As a critical infrastructure in modern cities, the functionality of the transportation network directly impacts economic development, social activities, and emergency response capabilities. With the acceleration of urbanization and increased transportation demand, the frequency of traffic accidents and congestion is rising. Particularly in the face of emergencies and human disruptions, For example, Houston was hit by Hurricane "Rita", several major roads out of the city were congested for hundreds of kilometers, and Beijing was paralyzed by heavy rain caused by a large area of traffic, the robustness of the transportation network largely determines its overall performance. Therefore, evaluating and enhancing the robustness of the transportation network is of significant research importance for urban traffic management.

(Jie & Qizhou, 2007) researched the system's anti-destruction reliability in urban rail transit. They conducted a comprehensive evaluation of urban rail transit network topology and passenger flow distribution, providing a significant theoretical basis for improving the structure of urban rail transit. (Yi & Chao, 2009) investigated the complex network characteristics of Shanghai's rail transit using network features such as degree and clustering coefficient. (Houli et al., 2010) proposed a network robustness analysis method based on a bipartite graph model, studying the robustness differences between Beijing's bus network and random networks under various attack conditions.(Peng et al., 2013)researched the robustness of Beijing's urban rail transit network under different weights, calculating and optimizing the robustness by weighting different traffic nodes. (Fan, 2016) studied the anti-destruction capabilities of rail transit networks based on their topological characteristics and identified key nodes for city management. (Haiping, 2016) examined Wuhan's public transportation network using node degree and clustering coefficient, finding that nodes with high degree values and clustering coefficients have excellent connectivity, though they are not necessarily the busiest in actual bus routes. Based on this, relevant recommendations were proposed to address traffic congestion issues.

In recent years, (Ruimin & Jinli, 2018) researched the robustness of Shanghai's bus network and found that random attacks are more robust than deliberate attacks. (Hieu et al., 2019) studied the robustness of Vietnam's road network using topological metrics such as average path length and global efficiency, considering both random and deliberate attacks. (Tiangang et al., 2019) established a multimodal transport network topology based on complex network principles, comparing network characteristics through network feature metrics. (Kun et al., 2022) built an enhanced network to study the robustness of Nanjing's bus-rail mixed network, finding that initial node capacity has a significant impact on cascading failures. (Jie & Xinyu, 2024) considers the impact of geological hazards, evaluates the robustness of the network in terms of structure and performance, and identifies key road sections.(Lei & Shubin, 2024) Combined with the accessibility index of subway stations, the node importance evaluation system of the rail transit network was constructed, and the robustness of Hangzhou metro network was studied by taking the global efficiency of the network and the maximum connectivity subgraph as the evaluation indexes. From the perspective of the current research status at home and abroad, the robustness of the complex transportation network is mainly focused on the bus network and rail transit network, while the research on the urban road traffic network is rare. In terms of robustness research methods, most of the studies focus on the robustness of the road network after removing the failed nodes through the analysis of network topological characteristics, and the traffic flow evaluation index is rarely used. In addition, the real road traffic flow analysis cascade failure process is not used in the analysis process, and the research lacks a certain degree of authenticity.

This paper first introduces the use of the existing topology index and traffic flow index to evaluate the traffic network and explains the mechanism of the cascading failure model adopted in this paper. The real urban traffic network model is built through online traffic data, and the robustness of the urban transportation network is studied by using two attack methods: random attack and deliberate attack.

Based on the traffic network cascading failure model, this study investigates the robustness of urban road networks using two attack strategies: deliberate attacks based on segment traffic flow and random attacks. The analysis employs functional indicators such as total travel time, the relative size of the largest connected subgraph, and global network efficiency. The study uses the urban road traffic network within the second ring road of Hefei as a case example.

According toFigure 4a and Figure 4b, under the same number of attacks, the Hefei urban road network experiences a more significant decline in functionality under deliberate attacks based on edge traffic flow compared to random attacks. Particularly, after approximately 10 key segments are deliberately attacked, the network functionality shows a noticeable decline, whereas random attacks result in a relatively constant rate of functionality decrease. As the number of attacks increases, the gap between the two attack strategies gradually narrows, at which point network functionality is mainly influenced by node connectivity.

According toFigure 4c, when using traffic flow indicators, deliberate attacks lead to a more significant decline in network functionality compared to random attacks, and the declining trends for both are essentially consistent. This is because traffic flow indicators measure vehicle travel time. After deliberate attacks destroy key segments, traffic is redirected to other adjacent segments, increasing overall traffic flow and travel time.

By analyzing traffic flow distribution during peak hours, the Hefei urban road network was constructed and simulated. Under two different road network attack strategies, the maximum connectivity subgraph, global network efficiency and total system travel time were used as evaluation indicators, the random attack strategy causes relatively less damage to the network, indicating that the Hefei road network has strong robustness against random sudden events. However, under the deliberate attack strategy based on segment traffic flow, there is a sharp decline in network functionality, showing that the Hefei road network has weaker robustness against deliberate attacks. After attacking the top 4% of the most trafficked segments, there is a rapid decline in network efficiency. Segments with higher traffic have a greater impact on network robustness. According to the results, the topology index with the maximum connectivity subgraph and global network efficiency can better reflect the stepwise decline of the traffic network function after multiple attacks, while the traffic flow index with the total travel time does not reflect this characteristic.

During the road planning and design phase, it is advisable to increase the road capacity of segments with high anticipated traffic and their adjacent segments. In the traffic management phase, when high-traffic segments fail, it is important to quickly redirect vehicles while strictly controlling the number and nodes of redirected vehicles to prevent large-scale cascading failures.

In the future research on the robustness of the transportation network, the network modeling of the road sections that often occur in the actual city can be carried out, and the traffic distribution during the morning and evening peak hours can be simulated, so as to strengthen the traffic capacity of the congested road sections to improve the robustness.

The abstract of this paper was presented at the Resilient and Responsible Architecture and Urbanism (RRAU) Conference—6th Edition, which was held on the 8^th – 10^th of December 2024.