Uncertainty in vulnerability of metro transit networks: A global perspective

This study measures the “uncertainty in vulnerability” of 50 metro transit networks in the most populated cities across the globe under benign and malicious attack scenarios. Uncertainty in vulnerability delineates the gap between the performance loss trajectory formed by link percolation under benign and malicious attacks. Three observations are discerned. First, vulnerability and uncertainty in vulnerability are a function of both size and physics of the network explained by connectivity measures. A 1% increase in the ratio of links to nodes increases the vulnerability by 0.50% and increases the uncertainty in vulnerability by 2.24%. A 1% increase in the ratio of the number of links to the maximum possible number of links decreases vulnerability by 0.03% and the uncertainty in vulnerability by 0.12%. Second, the topology of metro transit networks with <100 nodes follows one of the three analogous forms of tree-shaped networks, networks with one undirected cycle, or single depot networks, while the topology of metro transit networks with ≥100 nodes is closer to grid and matching pairs. Third, metro transit networks (i) are less likely to resume the operation under malicious attacks, (ii) are more likely to resume the operation under benign attacks, and (iii) are susceptible to both severe and non-severe degradations under random attacks. Overall, it is shown that the most vulnerable transit networks experience the maximal uncertainty in vulnerability and own a topology analogous to a single depot. New York, Delhi, and London metro transit networks have the most vulnerable topology. Ahmedabad, Mumbai, and Sydney metro transit networks have the least vulnerable topology.