Markov Chains and Dependability Theory

Covers fundamental and applied results of Markov chain analysis for the evaluation of dependability metrics, for graduate students and researchers.

Gerardo Rubino (Author), Bruno Sericola (Author)

9781107007574, Cambridge University Press

Hardback, published 12 June 2014

284 pages, 32 b/w illus. 24 tables
25.4 x 18 x 1.8 cm, 0.64 kg

Dependability metrics are omnipresent in every engineering field, from simple ones through to more complex measures combining performance and dependability aspects of systems. This book presents the mathematical basis of the analysis of these metrics in the most used framework, Markov models, describing both basic results and specialised techniques. The authors first present both discrete and continuous time Markov chains before focusing on dependability measures, which necessitate the study of Markov chains on a subset of states representing different user satisfaction levels for the modelled system. Topics covered include Markovian state lumping, analysis of sojourns on subset of states of Markov chains, analysis of most dependability metrics, fundamentals of performability analysis, and bounding and simulation techniques designed to evaluate dependability measures. The book is of interest to graduate students and researchers in all areas of engineering where the concepts of lifetime, repair duration, availability, reliability and risk are important.

1. Introduction
2. Discrete time Markov chains
3. Continuous time Markov chains
4. State aggregation of Markov chains
5. Sojourn times in subsets of states
6. Occupation times
7. Performability
8. Stationary detection
9. Simulation of dependability models
10. Bounding techniques.

Subject Areas: Computer science [UY], Electrical engineering [THR], Mechanical engineering [TGB], Applied mathematics [PBW], Business mathematics & systems [KJQ]