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| Author and Study time | Case city | PTN type / Whether multilayered systems are considered | Resilience measurement indicator | Attack strategy | Major contribution or conclusion |
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Wu et al.[78]
2006 | Beijing | Bus / No | Network efficiency | Random node-based attacks, Deliberate node-based attacks based on node degree | Comparing the local efficiency changes between the BTN under random attacks and deliberate attacks, it can get the conclusions that due to the impacts of large clustering coefficient, the local network efficiency of BTN under deliberate attacks is much larger than that under random attacks. |
Berche et al.[20]
2009 | Berlin, Paris and other twelve cities | Bus, Electric trolleybus, Ferry, Subway, Tram, Urban train / Yes | Relative size of maximum connectivity cluster, Average shortest path length | Random node-based attacks (removing the nodes at random, or removing a randomly chosen neighbor of a randomly chosen node), Deliberate node-based attacks (according to node degree, closeness, graph, stress, betweenness, clustering coefficient, next nearest neighbors number) | Different PTNs under L-space and P-space have diverse behavioral characteristics when faced with random attacks and deliberate attacks. The resilience behavior of a network against different attack strategies gives additional insight into the network architecture, discovering structures on different scales. |
Leu et al.[21]
2010 | Melbourne | Tram, Urban train / Yes | Degree, Betweenness, Clustering coefficient, The number of non-overlapping sub-graphs in a network, Distance gap between stations, Spatial distribution of risk | Random node-based attacks | A multi-layers approach – physical, service and cognitive is proposed as an assessment framework, and its physical layer that are covered by a GPS map is focused on. Under random attacks, the tram network has the largest resilience when compared to other networks, demonstrating that the GPS based definition of this framework is practically applicable. |
Wang et al.[79]
2010 | Beijing, Shanghai, Nanjing, Hangzhou | Bus / No | Relative size of maximum connectivity cluster, Network efficiency | Random node-based attacks, Deliberate node-based attacks based on node degree | BTN is robust against random attacks and fragile to deliberate attacks, and the stability of key stations plays a decisive role in BTN resilience. |
Duan et al.[80]
2010 | Beijing | Bus / No | Average shortest path length | Random node-based attacks, Deliberate node-based attacks based on node degree, Deliberate node-based attacks based on node betweenness | Compared with the same scale stochastic network, BTN has the similar ability in resilience against random attacks, but it is less robust against deliberate degree attacks and deliberate betweenness attacks. |
Berche et al.[81]
2012 | Berlin, Paris and other twelve cities | Bus, Electric trolleybus, Ferry, Subway, Tram, Urban train / Yes | Relative size of maximum connectivity cluster, Area below the curve described by a function that characterizes the changing relative size of maximum connectivity cluster in attack process | Node-based attacks based on (random node, node with maximal recalculated degree, node with maximal initial degree, node with maximal recalculated betweenness, node with maximal initial betweenness), Edge-based attacks based on (random edge, edge with recalculated maximal degree, edge with maximal initial degree, edge with maximal recalculated betweenness, edge with maximal initial betweenness) | An empirical analysis of the reaction of different PTNs upon random attacks or deliberate attacks based on either nodes or edges is presented, so that it can contribute to identifying criteria, which allows to judge a priori on the attack stability of real world correlated networks of finite size checking how do these criteria correspond to the analytic results available for the infinite uncorrelated networks. |
Ferber et al.[82]
2012 | London, Paris | Bus, Subway, tram / Yes | Relative size of maximum connectivity cluster, Network efficiency, Maximal shortest path
Length, Area below the curve described by a function that characterizes the changing relative size of maximum connectivity cluster in attack process | Node-based attacks based on (random node, node with maximal recalculated degree, node with maximal recalculated betweenness), Edge-based attacks based on (random edge, edge with recalculated maximal degree, edge with maximal recalculated betweenness) | Paris’s PTN is significantly more resilient than London’s PTN because of a higher organization in almost all introduced respects. Furthermore, through taking into account cascading effects (a non-dynamic expression), the network integrity is controlled for both networks by less than 0.5% of the stations (19 for Paris and 34 for London). |
Wu et al.[83]
2013 | Nanjing | Subway / No | Network connectivity entropy | Random node-based attacks, Random edge-based attacks | In subway network, it is proved that the network connectivity entropy is practical and effective as a resilience measurement indicator. |
Zhang et al.[84]
2013 | Shanghai | Urban rail transit / No | Relative size of maximum connectivity cluster | Random node-based attacks, Random edge-based attacks, Deliberate attacks based on (highest betweenness edge-based attacks, largest degree node-based attacks, highest unit degree betweenness node-based attacks, highest betweenness node-based attacks) | Compared with other attack strategies, the deliberate attacks based on highest betweenness node-based attacks are the most effective way to destroy the URTN. |
Sun et al.[85]
2015 | Shanghai | Urban rail transit / No | Network efficiency, Network size, Connected origin-destination (OD) ratio | Random node-based attacks, Deliberate node-based attacks based on node degree, Deliberate node-based attacks based on node betweenness | In the study of network resilience, it finds that the URTN is rather robust to random attacks, but is vulnerable to the deliberate attacks. In the study of station resilience, station resilience model is further defined to evaluate the resilience of each station. |
Yang et al.[22]
