Cascading Delays for the High-Speed Rail Network under Different Emergencies:A Double Layer Network Approach

High-speed rail(HSR)has formed a networked operational scale in China.Any internal or external disturbance may deviate trains'operation from the planned schedules,result-ing in primary delays or even cascading delays on a network scale.Studying the delay propagation mechanism could help to improve the timetable resilience in the planning stage and realize cooperative rescheduling for dispatchers.To quickly and effec-tively predict the spatial-temporal range of cascading delays,this paper proposes a max-plus algebra based delay propagation model considering trains'operation strategy and the systems'constraints.A double-layer network based breadth-first search algorithm based on the constraint network and the timetable net-work is further proposed to solve the delay propagation process for different kinds of emergencies.The proposed model could deal with the delay propagation problem when emergencies occur in sections or stations and is suitable for static emergencies and dynamic emergencies.Case studies show that the proposed algo-rithm can significantly improve the computational efficiency of the large-scale HSR network.Moreover,the real operational data of China HSR is adopted to verify the proposed model,and the results show that the cascading delays can be timely and accu-rately inferred,and the delay propagation characteristics under three kinds of emergencies are unfolded.