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Metros (heavy rail transit systems) are integral parts of urban
transportation systems. Failures in their operations can have serious impacts
on urban mobility, and measuring their robustness is therefore critical.
Moreover, as physical networks, metros can be viewed as network topological
entities, and as such they possess measurable network prope...
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... the critical threshold f c is the first point at which the size of the largest connected component is one (i.e., the network is completely disintegrated). Figure 2 exemplifies the determination of the critical thresholds from the robustness curve in Tokyo metro network with 62 nodes. Computing the size of the largest connected component for removed nodes from 1 to 62 results in a robustness curve. ...
Citations
... Háznagy et al. (2015) identified similarities and differences within the urban public transportation systems of five Hungarian cities using CNT by comparing their network descriptors. Wang et al. (2015) quantified the robustness of metro networks subjected to random failures and targeted attacks. In the most recent literature, work tended toward more complete safety assessment models of resilience, including measuring network robustness and identifying effective recovery strategies (Ayyub 2015). ...
... Recently, many studies have used complex network theory to study city metro networks, including their topological properties [2][3][4][5][6], vulnerability [7,8], resilience [8][9][10] and robustness [6,9,11,12]. Derrible [6] examined 33 metro systems and found that most are scale-free and exhibit small-world network behavior. ...
... Recently, many studies have used complex network theory to study city metro networks, including their topological properties [2][3][4][5][6], vulnerability [7,8], resilience [8][9][10] and robustness [6,9,11,12]. Derrible [6] examined 33 metro systems and found that most are scale-free and exhibit small-world network behavior. ...
... In addition, he found that highest betweenness node-based attacks will cause the most damage to the Shanghai metro network. Wang [9] quantified the robustness of 33 metro networks under random failures or targeted attacks (degree-based node removal) using robustness metrics. Furthermore, Wang gave advice on enhancing the robustness of metro systems by creating more transfer stations to increase alternate routes in city centers and peripheral areas. ...
... Recent studies have focused on the resilience of metro networks in terms of the topological structure (Derrible and Kennedy 2010;Zhang et al. 2015), the system reliability of metro transit systems (Kim et al. 2016), and resilience using statistical methods (Wang et al. 2015). With an evolved mass transit system, the network has obviously changed its form from a simple to a more complicated form. ...
... The graph-theoretic measures are employed as they are well-established indices, and it is easy to modify the formula based on the specific condition of transportation systems. Given the number of vertices (v) and edges (e), four measures (α, β, γ, and δ) are used to evaluate the network's performance intuitively (Lin 2012;Wang et al. 2015;Shaw 1993). Basically, the measures are prescribed to understand the complexity of the entire network. ...
The growth of a city or a metropolis requires well-functioning transit systems to accommodate the ensuing increase in travel demand. As a result, mass transit networks have to develop and expand from simple to complex topological systems over time to meet this demand. Such an evolution in the networks’ structure entails not only a change in network accessibility, but also a change in the level of network reliability on the part of stations and the entire system as well. Network accessibility and reliability are popular measures that have been widely applied to evaluate the resilience and vulnerability of a spatially networked system. However, the use of a single measure, either accessibility or reliability, provides different results, which demand an integrated measure to evaluate the network’s performance comprehensively. In this paper, we propose a set of integrated measures, named ACCREL (Integrated Accessibility and Reliability indicators) that considers both metrics in combination to evaluate a network’s performance and vulnerability. We apply the new measures for hypothetical mass transit system topologies, and a case study of the metro transit system in Seoul follows, highlighting the dynamics of network performance with four evolutionary stages. The main contribution of this study lies in the results from the experiments, which can be used to inform how transport network planning can be prepared to enhance the network functionality, thereby achieving a well-balanced, accessible, and reliable system. Insights on network vulnerability are also drawn for public transportation planners and spatial decision makers.
... The critical thresholds f 90% and f c are obtained through simulations. These critical thresholds are well-known and have been successfully used in previous works to analyze robustness of networks [9], [14]. ...
The metro system plays a very important role in the urban multimodal transportation system, yet it is susceptible to accidents. A well-designed metro system needs to provide alternative routes to travellers both in the disruptive events and the normal operating conditions for providing rerouting opportunities and balancing crowded lines. This paper provides a new dimension of assessing metro network performance—travellers’ route redundancy (or route diversity), which is defined as the number of behaviourally effective routes between each origin-destination (O-D) pair in the network. The route redundancy of metro network is evaluated by statistical indicators of the distribution of the O-D-level number of effective routes. Compared with the existing connectivity and accessibility measures of topology network performance, route redundancy is also based on the topology network, but it takes the travellers’ route choice into consideration. Specifically, the effective routes between each O-D pair would provide disaggregated information from the travellers’ perspective. Case studies in four metropolises in the world, i.e., Shanghai, Beijing, London, and Tokyo, are conducted to examine the predisaster preparedness of the four metro networks explicitly from the perspective of route redundancy. The results indicate that the London metro network has the best route redundancy performance in terms of the statistical indicators of the distribution of the O-D level number of effective routes. Furthermore, the results of route redundancy are compared with typical measures of topology network performance in terms of measuring connectivity and accessibility of metro networks. Their differences are attributed to the fact that the route redundancy measure considers the travellers’ O-D-level route choice beyond the pure network topology and the shortest path considerations of the existing measures. The route redundancy proposed in this paper could assist in evaluating the predisaster preparedness of current or planning metro networks from O-D level to network level.
The assessment of networks is frequently accomplished by using time-consuming analysis tools based on simulations. For example, the blocking probability of networks can be estimated by Monte Carlo simulations and the network resilience can be assessed by link or node failure simulations. We propose in this paper to use Artificial Neural Networks (ANN) to predict the robustness of networks based on simple topological metrics to avoid time-consuming failure simulations. We accomplish the training process using supervised learning based on a historical database of networks. We compare the results of our proposal with the outcome provided by targeted and random failures simulations. We show that our approach is faster than failure simulators and the ANN can mimic the same robustness evaluation provide by these simulators. We obtained an average speedup of 300 times.