2015 | Beijing | Urban rail transit / No | Relative size of maximum connectivity cluster, Average shortest path length | Random node-based attacks, Deliberate node-based attacks based on a new node importance evaluation index that combines degree and betweenness | The scale-free characteristic makes the network be better resistant to random attacks, but its connection reliability is at a low level under deliberate attacks. |
Fu et al.[86]
2015 | Jinan | Bus / No | Network structure entropy, Network efficiency | Random node-based attacks, Deliberate node-based attacks based on node degree, Deliberate node-based attacks based on node betweenness | A novel betweenness importance based network structure entropy is proposed, revealing the interaction mechanism among static resilience of PTN, station heterogeneity and network structure entropy. |
Gu et al.[23]
2016 | Beijing, Nanjing | Urban rail transit / No | Network efficiency, Average shortest path length, Relative size of maximum connectivity cluster, Alpha index, Isolated node ratio | Random node-based attacks, Deliberate node-based attacks based on node betweenness | Resilience simulation analysis of URTN in 2020 (planning year) shows that the URTNs of two cities are both robust under random attacks and vulnerable under deliberate attacks. |
Feng et al.[87]
2016 | Lanzhou | Bus / No | Number of connected branches, Relative size of maximum connectivity cluster, Network efficiency | Random node-based attacks, Deliberate node-based attacks based on node degree, Deliberate node-based attacks based on node betweenness | Due to the special features of the valley terrain, the resilience under deliberate attacks is far stronger than that under random attacks, and the selection strategy based on the degree is more suitable for this BTN. |
Chen et al.[88]
2016 | Beijing | Urban rail transit / No | Network efficiency, Average shortest path length, Relative size of maximum connectivity cluster | Random node-based attacks, Deliberate node-based attacks based on node degree, Deliberate node-based attacks based on node strength, Deliberate node-based attacks based on node betweenness, Deliberate edge-based attacks based on edge betweenness | Comparing and analyzing the static resilience of the unweighted network and the passenger flow weighted network, it can get the conclusion that the resilience of weighted URTN is more obvious, i.e., analyzing static resilience through the topology alone will overestimate the network reliability. |
Ren et al.[89]
2016 | Shenyang | Bus / No | Relative size of maximum connectivity cluster, Average shortest path length, Network diameter, Network efficiency | Random node-based attacks, Deliberate node-based attacks based on node degree | Comparing the static resilience of the bus transit station (geography)-route coupled network and each sub-network, the interaction between the sub-networks has little effect on the resilience of bus transit station network, but it makes the bus transit route network be less robust. Comparing the static resilience of the bus transit route-transfer coupled network and each sub-network, the interaction between the sub-networks has little effect on the resilience of bus transit route network, but the collapse extent of bus transit transfer network is reduced. |
Sun et al.[24]
2016 | Shanghai | Urban rail transit / No | A composite indicator considering the impacts of weighted average path length, weighted global efficiency, the number of route service passengers, and relative disruption probability | Route-based attacks | Based on simulation analysis under route-based attacks, it can get the conclusions that routes carrying a large number of passengers generally have a significant impact on network static resilience. Additionally, the circular routes also have a significant influence on passenger flow redistribution (non-dynamic). |
Bao et al.[25]
2017 | A city in western China | Bus, Subway / Yes | Relative size of maximum connectivity cluster, Average shortest path length, Network diameter, Network efficiency | Random node-based attacks, Deliberate node-based attacks based on node degree | A composite method for bus station and subway station that considers the geographical proximity is proposed. The resilience of bus sub-network, the subway sub-network, and the bus-subway interdependent network under random attacks are all much larger than that under deliberate attacks. |
Wang et al.[90]
2017 | Tokyo, Rome and other thirty-one cities | Urban rail transit / No | Relative size of maximum connectivity cluster, Network efficiency, Clustering coefficient, Algebraic connectivity, Robustness indicator, Effective graph resistance, Reliability, Average degree, Natural connectivity, Degree diversity, Meshedness coefficient, Critical thresholds | Random node-based attacks, Deliberate node-based attacks based on node degree | Among all used indicators, several indicators place an emphasis on alternative paths, and the others place an emphasis on the length of the paths. Additionally, among all the URTNs of thirty-three cities, the URTNs of Tokyo and Rome are the most robust, because Rome’s URTN benefits from short transferring and Tokyo’s URTN has a significant number of transfer stations, which both promote a larger number of alternative paths and overall relatively short path-lengths. |
Wu et al.[91]
2017 | Beijing, London, Paris, Hong Kong, Tokyo, New York | Urban rail transit / No | Disabled route ratio, Cost adjustment | Random node-based attacks, Deliberate node-based attacks based on node occupying probability, Deliberate node-based attacks based on node betweenness | A new node centrality measure, the node occupying probability, is proposed for evaluating the level of utilization of stations, thus a new deliberate attack mode, the deliberate node-based attacks based on node occupying probability, is proposed. Furthermore, simulation results show that the resilience of Tokyo and Hong Kong’s URTNs are the largest under random attacks and deliberate attacks. |
Zhang et al.[92]
2018 | Beijing, Shanghai, Guangzhou | Urban rail transit / No | Network efficiency, Network functionality loss | Deliberate node-based attacks based on node degree, Deliberate node-based attacks based on node betweenness | Comparing the resilience of three cities’ URTNs under deliberate attacks, it can get conclusions that three URTNs are all vulnerable to deliberate attacks, and Guangzhou’s URTN has the optimal topology and reliability among three networks. |
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