A markovian dependability model with cascading failures

Document Type

Article

Publication Date

8-25-2009

Abstract

We develop a continuous-time Markov chain model of a dependability system operating in a randomly changing environment and subject to probabilistic cascading failures. A cascading failure can be thought of as a rooted tree. The root is the component whose failure triggers the cascade, its children are those components that the root's failure immediately caused, the next generation are those components whose failures were immediately caused by the failures of the root's children, and so on. The amount of cascading is unlimited. We consider probabilistic cascading in the sense that the failure of a component of type i causes a component of type j to fail simultaneously with a given probability, with all failures in a cascade being mutually independent. Computing the infinitesimal generator matrix of the Markov chain poses significant challenges because of the exponential growth in the number of trees one needs to consider as the number of components failing in the cascade increases. We provide a recursive algorithm generating all possible trees corresponding to a given transition, along with an experimental study of an implementation of the algorithm on two examples. The numerical results highlight the effects of cascading on the dependability of the models. © 2009 IEEE.

Identifier

68949166208 (Scopus)

Publication Title

IEEE Transactions on Computers

External Full Text Location

https://doi.org/10.1109/TC.2009.31

ISSN

00189340

First Page

1238

Last Page

1249

Issue

9

Volume

58

Grant

IIS-0324816

Fund Ref

National Science Foundation

This document is currently not available here.

Share

COinS