Network Reliability: Experiments with a Symbolic Algebra Environment, 1st Edition (Hardback) book cover

Network Reliability

Experiments with a Symbolic Algebra Environment, 1st Edition

By Daryl D Harms, Miroslav Kraetzl, Charles J. Colbourn, Stanley J. Devitt

CRC Press

240 pages

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Hardback: 9780849339806
pub: 1995-06-16
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Description

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.

Table of Contents

BLOCKING PROPERTIES OF CHANNEL GRAPHS

Introduction for Channel Graphs

Motivation

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

Reachability

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

Renormalization

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

A SYSTEM FOR TWO-TERMINAL RELIABILITY

Introduction for Two-Terminal Reliability

Overview of the Part

Two-Terminal Reliability

Network Model Graph Theoretic Definitions

Existing Connectivity Algorithms

Performability

New or Improved Methods

The Renormalization Method

Coefficient-Wise Bounds

Consecutive Cuts Orderings

Hybrid Methods for Performability

The System Developed

Requirements

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

Summary

Current (Ongoing) Research and System Development

Future of the System

APPENDICES

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

Bibliography

About the Authors/Editor

Harms\, Daryl D; Kraetzl\, Miroslav; Colbourn\, Charles J.; Devitt\, Stanley J.

About the Series

Discrete Mathematics and Its Applications

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT003000
MATHEMATICS / Applied
MAT036000
MATHEMATICS / Combinatorics
TEC007000
TECHNOLOGY & ENGINEERING / Electrical