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Author: Gerardo Rubino
Publisher: Cambridge University Press
ISBN: 1139991841
Category : Technology & Engineering
Languages : en
Pages : 287
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Book Description
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.
Author: Gerardo Rubino
Publisher: Cambridge University Press
ISBN: 1139991841
Category : Technology & Engineering
Languages : en
Pages : 287
Get Book Here
Book Description
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.
Author: Gerardo Rubino
Publisher: Cambridge University Press
ISBN: 1107007577
Category : Business & Economics
Languages : en
Pages : 287
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Book Description
Covers fundamental and applied results of Markov chain analysis for the evaluation of dependability metrics, for graduate students and researchers.
Author: Gerardo Rubino
Publisher:
ISBN: 9781316007891
Category : Electronic books
Languages : en
Pages : 288
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Book Description
Covers fundamental and applied results of Markov chain analysis for the evaluation of dependability metrics, for graduate students and researchers.
Author: Bruno Sericola
Publisher: John Wiley & Sons
ISBN: 1118731530
Category : Mathematics
Languages : en
Pages : 306
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Book Description
Markov chains are a fundamental class of stochastic processes. They are widely used to solve problems in a large number of domains such as operational research, computer science, communication networks and manufacturing systems. The success of Markov chains is mainly due to their simplicity of use, the large number of available theoretical results and the quality of algorithms developed for the numerical evaluation of many metrics of interest. The author presents the theory of both discrete-time and continuous-time homogeneous Markov chains. He carefully examines the explosion phenomenon, the Kolmogorov equations, the convergence to equilibrium and the passage time distributions to a state and to a subset of states. These results are applied to birth-and-death processes. He then proposes a detailed study of the uniformization technique by means of Banach algebra. This technique is used for the transient analysis of several queuing systems. Contents 1. Discrete-Time Markov Chains 2. Continuous-Time Markov Chains 3. Birth-and-Death Processes 4. Uniformization 5. Queues About the Authors Bruno Sericola is a Senior Research Scientist at Inria Rennes – Bretagne Atlantique in France. His main research activity is in performance evaluation of computer and communication systems, dependability analysis of fault-tolerant systems and stochastic models.
Author: Vlad Stefan Barbu
Publisher: Springer Science & Business Media
ISBN: 0387731733
Category : Mathematics
Languages : en
Pages : 233
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Book Description
Here is a work that adds much to the sum of our knowledge in a key area of science today. It is concerned with the estimation of discrete-time semi-Markov and hidden semi-Markov processes. A unique feature of the book is the use of discrete time, especially useful in some specific applications where the time scale is intrinsically discrete. The models presented in the book are specifically adapted to reliability studies and DNA analysis. The book is mainly intended for applied probabilists and statisticians interested in semi-Markov chains theory, reliability and DNA analysis, and for theoretical oriented reliability and bioinformatics engineers.
Author: Nicolas Privault
Publisher: Springer
ISBN: 9811306591
Category : Mathematics
Languages : en
Pages : 379
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Book Description
This book provides an undergraduate-level introduction to discrete and continuous-time Markov chains and their applications, with a particular focus on the first step analysis technique and its applications to average hitting times and ruin probabilities. It also discusses classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes. It first examines in detail two important examples (gambling processes and random walks) before presenting the general theory itself in the subsequent chapters. It also provides an introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times, together with a chapter on spatial Poisson processes. The concepts presented are illustrated by examples, 138 exercises and 9 problems with their solutions.
Author: Kishor S. Trivedi
Publisher: Cambridge University Press
ISBN: 1107099501
Category : Computers
Languages : en
Pages : 729
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Book Description
Learn about the techniques used for evaluating the reliability and availability of engineered systems with this comprehensive guide.
