Cascading failure analysis and robustness optimization of metro networks based on coupled map lattices: a case study of Nanjing, China

Measuring Method of Node Importance of Urban Rail Network Based on H Index

“…In order to calculate the accuracy of the node importance calculation method, it is necessary to know the order of importance of the nodes in the urban rail network in advance. Here, the accuracy of the The first 10 elements of h r and g r after sorting are h r = {94, 46, 20, 179, 35, 43, 44, 165, 21, 51}, g r = {179, 20, 44, 46, 35, 165, 21, 45, 164, 161}, the intersection of h r and g r has seven elements {179, 20, 44, 46, 35, 165, 21}, these seven elements are sorted in the h r and g r sets as (4,3,7,2,5,8,9) and (1,2,3,4,5,6,7), respectively. Then Sim top 10 h r , top 10 g r = 7/10 = 0.7, rank 10 h r (h r ∩ g r ) = (4 + 3 + 7 + 2 + 5 + 8 + 9)/7 = 5.429, rank 10 g r (h r ∩ g r ) = (1 + 2 + 3 + 4 + 5 + 6 + 7)/7 = 4, ∆rank(h r , g r , 10) = rank 10 h r (h r ∩ g r ) − rank 10 g r (h r ∩ g r ) = 1.429 > 0, it means that the node identified by g r index is more important than the node identified by h r index.…”

“…With the network operation of rail transit and the rapid increase of passenger flow, the operation safety risks of rail transit are increased, for instance, operational accidents can cause trains in local section stops or can even lead to severe casualties and breakdown of the entire network system. Meanwhile, many scholars have discussed the cascading failure phenomenon in urban rail network [1][2][3]. This shows that when some key stations fail, they will cause other stations to fail through the connection between stations, which greatly reduces the transmission efficiency of the urban rail network, and even leads to a global crash.…”

“…It is found that the attack strategy based on the number of betweenness centrality has the most devastating impact on the urban rail network, that is, nodes with a large number of betweenness centrality are more important. In the literature [2,3], considering the distribution characteristics of passenger flow in the Nanjing metro network, the cascading failure mechanism of metro network stations is analyzed based on the "capacity-load" model, and different passenger flow distribution methods are proposed. In this way, the evaluation index of node importance is the ratio of the station capacity to the actual passenger flow.…”

Dynamic Robustness Analysis for Subway Network With Spatiotemporal Characteristic of Passenger Flow

“…Currently, there exists two types of methods for SN robustness analysis, namely, the rail structure-based analysis [8]- [11] and passenger flow-based analysis [12]- [15]. The rail structure-based analysis focuses on the topological properties of subway.…”

“…In order to explore the cascading failure caused by the passenger flow in SN, some cascading failure models (such as the load capacity model [25], coupled map lattice model [26] and linear threshold model [27], [28]) have been improved to simulate this cascading failure process. For example, both Ma et al and Shen et al have proposed an improved coupled map lattices model to analyze the cascading failure process of Xi'an SN [14] and Nanjing SN during a certain time period [15], respectively. Ma et al have found there is a two-stage cascading failure process of a network under the condition of passenger flow overload.…”