Home // International Journal On Advances in Systems and Measurements, volume 11, numbers 3 and 4, 2018 // View article

Investigating Stochastic Dependencies Between Critical Infrastructures

Authors:
Sandra König
Stefan Rass

Keywords: critical infrastructure; stochastic dependencies; Markov chain; risk propagation; copula

Abstract:
Critical infrastructures (CIs) are essential for the welfare and prosperity of a society, and failure of one infrastructure has a significant impact on our everyday life. However, a problem in one critical infrastructure is rarely local but often affects other infrastructures, e.g., limited availability of electricity affects hospitals, water providers and food suppliers. Even a partial failure of critical infrastructures has consequences that are hard to predict unless under stringent assumptions. Among other things, the damage on another infrastructure depends on the availability of substitutes. While such factors are mostly known, many external factors such as weather, temporary demand or load peaks are not precisely predictable so that a stochastic model is required to describe the state of an infrastructure. The state of each infrastructure is described by a random variable and changes its state according to a transition regime that depends on the state of other CI but also the type of dependency. This yields a model of complex interdependencies with unknown dynamics where the state of a CI is determined by several Markov chains. Several ways exist to determine the actual state of the CI under several influences; the most conservative one is to assume the worst case (by applying the maximum principle). In this work, we provide a more general view that allows incorporating dependencies between input providers. Further, we discuss practical issues such as assessments from several experts and investigate chances for healing and total failure. An implementation of the model in R is used to illustrate how the model may be used in practice to estimate the states of a dependent CI due to limited availability of a provider. This paper describes a stochastic model of dependencies between CIs and discusses issues that arise when applying it.

Pages: 250 to 258

Copyright: Copyright (c) to authors, 2018. Used with permission.

Publication date: December 30, 2018

Published in: journal

ISSN: 1942-261x