Exploring the robustness of metro-bus composite networks considering the heterogeneity of travel time and passenger flow

As the backbone of urban public transport systems, the reliable operation of metro-bus composite networks (MBCNs) is essential for urban sustainable development. This work aims to explore the construction method of MBCNs and the coupling robustness affected by complex properties of MBCNs. Considering the travel time and passenger flow heterogeneity among various routes and modes, firstly, we propose a two-layer metro-bus composite network (TL-MBCN) model that captures interactions between the topology network and its corresponding passenger flow network. Building on this structure, the passenger demand characteristics are incorporated into the network robustness simulation to describe the rerouting and mode choice behaviors of passengers. Three indicators are proposed to evaluate the robustness of the MBCN from three aspects: connectivity robustness, travel time robustness, and passenger flow robustness. Taking the Nanjing MBCN as an example, the network characteristics, critical stations, and robustness are analysed under different attack modes and strategies. The research results show that (1) The metro network is crucial in the MBCN and can greatly improve operational efficiency and reduce the average time spent by 13%; (2) Degree-based attack leads to a faster decline in topological accessibility, while flow-degree-based attack has a greater impact on functional robustness; (3) Compared to the first attack mode, the MBCN exhibits less degradation under the second attack mode.