Cascading failure and recovery of metro–bus double-layer network considering recovery propagation

Normal operation of metros and buses is essential for sustainable urban development. Studies have shown that a disaster occurring on one transport station leads to the cascading failure of transportation networks, but the functions will be restored successively after post-disaster repairs. However, most studies have focused on cascading failures, ignoring the impact of recovery propagation. Therefore, this study proposes a cascading failure and recovery model to illustrate the evolution process of a metro–bus double-layer network considering recovery propagation and investigates factors including failure and recovery spreading mechanisms, different initial loads, node capacities, and repair speeds. The proposed model is applied to an actual case study of Xi’an City under different scenarios. The effects of node capacity and repair speed exhibit a marginal decreasing trend. The coexistence of cascading failure and recovery propagation enhances network minimum performance. This study has implications for strategic development of sustainable and stable transportation systems.