Author: N. Limnios
Publisher: Springer Science & Business Media
ISBN: 1461201616
Category : Technology & Engineering
Languages : en
Pages : 226
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Book Description
At first there was the Markov property. The theory of stochastic processes, which can be considered as an exten sion of probability theory, allows the modeling of the evolution of systems through the time. It cannot be properly understood just as pure mathemat ics, separated from the body of experience and examples that have brought it to life. The theory of stochastic processes entered a period of intensive develop ment, which is not finished yet, when the idea of the Markov property was brought in. Not even a serious study of the renewal processes is possible without using the strong tool of Markov processes. The modern theory of Markov processes has its origins in the studies by A. A: Markov (1856-1922) of sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian mo tion. Later, many generalizations (in fact all kinds of weakenings of the Markov property) of Markov type stochastic processes were proposed. Some of them have led to new classes of stochastic processes and useful applications. Let us mention some of them: systems with complete connections [90, 91, 45, 86]; K-dependent Markov processes [44]; semi-Markov processes, and so forth. The semi-Markov processes generalize the renewal processes as well as the Markov jump processes and have numerous applications, especially in relia bility.
Author: Kishor S. Trivedi
Publisher: John Wiley & Sons
ISBN: 0471460818
Category : Computers
Languages : en
Pages : 881
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Book Description
An accessible introduction to probability, stochastic processes, and statistics for computer science and engineering applications Second edition now also available in Paperback. This updated and revised edition of the popular classic first edition relates fundamental concepts in probability and statistics to the computer sciences and engineering. The author uses Markov chains and other statistical tools to illustrate processes in reliability of computer systems and networks, fault tolerance, and performance. This edition features an entirely new section on stochastic Petri nets—as well as new sections on system availability modeling, wireless system modeling, numerical solution techniques for Markov chains, and software reliability modeling, among other subjects. Extensive revisions take new developments in solution techniques and applications into account and bring this work totally up to date. It includes more than 200 worked examples and self-study exercises for each section. Probability and Statistics with Reliability, Queuing and Computer Science Applications, Second Edition offers a comprehensive introduction to probability, stochastic processes, and statistics for students of computer science, electrical and computer engineering, and applied mathematics. Its wealth of practical examples and up-to-date information makes it an excellent resource for practitioners as well. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.
Author: Paul A. Gagniuc
Publisher: John Wiley & Sons
ISBN: 1119387558
Category : Mathematics
Languages : en
Pages : 252
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Book Description
A fascinating and instructive guide to Markov chains for experienced users and newcomers alike This unique guide to Markov chains approaches the subject along the four convergent lines of mathematics, implementation, simulation, and experimentation. It introduces readers to the art of stochastic modeling, shows how to design computer implementations, and provides extensive worked examples with case studies. Markov Chains: From Theory to Implementation and Experimentation begins with a general introduction to the history of probability theory in which the author uses quantifiable examples to illustrate how probability theory arrived at the concept of discrete-time and the Markov model from experiments involving independent variables. An introduction to simple stochastic matrices and transition probabilities is followed by a simulation of a two-state Markov chain. The notion of steady state is explored in connection with the long-run distribution behavior of the Markov chain. Predictions based on Markov chains with more than two states are examined, followed by a discussion of the notion of absorbing Markov chains. Also covered in detail are topics relating to the average time spent in a state, various chain configurations, and n-state Markov chain simulations used for verifying experiments involving various diagram configurations. • Fascinating historical notes shed light on the key ideas that led to the development of the Markov model and its variants • Various configurations of Markov Chains and their limitations are explored at length • Numerous examples—from basic to complex—are presented in a comparative manner using a variety of color graphics • All algorithms presented can be analyzed in either Visual Basic, Java Script, or PHP • Designed to be useful to professional statisticians as well as readers without extensive knowledge of probability theory Covering both the theory underlying the Markov model and an array of Markov chain implementations, within a common conceptual framework, Markov Chains: From Theory to Implementation and Experimentation is a stimulating introduction to and a valuable reference for those wishing to deepen their understanding of this extremely valuable statistical tool. Paul A. Gagniuc, PhD, is Associate Professor at Polytechnic University of Bucharest, Romania. He obtained his MS and his PhD in genetics at the University of Bucharest. Dr. Gagniuc’s work has been published in numerous high profile scientific journals, ranging from the Public Library of Science to BioMed Central and Nature journals. He is the recipient of several awards for exceptional scientific results and a highly active figure in the review process for different scientific areas.
