## Interactive Markov Chains: The Quest for Quantified QualityMarkov 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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### Contents

1 Introduction | 1 |

2 Interactive Processes | 7 |

3 Markov Chains | 35 |

4 Interactive Markov Chains | 56 |

5 Algebra of Interactive Markov Chains | 89 |

6 Interactive Markov Chains in Practice | 129 |

7 Conclusion | 155 |

A Proofs for Chapter 3 and Chapter 4 | 160 |

B Proofs for Chapter 5 | 174 |

Bibliography | 207 |

### Other editions - View all

Interactive Markov Chains: The Quest for Quantified Quality Holger Hermanns No preview available - 2002 |

Interactive Markov Chains: The Quest for Quantified Quality Holger Hermanns No preview available - 2014 |

### Common terms and phrases

according to Definition action transitions algorithm arbitrary expressions assume axiomatisation behaviour buffer Chapter compositional aggregation compute constraint contains CTMC defined Deﬁnition delay denote depicted in Figure discrete-time DTMC elapse operator equivalence classes equivalence relation example exponentially distributed ﬁrst function ill-definedness IMCL IMCXXL implies Q induction Interactive Markov Chains interactive processes interactive transitions interleaving internal transitions Lemma Markov property Markovian chains Markovian transitions maximal progress means multiset nondeterminism nondeterministic notion O(mI obtain operational semantics parallel composition Petri nets phase-type distribution possible probabilistic chain probabilistic transitions probability process algebra proof provably satisfy queueing recursion satisﬁes Section semantics sound and complete specification splitters stochastic process strong bisimilarity strong bisimulation strongly guarded symmetric composition synchronisation Table TCPart Theorem time-divergent tion transition relation transition system User1 weak bisimilarity weak bisimulation weak congruence weakly guarded λ λ