Correlating the fractal dimensions of complex multi-layer rail networks to the underlying network resilience can provide operators with valuable and insightful knowledge that can be useful in their planning and development. These networks are subject to service disruptions or retardation due to failures from various causes including those related to natural hazards in a changing climate, age, accidents, or intentional causes. Network resilience measures the ability of the network to adapt to and maintain an acceptable level of service in the presence of uncertainties and potential failure and disruptions. A multi-layer rail network represents sets of individual networks plus the links between them. Fractal networks are a class of scale-free networks with a wide node degree distribution. Insights into the fractal dimensions of these complex networks though renormalization enhances the understanding of their evolution and behavior and could enhance methodologies for understating network resilience.&nbsp;A multi-layer network is a set of individual networks, each representing nodes of a particular type and their connections, plus interlinking edges and boundaries between networks. The rail network examined in this work consists mainly of networks of individual US class 1 carriers and the links between them that when combined represent the larger national network. This type of network structure allows for the study of the individual regional or company-wide network resilience, the importance of the critical links between networks, and the impact of degradation or evolution in one network on the larger network resilience. This understanding should enable stakeholders to collaborate to enhance critical edge or boundary structures per each network and to plan and develop a more resilient and efficient national network.&nbsp;Fractal networks are characterized by the small world property resulting from the shortcuts in the networks, wide distribution of node degree, and modular hierarchical structures. A distinguishing feature of fractal networks is that the highly connected nodes tend not to be directly linked to one another. Hub-to-non-hub connections are favored in fractal networks. This property leads to increased robustness of fractal networks against adverse events compared to typical scale-free networks. This property results in increased network efficiency and resilience.&nbsp;Resilience in complex networks is typically assessed using topological characteristics of the networks. These can be node degree distribution, mean degree or small world properties. One method to assess fractal dimension in complex networks is obtained using the box-counting method. This method was used on the individual class 1 railroad networks as well as on the national network to gather their fractal dimensions. The method uses a renormalization scheme for replacing each box by a single node in the network. The renormalization process is applied until a single node remains. Although this transformation can only be applied a limited number of times because of the small-world characteristics of such a network, it is enough to uncover the main properties of the network, like node degree distribution.This presentation introduces and examines the correlation of fractal dimension and resilience in regional (or company-wide) and national rail transportation networks. An understanding of this property and its potential applications may help to identify methodologies to encourage network evaluation in economically favorable directions with benefits that include enhancing robustness and resilience to adverse events. In addition, future work is proposed using dynamic networks to study ideal fractal growth to enhance resilience by providing understanding of evolution and behaviors over time of these networks using inverse renormalization.

Multi-Layer Rail Network Topology: Understanding Resilience Through Network Fractal Properties

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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