Dynamic and disequilibrium analysis of interdependent infrastructure systems

There is a growing awareness in recent years that the interdependencies among the civil infrastructure systems have significant economic, security and engineering implications that may influence their resiliency, efficiency and effectiveness. To capture the various types of infrastructure interdependencies and incorporate them into decision-making processes in various application domains, Zhang and Peeta (2011) propose a generalized modeling framework that combines a multilayer infrastructure network (MIN) concept and a market-based economic approach using computable general equilibrium (CGE) theory and its spatial extension (SCGE) to formulate a static equilibrium infrastructure interdependencies problem. This paper extends the framework to address the dynamic and disequilibrium aspects of the infrastructure interdependencies problems. It briefly reviews the static model, and proposes an alternative formulation for it using the variational inequality (VI) technique. Based on this equivalent VI formulation, a within-period equilibrium-tending dynamic model is proposed to illustrate how these systems evolve towards an equilibrium state within a short duration after a perturbation. To address a longer time scale, a multi-period dynamic model is proposed. This model explicitly considers the evolution of infrastructure interdependencies over time and the temporal interactions among the various systems through dynamic parameters that link the different time periods. Using this model, numerical experiments are conducted for a special case with a single region to analyze the sensitivity of the model to the various parameters, and demonstrate the ability of the modeling framework to formulate and solve practical problems such as cascading failures, disaster recovery, and budget allocation in a dynamic setting.