Interactive Markov Chains: And the Quest for Quantified Quality

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.

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.

Introduction....Pages 1-6 Interactive Processes....Pages 7-33 Markov Chains....Pages 35-55 Interactive Markov Chains....Pages 57-88 Algebra of Interactive Markov Chains....Pages 89-128 Interactive Markov Chains in Practice....Pages 129-154 Conclusion....Pages 155-159 Proofs for Chapter 3 and Chapter 4....Pages 161-173 Proofs for Chapter 5....Pages 175-205 The purpose of this book is to provide a compositional methodology of modelling and analysis with Markov chains.