Book description
Featuring previously unpublished results, Semi-Markov Models: Control of Restorable Systems with Latent Failures describes valuable methodology which can be used by readers to build mathematical models of a wide class of systems for various applications. In particular, this information can be applied to build models of reliability, queuing systems, and technical control.
Beginning with a brief introduction to the area, the book covers semi-Markov models for different control strategies in one-component systems, defining their stationary characteristics of reliability and efficiency, and utilizing the method of asymptotic phase enlargement developed by V.S. Korolyuk and A.F. Turbin. The work then explores semi-Markov models of latent failures control in two-component systems. Building on these results, solutions are provided for the problems of optimal periodicity of control execution. Finally, the book presents a comparative analysis of analytical and imitational modeling of some one- and two-component systems, before discussing practical applications of the results
- Reflects the possibility and effectiveness of this method of modeling systems, such as phase merging algorithms developed by V.S. Korolyuk, A.F. Turbin, A.V. Swishchuk, little covered elsewhere
- Focuses on possible applications to engineering control systems
Table of contents
- Cover
- Title page
- Table of Contents
- Copyright
- Preface
- List of Notations and Abbreviations
- Introduction
- Chapter 1: Preliminaries
-
Chapter 2: Semi-Markov Models of One-Component Systems with Regard to Control of Latent Failures
- Abstract
- 2.1. The system model with component deactivation while control execution
- 2.2. The System Model Without Component Deactivation While Control Execution
- 2.3. Approximation of Stationary Characteristics of One-Component System Without Component Deactivation
- 2.4. The System Model With Component Deactivation and Possibility Of Control Errors
- 2.5. The System Model With Component Deactivation and Preventive Restoration
-
Chapter 3: Semi-Markov Models of Two-Component Systems with Regard to Control of Latent Failures
- Abstract
- 3.1. The model of Two-Component serial system with immediate control and restoration
- 3.2. The model of Two-Component parallel system with immediate control and restoration
- 3.3. The model of Two-Component serial system with components deactivation while control execution, the distribution of components operating TF is exponential
- 3.4. The model of Two-Component parallel system with components deactivation while control execution, the distribution of components operating TF is exponential
- 3.5. Approximation of stationary characteristics of Two-Component serial systems with components deactivation while control execution
- Chapter 4: Optimization of Execution Periodicity of Latent Failures Control
- Chapter 5: Application and Verification of the Results
- Chapter 6: Semi-Markov Models of Systems of Different Function
- Appendix A: The Solution of the System of Integral Equations (2.24)
- Appendix B: The Solution of the System of Integral Equations (2.74)
- Appendix C: The Solution of the System of Integral Equation (3.6)
- Appendix D: The Solution of the System of Equation (3.34)
- References
- Index
Product information
- Title: Semi-Markov Models
- Author(s):
- Release date: February 2015
- Publisher(s): Academic Press
- ISBN: 9780128024867
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