Multi‐period model for disruptive events in interdependent systems

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Abstract

Abstract This paper develops the Multi‐Period Model for Disruptive Events in Interdependent Systems (MPMDEIS). The analysis is divided into two principal periods: (1) an event period that lasts for the duration of the active perturbation and results in the degradation of the interdependent systems, and (2) a recovery period during which the systems evolves to a new equilibrium. The event period perturbation is modeled as a shock that cascades among the interdependent systems and reduces their production capacity. The state of the systems at the end of the event period is specified by its operational unavailability vector, which is given by the initial perturbation strength vector multiplied by an exponential matrix with the interdependency matrix P as the exponent. The coefficients of P represent the relative contribution of the loss of capacity of one system to the loss of another system as the perturbation propagates from one to the other. The quantification of the shock and interdependencies is critical for the realistic assessment of the inflicted damage and formulating effective defensive strategies against terrorist attacks, natural hazards, and technological failures or accidents. The recovery period depends on the implemented response actions and it can be modeled using a systems dynamics approach. The standard economic input‐output tables are unlikely to be appropriate for the events of interest. However, there are probabilistic risk analysis techniques such as eliciting expert opinions and analytic methods which can be used to reliably assess these data. The MPMDEIS is compared with the Inoperability Input‐Output Model (IIM) and Dynamic Input‐Output Inoperability Model (DIIM) and it is demonstrated to avoid IIM and DIIM assumptions that can lead to significant errors for disruptive events in interdependent systems. © 2006 Wiley Periodicals, Inc. Syst Eng 9: 281– 295, 2006

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