Modeling vulnerability envelope of urban rail transit networks under simultaneous disruptions of stations and line sections

This paper develops a modeling approach to analyze the vulnerability of an urban rail transit network (URTN) under disruptions of rail stations, line sections, and their various combinations. The recently developed concept of vulnerability envelope is adapted to understand the possible performances of URTN under different severities of disruptions. Single-level optimization models are developed to derive the upper and lower bounds of URTN vulnerability envelope with consideration of rail transit route redundancy, which reflects the required level of service quality from the perspective of rail transit passengers. The difference between upper and lower URTN vulnerability bounds captures the range of URTN performance losses among all possible disruption scenarios. Numerical examples based on the Nanjing and Hong Kong metro networks are conducted to illustrate the properties and verify the applicability of the developed models. The results show that the proposed URTN vulnerability envelope is effective to analyze the possible range of URTN with different operability requirements under combined multi-infrastructure disruptions. Outcome of the developed method is useful for vulnerability assessment and important infrastructure identification, which may facilitate the vulnerability-oriented decision-making in URTNs.