Robustness Optimization of Aviation-High-Speed Rail Coupling Network

Recently, interdependencies between the real networks have received extensive attention from scholars. Considering the existing of edge coupling relationship between aviation networks (AN) and high-speed rail networks (HRN), we established the aviation-high-speed rail coupling network (AHSRCN) model of China according to the real database of flights and trains. We use the importance evaluation method to find out an important index of edges in each network, and define the initial load of each edge, establishing a nonlinear load capacity model based on this importance index of edges. Furthermore, according to the actual situation, we propose a load distribution model for double-layer edge-coupling networks, and apply two dynamic load distribution strategies for each single network. The network congestion coefficient is used to measure the robustness of the networks. The effects of different load distribution strategies on the robust performance of coupled networks are studied under the changes of attack scale, load capacity exponential parameter and load capacity coefficient parameter. The results show that as the proportion of reserved edges increases, the aviation network and the high-speed rail network reach the peak of network congestion at 6% and 2% of the reserved edges, respectively. The increase of load capacity parameters can effectively reduce the congestion degree of networks, and the relationship between them presents typical nonlinear characteristics. For the case that the load capacity exponential parameter is less than 0, the Load Balancing Distribution (LBD) strategy can reduce the network congestion to the maximum extent. However, for the case that the load capacity exponential parameter is greater than 0, the Load Extreme Distribution (LED) strategy can suppress the network congestion more effectively, while the change of load capacity coefficient parameter will not cause this difference.