Interactive Markov Chains

The Quest for Quantified Quality

Holger Hermanns

230 pages, parution le 18/11/2002

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Résumé

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 telephone system are analyzed.

Contents

1- Introduction

Performance Estimation with Markov Chains
The Challenge of Compositional Performance Estimation
Roadmap

2. Interactive Processes

Transition Systems and Interactive Processes
Equivalences on Interactive Processes
Algorithmic Computation of Equivalences
Application Example: A Distributed Mail System
Discussion

3. Markov Chains

Stochastic Processes
Discrete-Time Markov Chains
Continuous-Time Markov Chains
Analysing Markov Chains
Equivalences on Markov Chains
Algorithmic Computation of Equivalences
Discussion

4. Interactive Markov Chains

Design Decisions
Interactive Markov Chains
Strong Bisimilarity
Weak Bisimilarity
Algorithmic Computation
Application Example: Leaky Bucket
Discussion

5. Algebra of Interactive Markov Chains

Basic Language
Strong Bisimilarity and Weak C ongruence
Algebra of Strong Bisimilarity and Weak Congruence
Parallel Composition and Abstraction
Time Constraints and Symmetric Composition
Discussion

6. Interactive Markov Chains in Practice

State Space Aggregation by Example
Application Study: An Ordinary Telephony System
Nondeterminism and Underspecification
Discussion

7. Conclusion

Major Achievements
Has the Challenge Been Met?
The Challenge Continues

A. Proofs for Chapter 3 and Chapter 4
B. Proofs for Chapter 5

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Holger Hermanns
Parution	18/11/2002
Nb. de pages	230
Format	15,5 x 23,5
Couverture	Broché
Poids	351g
Intérieur	Noir et Blanc
EAN13	9783540442615