect of evolving network can be reached by changing the preferential attachment and module scale, so as to generate the network structure with specific properties.

Some local events, such as road extensions, road demolition and intersection rebuilding, exist during the evolving process under real-world situation. While those cases have not been considered in preferential attachment. Therefore, researchers are encouraged to take these factors into consideration in further research.

The paper has implications for practice in urban transportation planning and roadway constructions, which can help to guide the planning of urban roadway and to adjust or restore partial network when broken down according to the evolving law.

The impact of preferential attachment, module scale and module structure on the evolving network model is measured. And the relationship between different network properties can be used to build some patterns of network. From this point of view, the development of urban roadway network can be predicted and intervened.