Operational Models of Infrastructure Resilience

Abstract

We propose a definition of infrastructure resilience that is tied to the operation (or function) of an infrastructure as a system of interacting components and that can be objectively evaluated using quantitative models. Specifically, for any particular system, we use quantitative models of system operation to represent the decisions of an infrastructure operator who guides the behavior of the system as a whole, even in the presence of disruptions. Modeling infrastructure operation in this way makes it possible to systematically evaluate the consequences associated with the loss of infrastructure components, and leads to a precise notion of "operational resilience" that facilitates model verification, validation, and reproducible results. Using a simple example of a notional infrastructure, we demonstrate how to use these models for (1) assessing the operational resilience of an infrastructure system, (2) identifying critical vulnerabilities that threaten its continued function, and (3) advising policymakers on investments to improve resilience.

Stability of a giant connected component in a complex network

“…There is a growing body of work in largescale optimization and game theory that leverages the specialized structure of these networks to discover specific vulnerabilities and to identify limited defensive investments that can maximally increase robustness and resilience (e.g., Ref. [4,25]). Bridging the gap between the specific recommendations of these highly detailed models and the insights from more general models described here is an important goal for ongoing research.…”

Vulnerability Mitigation of Multiple Spatially Localized Attacks on Critical Infrastructure Systems

“…In the outer level, the defender can use many strategies, such as those summarized in the literature (Ouyang et al., ; Ouyang, ; Hausken and Levitin, ) to mitigate system vulnerability against disruptive events. For illustrative purposes, this article considers two typical preevent defense strategies, which have also been considered by other scholars in the literature (Brown et al., ; Alderson et al., , ). One is to protect some components (nodes or lines) to make them invulnerable under attacks; the other is to build new invulnerable lines to increase system redundancy.…”

“…If we denote all operation decision variables , , P L = ( ) by a single vector y , and the attack decision variables by a single vector x (the attack center variables are not included, as they are fully correlated with x V , x L ), then the proposed VM‐MSLAs model is simply described by min w max x min y , V ( w , x , y ). This type of tri‐level model is usually solved by the following solution framework (Brown et al., ; Alderson et al., , ; Zeng and Zhao, ). This framework begins by solving a subproblem max x , min y , and V (…”

“…By solving the subproblem and the master problem iteratively, the gap between the upper and the lower bound of the optimal will decrease until less than a small acceptable value , then the original model is solved. Note that when the objective function and the constraints are all linear, the above algorithm converges to an optimal solution in finite steps (Brown et al., ; Alderson et al., , ; Zeng and Zhao, ). As the proposed VM‐MSLAs model in Section 2 includes some nonlinear constraints, such as constraints and that need to identify several sets of system components, with each covered by a circle‐shaped attack area, and constraints and that include nonlinear terms, it cannot directly use the above solution framework.…”

“…In the literature, scholars have studied CIS vulnerability under different types of disruptive events, including (1) random failures, which are modeled by randomly selecting a certain fraction of system components to make them fail (Motter and Lai, ; Crucitti et al., ; Albert et al., ; Yazdani and Jeffrey, ; Dobson et al., ; Ouyang and Dueñas‐Osorio, ; Carreras et al., ; Dobson et al., ; Ren and Dobson, ; Ouyang et al., ; Newman, ; Hong et al., ); (2) natural hazards, whose scenarios are simulated by hazard generation models (FEMA, ) and their impacts on system components are described by fragility curves (Dueñas‐Osorio et al., ; Adachi and Ellingwood, ; Esposito et al., ; Franchin and Cavalieri, ; Cavallaro et al., ; FEMA, ; Ouyang and Dueñas‐Osorio, ); (3) malicious attacks, which are simulated by removing important components (Hines et al., ; Holmgren, ; Rosas‐Casals et al., ; Holme et al., ; Bompard et al., ; Mishkovski et al., ; Zio et al., ; Alderson et al., ; Ouyang et al., ; Wang et al., ; Afshari Rad and Kakhki, ; Hasani and Khosrojerdi, ; Newell, ; Bogloee et al. ); and (4) some combinations of the above events (Levitin and Hausken, ; Levitin, ; Miller‐Hooks et al., ).…”