Network Importance Measures for Multi-Component Disruptions

The identification of important components with the potential for the most disruption is vital in network planning and analysis. Critical infrastructure systems are vulnerable to a variety of failures, whether natural (e.g., space weather, earthquakes) or intentional (e.g., malevolent acts). These systems are increasingly interconnected, which increases the risk of the propagation of disruptions. Prior research has focused largely on component importance measures that evaluate the disruption of one-at-a-time failures. However, the focus on single elements often ignores the functional and informational interdependencies between components, which can become dangerous with larger disruptions. We extend the problem of single-component disruption to multiple-component disruption using the technique for order preference by similarity to ideal solution (TOPSIS), a popular multi-criteria decision-making method. With this framework, the question becomes how to calculate the contribution of a single component to a disruption when there are multiple (n) components involved. We propose a method to calculate this contribution using a recursive formula. The technique uses lower-order disruptions to calculate higherorder disruptions, making the TOPSIS criteria dependent on one another. Ranking of the similarity scores follows the standard TOPSIS procedure to produce an ordered list of the most critical components. The methodology developed in this work is illustrated with a case study dealing with the Swedish power and telecommunications system, using loss of power and loss of flow as two impact measures. In this network, the proposed approach produces very little variability in the rankings of the nodes and edges. This is to be expected, given that the criteria and formula for calculating impact are not independent. This is also likely a result of the network itself - for n=1, very few components had any impact. To better visualize the variability in ranking for the nodes, we produced a heatmap. This work can be applied to a variety of network types, as the total number of disruption scenarios and the evaluation measures are left to the decision-maker