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Infrastructure Resilience Conference 2018

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Towards Resilient Yet Economically Viable Networked Infrastructures: Quantitative Metrics and Systemic Risk-Aware Design

Statement of the Problem. DHS’s 2009 National Infrastructure Protection Plan defined resilience as “the ability to resist, absorb, recover from, or successfully adapt to adversity or a change in conditions.” While for military systems, resiliency is the primary requirement, large-scale and especially nation-wide critical infrastructures, such as power grid, communication networks, computing cloud, etc., must combine resiliency with economic viability. Managing resiliency vs. economic viability tradeoff involves (a) keeping the system on the corresponding Pareto frontier, and (b) ability to adjust the system operating point on the Pareto frontier in accordance with the current exogenous risks either due to adverse natural events or malicious actions.

The Goals of the Contribution and the Issues Discussed. While economics incentivizes current trend for interconnectivity, recent numerous systemic failures in various critical networked infrastructures demonstrated risks of interconnectivity due to enabling undesirable contagion. The goal of the contribution is to propose and justify quantitative metrics for the resiliency and economic viability for a wide range of networked infrastructures to be used for optimization of the corresponding tradeoffs.

The Scientific Approach. Our approach, which is based on Perron-Frobenius (P-F) theory, assumes that undesirable contagion in the networked infrastructure has self-reinforcing dynamics, which is described by a non-negative evolutionary operator. This assumption holds for a wide range of contagion phenomena, including systemic overload. P-F theory allows us to associate the point of systemic contagion with the P-F eigenvalue of the linearized evolutionary operator and describe the emergence of the systemic contagion in one-dimensional space associated with the corresponding P-F eigenvector.

The Main Findings. We propose and justify a quantitative metric for the resiliency vs. economic viability tradeoff in networked infrastructures. The economic benefits of interconnectivity are quantified by the system operational region with respect to all possible combinations of the exogenous demand and system resources which can sustain this demand. Interconnectivity, which enables dynamic resource sharing, increases the system operational region by allowing for the exogenous load to be shifted from overloaded to under loaded system segments. The resiliency is characterized by the type of systemic instability. System interconnectivity may induce hard/discontinuous instability associated with existence of undesirable metastable states, and thus may negatively affect system resilience by increasing system fragility and inhibiting system ability to recover. Based on these metrics, we suggest a concept of systemic risk aware networked infrastructure design, which maximizes the economic benefits of interconnectivity subject to constraining risk of abrupt systemic instability.

The Implications of the Findings including Future Work. Hopefully, our results will lead to future research, which will address practical viability of the proposed concept of systemic risk aware networked infrastructure design. Our preliminary results indicate that practical implementation of this concept requires a combination of (a) anomaly detection to generate warning signals as risk of systemic instability exceeds certain threshold, and (b) controlling system interconnectivity in accordance with exogenous threats by concentrating on the most likely paths of the undesirable contagion spreading.

Vladimir Marbukh
United States


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