Interactive Markov Chains

The Quest for Quantified Quality

By: Holger Hermanns

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Paperback | 11 September 2002

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Markov Chains are widely used as stochastic models to study a broad spectrum of system performance and dependability characteristics. This monograph is devoted to compositional specification and analysis of Markov chains.
Based on principles known from process algebra, the author systematically develops an algebra of interactive Markov chains. By presenting a number of distinguishing results, of both theoretical and practical nature, the author substantiates the claim that interactive Markov chains are more than just another formalism: Among other, an algebraic theory of interactive Markov chains is developed, devise algorithms to mechanize compositional aggregation are presented, and state spaces of several million states resulting from the study of an ordinary telefone system are analyzed.

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Introduction	p. 1
Performance Estimation with Markov C hains	p. 1
The Challenge of Compositional Performance Estimation	p. 2
Roadmap	p. 6
Interactive Processes	p. 7
Transition Systems and Interactive Processes	p. 7
Equivalences on Interactive Processes	p. 13
Algorithmic C omputation of Equivalences	p. 22
Application Example: A Distributed Mail System	p. 28
Discussion	p. 33
Markov Chains	p. 35
Stochastic Processes	p. 35
Discrete-Time Markov C hains	p. 37
C ontinuous-Time Markov C hains	p. 39
Analysing Markov C hains	p. 43
Equivalences on Markov C hains	p. 45
Algorithmic C omputation of Equivalences	p. 51
Discussion	p. 54
Interactive Markov Chains	p. 57
Design Decisions	p. 57
Interactive Markov C hains	p. 68
Strong Bisimilarity	p. 71
Weak Bisimilarity	p. 74
Algorithmic C omputation	p. 77
Application Example: Leaky Bucket	p. 84
Discussion	p. 87
Algebra of Interactive Markov Chains	p. 89
Basic Language	p. 89
Strong Bisimilarity and Weak C ongruence	p. 92
Algebra of Strong Bisimilarity and Weak Congruence	p. 95
Parallel Composition and Abstraction	p. 109
Time Constraints and Symmetric Composition	p. 111
Discussion	p. 124
Interactive Markov Chains in Practice	p. 129
State Space Aggregation by Example	p. 129
Application Study: An Ordinary Telephony System	p. 139
Nondeterminism and Underspecification	p. 149
Discussion	p. 153
Conclusion	p. 155
Major Achievements	p. 155
Has the C hallenge Been Met?	p. 156
The C hallenge C ontinues	p. 157
Appendix
Proofs for Chapter 3 and Chapter 4	p. 161
Theorem 3.6.1	p. 161
Theorem 4.3.1	p. 163
Theorem 4.3.2	p. 163
Lemma 4.4.2	p. 164
Theorem 4.4.1	p. 166
Theorem 4.4.2	p. 166
Theorem 4.5.1	p. 166
Theorem 4.5.2	p. 168
Lemma 4.5.1	p. 169
Theorem 4.5.3	p. 169
Proofs for Chapter 5	p. 175
Theorem 5.2.2	p. 175
Theorem 5.3.2	p. 182
Theorem 5.3.3	p. 183
Theorem 5.3.6	p. 188
Lemma 5.3.3	p. 192
Theorem 5.3.8	p. 194
Theorem 5.5.2	p. 198
Theorem 5.5.3	p. 199
Theorem 5.5.4	p. 201
Bibliography	p. 207
Table of Contents provided by Publisher. All Rights Reserved.

Interactive Markov Chains

The Quest for Quantified Quality

At a Glance

Paperback

Shipping

How to return your order

Defective items

You Can Find This Book In

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