New Topological Formula and Rapid Algorithm for Reliability Analysis of Complex Networks
- 1 June 1978
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Reliability
- Vol. R-27 (2) , 82-100
- https://doi.org/10.1109/tr.1978.5220266
Abstract
Part I derives a new topological formula for the terminalpair reliability of complex networks. The formula generates only non-cancelling terms. The non-cancelling terms in the reliability expression correspond one-to-one with the acyclic subgraphs of the given probabilistic graph. Part II introduces the concept of neutral sequences in acyclic graphs; several of their important properties are established. Based on these results a powerful algorithm for generating the reliability expression is presented. The reliability expression is obtained in symbolic factored form. Examples indicate that the present algorithm is appreciably faster than earlier methods. The properties of cyclic and acyclic graphs established in this paper are significant new results in the theory of digraphs and have further ramifications and wider application than in reliability.Keywords
This publication has 22 references indexed in Scilit:
- A New Algorithm for Symbolic System Reliability AnalysisIEEE Transactions on Reliability, 1976
- Exact calculation of computer network reliabilityNetworks, 1974
- A Fast Recursive Algorithm to Calculate the Reliability of a Communication NetworkIEEE Transactions on Communications, 1972
- Topological analysis of general linear networksElectronics Letters, 1966
- Topological Analysis of General Linear NetworksIEEE Transactions on Circuit Theory, 1965
- Analysis of Probabilistic NetworksIEEE Transactions on Communications, 1964
- The path matrix and switching functionsJournal of the Franklin Institute, 1959
- Analysis of Switching NetworksBell System Technical Journal, 1955
- The solution of passive electrical networks by means of mathematical treesProceedings of the IEE - Part III: Radio and Communication Engineering, 1953
- Ueber die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Ströme geführt wirdAnnalen der Physik, 1847