Methods for communication-network reliability analysis: probabilistic graph reduction

The authors have designed and implemented a graph-reduction algorithm for computing the k-terminal reliability of an arbitrary network with possibly unreliable nodes. The two contributions of the present work are a version of the delta-y transformation for k-terminal reliability and an extension of Satyanarayana and Wood´s polygon to chain transformations to handle graphs with imperfect vertices. The exact algorithm is faster than or equal to that of Satyanarayana and Wood and the simple algorithm without delta-y and polygon to chain transformations for every problem considered. The exact algorithm runs in linear time on series-parallel graphs and is faster than the above-stated algorithms for huge problems which run in exponential time. The approximate algorithms reduce the computation time for the network reliability problem by two to three orders of magnitude for large problems, while providing reasonably accurate answers (relative error less than 10^-3) in most cases