Network Reliability: Experiments with a Symbolic Algebra Environment (Hardcover)

BLOCKING PROPERTIES OF CHANNEL GRAPHSIntroduction for Channel GraphsMotivationSummary and OverviewBackground for Channel GraphsChannel GraphsOptimal Channel GraphsReliability Polynomial and Kruskal-Katona BoundsConsecutive Minimal CutsetsThe Esary-Proschan Upper BoundReachabilityMonte Carlo MethodsTransformations on Channel GraphsThe Swap TransformationAn Application to Takagi's and Chung and Hwang's ResultInsplit and Outsplit TransformationRenormalizationThreshold Channel GraphsShifting for Threshold Channel GraphsLeast Reliable Threshold Channel GraphMost Reliable Threshold Channel GraphShifting in Many Stages and a Lower BoundDifferent Operational ProbabilitiesThe Averaging TransformationSubgraph Counting BoundsImproving the Kruskal-Katona BoundsLower Bounds on the CoefficientsUpper Bounds on the CoefficientsTest ResultsAn Empirical EvaluationInterconnection NetworksConclusions for Channel GraphsSummary of ContributionsDirections for Future WorkA SYSTEM FOR TWO-TERMINAL RELIABILITYIntroduction for Two-Terminal ReliabilityOverview of the PartTwo-Terminal ReliabilityNetwork Model Graph Theoretic DefinitionsExisting Connectivity AlgorithmsPerformabilityNew or Improved MethodsThe Renormalization MethodCoefficient-Wise BoundsConsecutive Cuts OrderingsHybrid Methods for PerformabilityThe System DevelopedRequirementsDevelopment DecisionsPre-Existing SystemNew DevelopmentDevelopment ExperienceUsing the Package as a Research ToolTest ResultsTest Network TopologiesPerformance of Upper Bounding MethodsPerformance of the Lower Bounding MethodsConclusions for Two-Terminal ReliabilitySummaryCurrent (Ongoing) Research and System DevelopmentFuture of the SystemAPPENDICESInteractive Session Using the SystemUsing the Networks PackageUsing the Reliability PackageUsing the Channel PackagePerformance of the Connectivity BoundsAbsolute Performance Versus Exact ValuesRelative Performance of Upper BoundsInterpolating Reliability PolynomialsBibliography