Time‐Varying Input‐Output Inoperability Model

Representing interdependent critical infrastructures is mandatory for implementing protection policies and strategies. Among the several interdependency models provided over the years, the input-output inoperability model (IIM) has attracted widespread attention due to its simplicity and compactness. Such a model can emphasize cascading effects induced in a complex scenario by dependencies and interdependencies; however, the model is typically set up based on economic data, and the stationary assumption greatly reduces the applicability of the framework. These aspects are crude approximations due to the intrinsic limits of the methodology. Indeed, in modeling realistic scenarios, the coupling of different infrastructures and sectors is expected to increase with outage duration. In this paper, a different formulation of the IIM is proposed where time-varying interdependency coefficients are considered. Such coefficients are defined to explicitly account for the severity and duration of negative phenomena. Some interesting results are obtained from a complex case study including several infrastructures in Italy, emphasizing the features of the proposed methodology. The proposed framework, based directly on operator experience, captures the behaviors induced by the various backup strategies.