Models of network reliability : analysis, combinatorics, and Monte Carlo / Ilya B. Gertsbakh, Yoseph Shpungin.

Includes bibliographical references and index.

Preface -- Notation and Abbreviations -- What is Monte Carlo Method? -- Area Estimation -- Optimal Location of Components -- Reliability of a Binary System -- Statistics: a Short Reminder -- What is Network Reliability? -- Introduction -- Spanning Trees and Kruskal’s Algorithm -- Introduction to Network Reliability -- Multistate Networks -- Network Reliability Bounds -- Exponentially Distributed Lifetime -- Characteristic Property of the Exponential Distribution -- Exponential Jump Process -- Examples -- Static and Dynamic Reliability -- System Description. Static Reliability -- Dynamic Reliability -- Stationary Availability -- Burtin-Pittel Formula -- Pivotal Formula. Birnbaum Importance Measure -- Cumulative Spectrum -- BIM and the Cumulative C*-spectrum -- BIM and the Invariance Property -- Examples -- Optimal Network Synthesis -- Introduction to Network Synthesis -- "Asymptotic" Synthesis -- Synthesis Based on Importance Measures -- Dynamic Networks -- Introduction: Network Exit Time -- Bounds on the Network Exit Time -- Examples of Network Reliability -- Colbourn & Harms’ Ladder Network -- Integrated Communication Network (ICN) -- Appendix A: O(·) and o(·) symbols -- Appendix B: Convolution of exponentials -- Appendix C: Glossary of D-spectra -- References -- Index -- Each chapter includes problems and exercises