Network Reliability: Experiments with a Symbolic Algebra Environment

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Network Reliability: Experiments with a Symbolic Algebra Environment examines two intertwined topics: computational methods for computing bounds on three measures of network reliability, and a symbolic algebra system to support these computations. It describes, in algorithmic outlines, efficient techniques for reliability bounds and discusses the implementation of the techniques. It explores all-terminal reliability, two-terminal reliability, and reliability of interconnection networks. Consistent with real-world experience, the computational environment and results are strongly supported by sound theoretical development.

Written for researchers and practitioners in telecommunications networks, operations research, symbolic algebra, and discrete mathematics, this book explores all-terminal reliability, two-terminal reliability, and reliability of interconnection networks. Features extensive discussion of implementation issues and never-before-published results of computational experiments.

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Product Details

Table of Contents

Introduction for Channel Graphs
Summary and Overview
Background for Channel Graphs
Channel Graphs
Optimal Channel Graphs
Reliability Polynomial and Kruskal-Katona Bounds
Consecutive Minimal Cutsets
The Esary-Proschan Upper Bound
Monte Carlo Methods
Transformations on Channel Graphs
The Swap Transformation
An Application to Takagi's and Chung and Hwang's Result
Insplit and Outsplit Transformation
Threshold Channel Graphs
Shifting for Threshold Channel Graphs
Least Reliable Threshold Channel Graph
Most Reliable Threshold Channel Graph
Shifting in Many Stages and a Lower Bound
Different Operational Probabilities
The Averaging Transformation
Subgraph Counting Bounds
Improving the Kruskal-Katona Bounds
Lower Bounds on the Coefficients
Upper Bounds on the Coefficients
Test Results
An Empirical Evaluation
Interconnection Networks
Conclusions for Channel Graphs
Summary of Contributions
Directions for Future Work
Introduction for Two-Terminal Reliability
Overview of the Part
Two-Terminal Reliability
Network Model Graph Theoretic Definitions
Existing Connectivity Algorithms
New or Improved Methods
The Renormalization Method
Coefficient-Wise Bounds
Consecutive Cuts Orderings
Hybrid Methods for Performability
The System Developed
Development Decisions
Pre-Existing System
New Development
Development Experience
Using the Package as a Research Tool
Test Results
Test Network Topologies
Performance of Upper Bounding Methods
Performance of the Lower Bounding Methods
Conclusions for Two-Terminal Reliability
Current (Ongoing) Research and System Development
Future of the System
Interactive Session Using the System
Using the Networks Package
Using the Reliability Package
Using the Channel Package
Performance of the Connectivity Bounds
Absolute Performance Versus Exact Values
Relative Performance of Upper Bounds
Interpolating Reliability Polynomials

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