Robustness of bilayer railway-aviation transportation network considering discrete cross-layer traffic flow assignment

The examination of the robustness of transportation networks holds considerable importance in safeguarding network stability in the face of potential threats. However, previous studies have primarily focused on assessing the robustness of individual railway or aviation networks at a single layer for a long-distance traveling. Indeed, the demonstration of the interconnected robustness of a bilayer network that combines railway and aviation systems is approaching a state of actualization. In this study, the robustness of single-layer railway, aviation, and bilayer railway-aviation networks were assessed and compared, taking into account the interaction effects of various transportation modes in response to multiple attack scenarios. Several interesting patterns of bilayer transportation network robustness were discovered, such as the weak robustness to intentional attacks and node removals, the comparable average robustness combined with high heterogeneity against localized attacks, and other findings. Furthermore, the robustness patterns can be effectively explained by the proposed node/edge betweenness indicators.