Vulnerability metrics of multimodal composite transportation network

A topological model for multimodal composite transportation networks was constructed. The vulnerability metrics applicable to multimodal composite transportation networks were proposed from a new perspective combining the differences in each transportation mode, resource equity, and network accessibility. The metrics were sub-network sensitivity, station distribution balance, and accessibility index. Three different attack strategies were selected for Python simulation. The actual comprehensive transportation networks in developed coastal areas of Southeast China and mountainous border areas of Southwest China were taken as examples to comprehensively analyze the differences and commonalities of network structure vulnerability. In this way, the validity, stability, and applicability of the metrics were verified in multiple cases. Research results show that multimodal composite transportation networks in Zhejiang Province and Yunnan Province are in agreement with the characteristics of small-world networks. They are capable of making the advantages of each transportation mode complement each other and reducing network vulnerability. Under the three sets of contribution parameter values, regardless of the attack strategy, when the number of failed nodes is the same, the overall trend of the sub-network sensitivities from large to small in Zhejiang Province is highway network, waterway network and railway network, and Yunnan Province is aviation network, highway network and railway network. The Gini coefficients of the distribution of highway network stations in Zhejiang Province and Yunnan Province are 0.196 and 0.086, respectively, indicating equal distribution. The Gini coefficients of the distribution of railway network stations are 0.559 and 0.702, respectively, indicating highly unequal distribution. In addition, the Gini coefficient of the distribution of airports in Yunnan Province is 0.363, denoting a relatively reasonable distribution. The Gini coefficient of the distribution of ports in Zhejiang Province is 0.672, denoting highly unequal distribution. It can be concluded that the layouts of railway networks, waterway networks, and aviation networks should be further improved. The multimodal composite transportation network should be separated into multiple connected subgraphs or isolated nodes when subjected to continuous attacks. As a result, network accessibility is suddenly degraded. Recovery measures should be taken as early as possible to avoid this phenomenon. Therefore, the proposed vulnerability metrics are able to effectively describe the comprehensive transportation network vulnerability and discover the differences and commonalities of vulnerability among networks.