Formal Methods for Industrial Critical Systems
Continuous-time Markov chains (CTMCs) are widely used to describe stochastic phenomena in many diverse areas. They are used to estimate performance and reliability characteristics of various nature, for instance to quantify throughputs of manufacturing systems, to locate bottlenecks in communication systems, or to estimate reliability in aerospace systems. CTMCs are the underlying semantic model of major high level performance modelling formalisms such as stochastic Petri nets, stochastic process algebras, and Markovian queueing networks.
Model checking is a very successful technique to establish correctness of systems from very similar application domains, usually described in terms of a nondeterministic finite-state model. One of the major reasons for the success of model checking tools in practice is the efficient way to cope with the state-space explosion problem, using symbolic (BDD-based) techniques.
In this talk, I will introduce CTMCs and discuss the use of model checking to assess performance and reliability properties of CTMCs. With this approach, properties-of-interest are expressed as formulas of a stochastic extension of the logic CTL and interpreted over CTMCs. Model checking this logic requires the solution of linear systems of equations and of systems of Volterra integral equations. I will outline approximate techniques for solving the equation systems, and present a JAVA implementation of a Markov chain model checker.
My introduction to CTMC model checking will be complemented with a discussion of CTMC model construction techniques. I will survey formal methods that facilitate the construction of large CTMC models. In particular I will focus on high-level formalisms supporting a modern, hierarchical and compositional design methodology. Existing tool support, as well as techniques to combat the state space explosion problem will be discussed.
Note: The content of the following files is part of GMD Report No. 91 and subject to its copyright.
ERCIM FMICS Home Page,
GMD FOKUS Home Page
Last modified: Wednesday, 19-Apr-2000 08:57:51 MET DST, Axel Rennoch