<abstract xmlns="http://www.w3.org/1999/xhtml">We consider a pair of networks <italic>A </italic>and <italic>B </italic>which are subject to failures of their components. In <italic>A, </italic>edges are subject to failure, and <italic>A </italic>fails when it disintegrates into several isolated clusters each containing a single terminal. Edges of <italic>A </italic>fail in random order and their failure moments follow Poisson process. After <italic>A </italic>has failed, terminal α of <italic>A </italic>causes a failure (”attacks”) on <italic>R</italic>α randomly chosen non terminal nodes of network <italic>B</italic>. All edges incident to an attacked node are erased. The ”attacks” take negligible time. Network <italic>B </italic>failure takes place if it loses its terminal connectivity. We study the probability that <italic>B </italic>will be in failure state at moment <italic>t </italic>as a function of <italic>t </italic>and <italic>R </italic> = ∑ Rα The main formal tools which we use are the D-spectra (signatures) of networks <italic>A </italic>and <italic>B </italic>and de Moivre’s combinatorial formula.</abstract>

We consider a pair of networks A and B which are subject to failures of their components. In A, edges are subject to failure, and A fails when it disintegrates into several isolated clusters each containing a single terminal. Edges of A fail in random order and their failure moments follow Poisson process. After A has failed, terminal α of A causes a failure (”attacks”) on Rα randomly chosen non terminal nodes of network B. All edges incident to an attacked node are erased. The ”attacks” take negligible time. Network B failure takes place if it loses its terminal connectivity. We study the probability that B will be in failure state at moment t as a function of t and R  = ∑ Rα The main formal tools which we use are the D-spectra (signatures) of networks A and B and de Moivre’s combinatorial formula.

Failure Development in a System of Two
Connected Networks

Department of Mathematics, Ben-Gurion University P. O. Box 653, Beer-Sheva, 84105, Israel

Software Engineering Department Sami Shamoon College of Engineering, Beer Sheva, 84100, Israel

Transport and Telecommunication Journal

{"article-title":"Failure Development in a System of Two\nConnected Networks"}

We consider a pair of networks A and B which are subject to failures of their components. In A, edges are subject to failure, and A fails when it disintegrates...

Failure Development in a System of Two Connected Networks

Published Online: Dec 04, 2012

Page range: 255 - 260

DOI: https://doi.org/10.2478/v10244-012-0020-x

This content is open access.