Exploring the robustness of public transportation for sustainable cities: A double-layered network perspective

The reliable and safe operation of an urban public transportation (UPT) system is of great significance to the sustainable development of a city. In-depth analyses of UPT network by exploring the topological structure and passenger travel features can help explain the mechanisms driving reliable UPT operations. Based on complex network theory, we proposed a robust model for a Bus-Subway double-layered network (B–S DLN) from the structural and functional perspectives. The following indicators were used to quantify the structural robustness of B–S DLN: average path length (APL), relative size of giant component (RSGC) and global network efficiency (GNE). The functional robustness was measured using the ratio of passenger flow loss (R). Using urban traffic data from the Xicheng District of Beijing, we analyzed the cascading failure of B–S DLN based on a nonlinear load-capacity model with two capacity control parameters: α and β. The simulation results show that α and β significantly impact the cascading failure process of B–S DLN. An increase in β or decrease in α can enhance the network's ability to resist cascading failure. The parameter control method revealed that the B–S DLN achieves strong robustness when α = 0.2 and β = 0.5. Comparing the network robustness under a random attack and intentional attack, the B–S DLN is more robust under an intentional attack than in the random attack mode. This indicates that the robustness of B–S DLN can be significantly improved by rationally increasing station capacities.