This paper reviews the model of interactive Markov chains (IMCs, for short), an extension of labelled transition systems with exponentially delayed transitions. We show that IMCs are closed under parallel composition and hiding, and show how IMCs can be compositionally aggregated prior to analysis by e.g., bisimulation minimisation or aggressive abstraction based on simulation pre-congruences. We survey some recent analysis techniques for IMCs, i.e., explaining how measures such as reachability probabilities can be obtained. Finally, we demonstrate that IMCs are a natural (and simple) semantic model for stochastic process algebras and generalised stochastic Petri nets and can be used for engineering formalisms such as AADL and dynamic fault trees.
|Title of host publication||Symposium on Formal Methods for Components and Objects, FMCO 2009|
|Editors||F.S de Boer, S.H. Bonsangue, M Leuschel|
|Place of Publication||Berlin|
|Number of pages||27|
|Publication status||Published - 2010|
|Name||Lecture Notes in Computer Science|
Hermanns, H., & Katoen, J. P. (2010). The How and Why of Interactive Markov Chains. In F. S. de Boer, S. H. Bonsangue, & M. Leuschel (Eds.), Symposium on Formal Methods for Components and Objects, FMCO 2009 (pp. 311-337). (Lecture Notes in Computer Science; Vol. 6286). Berlin: Springer. https://doi.org/10.1007/978-3-642-17071-3_16