Exploring cascading failure processes of interdependent multi-modal public transit networks

Maintaining the reliable operation of multi-modal public transit networks (MPTNs) is of great significance in improving urban public transit systems. However, most of the studies on the dynamic robustness of PTNs focus on individual modes and cannot reveal the complexity caused by the coupling of different modes in MPTNs. In addition, there is still a gap in the research on the modeling of MPTNs and cascading reliability of MPTNs that fully take into account the third or fourth transit modes to meet more flexible and more variety of travel combination demand, such as taxis/car-hailing and public bicycles, especially the lack of weight measurement metrics for different transit modes. Therefore, the objective of this work is to explore the construction method of MPTNs and the coupling robustness under cascading failures affected by complex properties of MPTNs. Considering the behavior choice of different transit modes, firstly, we propose a modeling method of multilayer interdependent MPTN in the expanded L-space, in which the coupling relationship of multi modes are represented, which is composed of bus transit, rail transit, taxi/car-hailing and public bicycle. Then the metrics of topological complexity and the cascading failure model of MPTNs based on coupled map lattice (CML) model are designed. Taking Beijing as an example, in order to verify the feasibility and validity of the model, eight MPTNs covering different transit modes are established, and a comparative analysis of two network construction methods, i.e., the L-space method and the expanded L-space method, is conducted to verify the feasibility and validity of the model. Additionally, by deliberately attacking different stations, the dynamic vulnerability characteristics of the eight MPTNs subjected to cascading failures are explored. Finally, we estimate the embedding impacts of walking distance and cycling distance on the interdependent coupling MPTN by the sensitivity analysis. The results show that on the one hand, in L-space, MPTNs present scale-free network characteristics, while in expanded L-space, MPTNs are more inclined to random network; on the other hand, MPTNs in expanded L-space which remain reliable at low perturbations and instead become more vulnerable at high perturbations have higher critical thresholds for facing cascading failures. Our work is helpful to understand the essences of MPTNs' structure and cascading reliability, and can provide guidance for the future's planning protection of the large-scale MPTNs.