## 5 Case Study
### Evaluation of the Importance of Urban Rail Network Nodes
#### 5.2.3 Results and Analysis of Node Importance Evaluation  
Based on the actual fault failure mechanism of the urban rail transit signaling system, the group utility value and individual regret value of each rail transit station are obtained according to Formulas (9)-(17), and the compromise evaluation value of each station is calculated by combining Formula (18). The compromise evaluation value is ranked from low to high to obtain the results of the ranking of the importance of each station of the Nanjing Metro network. The top 20 stations in terms of node importance are listed as critical stations, as shown in Table 3.  
As shown in Table 3, there are 11 interlocking stations and 6 ECC stations in the top 20 stations in terms of node importance, with 85% of the total number of critical stations. Each interlocking sub-district manages multiple stations, which will indirectly lead to the disability of the stations in the whole interlocking sub-district to operate normally once its signaling system fails. For example, the Jiqingmen Street interlocking zone manages 16 stations in the Yuzui-Daxinggong zone, and the failure of this interlocking station will prevent 675,576 passengers across the region from completing their journeys on the metro, so its importance is very high. In reality, this conclusion has also been verified; for example, on 6 November 2023 at 6:54 A.M. during the morning high peak, the Nanjing Metro interlocking station, Andemen Station, suffered a sudden signaling equipment failure, which resulted in a temporary stop of the train, affecting a large number of passengers' commuting trips [50]. Some non-interlocked stations, such as the Nanjing South Station of Lines 1, S1, and S3, have a greater impact on the Nanjing Metro network, and even the transport network, which is due to their transport hub properties, making their importance relatively high. Combined with Table 2, it can be seen that there are large differences in the identification results of critical stations based on the two attack methods. On the one hand, it is because the original attack method ignores the relatively independent characteristics of rail transit line operation, which overestimates the importance of some interchange stations in the network. On the other hand, it is because the original attack method does not consider the network failure mechanism after the disturbance occurs, that is, the failure of the interlocking stations will lead to the disruption of the operation of other stations in their interlocking interval, so the importance of some interlocking stations is underestimated. Figure 6 shows the distribution of the top 20 critical stations in the network of the Nanjing Metro before and after the improvement of the attack method. From Figure 6a, it can be seen that the critical stations identified based on the original attack method are mainly distributed in the transfer stations in the central area of the network and some  
non-transfer stations with heavy passenger traffic. This is because the original attack method only considers a single station, and the interchange stations in the central area of the network have high traffic volume and contribute more to the network performance; thus, the assessed stations have a high degree of importance. Figure 6b shows the critical stations identified based on the failure mechanism of the signaling system; most of the critical stations are the interlocking stations of the signaling system, such as Jiqingmendajie Station and Linchang Station. The failure of such stations in the original attack method does not have a great impact on the network directly, but because the interlocking zone under their management contains other important stations, the failure of such stations has a wider impact. Most of the critical stations are located on Lines 1, 2, and 3, which are the backbone of the Nanjing Metro passenger flow, carrying most of the interchange traffic and relying on the interchange function of the metro network in the city center.