Measure Vulnerability of Metro Network Under Cascading Failure

Metro network is the important lifeline in modern cities. Its stability and reliability are critical for guaranteeing the urban residents' efficient commuting and continuous operation of urban functions. A series of disruptions show the vulnerability of metro network, and even the breakdown of a single node is sufficient to collapse the entire network due to cascading failure. However, the vulnerability assessments of metro network in the previous studies neglect the impact of cascading failure on the drop of network service performance. This paper measures the vulnerability of metro network by capturing the demand loss and travel delay under cascading failure. First, a load-capacity based model is developed to describe the dynamic process of cascading failures. Then, a weighted composite index composed of demand loss and travel time delay under cascading failure is used to measure metro network vulnerability. Finally, taking Shanghai metro network as an example, five attack scenarios are simulated to investigate cascading failure process and network vulnerability. The results reveal that cascading failures result in severe consequences in the metro network. The vulnerability of metro network without considering cascading failure is underestimated. The decrease in the tolerance parameter leads to the increase in metro network vulnerability. Random attack on one node is the most sensitive to the tolerance parameter. Node betweenness, cascading failure path and the initial load on the overloaded nodes also affect metro network vulnerability. This study provides a new perspective for understanding vulnerability of metro network, and also provides insights for improving operation reliability and stability of the network, as well as for designing emergency strategies to protect the network.