Mathematical modeling of interdependent infrastructure: An object-oriented approach for generalized network-system analysis

Risk and resilience analysis research has favored simpler models such as topological connectivity and maximum flow algorithm to model infrastructure performance. However, modeling of dependencies and interdependencies requires high-fidelity flow analyses. Developing a rigorous mathematical formulation to model interdependent infrastructure encounters three sets of challenges: (1) Identifying and understanding the different types of interactions within and across the infrastructure, (2) Modeling the time-varying performance of each infrastructure accurately, and (3) Modeling the interdependencies among infrastructure. This paper presents a mathematical formulation that models infrastructure as a set of generalized flow network objects. The proposed formulation then models infrastructure interdependencies using dynamic interfaces among the network objects, enabling infrastructure-specific multi-fidelity analyses. This formulation is the first in the literature that can model bilateral and looped interdependencies. The paper also presents guidelines for selecting boundaries and resolutions and introduces novel aggregated performance measures that address the disparity in the performance of spatially distributed infrastructure. Finally, the paper illustrates the proposed formulation using two examples. First, a simple example conceptually illustrates the formulation’s details. Second, a real-world example models the performance of interdependent infrastructure for Shelby County, Tennessee, in a post-earthquake scenario to illustrate scalability.