Quantitative Timed Analysis of Interactive Markov Chains

Abstract This paper presents new algorithms and accompanying tool support for analyzing interactive Markov chains (IMCs), a stochastic timed 1 1 2-player game in which delays are exponentially distributed. IMCs are compositional and act as semantic model for engineering for-malisms such as AADL and dynamic fault trees. We provide algorithms for determining the extremal expected time of reaching a set of states, and the long-run average of time spent in a set of states. The prototypical tool Imca supports these algorithms as well as the synthesis of ε-optimal piecewise constant timed policies for timed reachability objectives. Two case studies show the feasibility and scalability of the algorithms.

A tutorial on interactive Markov chains

Interactive Markov chains (IMCs) constitute a powerful sto- chastic model that extends both continuous-time Markov chains and labelled transition systems. IMCs enable a wide range of modelling and analysis techniques and serve as a semantic model for many industrial and scientific formalisms, such as AADL, GSPNs and many more. Applications cover various engineering contexts ranging from industrial system-on-chip manufacturing to satellite designs. We present a survey of the state-of-the-art in modelling and analysis of IMCs.\ud We cover a set of techniques that can be utilised for compositional modelling, state space generation and reduction, and model checking. The significance of the presented material and corresponding tools is highlighted through multiple case studies

On Statistical Model Checking of Stochastic Systems

Statistical methods to model check stochastic systems have been, thus far, developed only for a sublogic of continuous stochastic logic (CSL) that does not have steady state operators and unbounded until formulas. In this paper, we present a statistical model checking algorithm that also verifies CSL formulas with unbounded untils. The algorithm is based on Monte Carlo simulation of the model and hypothesis testing of the samples, as opposed to sequential hypothesis testing. The use of statistical hypothesis testing allows us to exploit the inherent parallelism in this approach. We have implemented the algorithm in a tool called VESTA, and found it to be effective in verifying several examples

Finite projective planes with a large abelian group

Markov automata (MA) constitute an expressive continuous-time compositional modelling formalism. They appear as semantic backbones for engineering frameworks including dynamic fault trees, Generalised Stochastic Petri Nets, and AADL. Their expressive power has thus far precluded them from effective analysis by probabilistic (and statistical) model checkers, stochastic game solvers, or analysis tools for Petri net-like formalisms. This paper presents the foundations and underlying algorithms for efficient MA modelling, reduction using static analysis, and most importantly, quantitative analysis. We also discuss implementation pragmatics of supporting tools and present several case studies demonstrating feasibility and usability of MA in practice

Review of International Geographical Education online : RIGEO

Application areas such as multimedia equipment, communication protocols and networks often feature systems which exhibit both probabilistic and timed behaviour. In this paper, we consider analysis of such probabilistic timed systems using the technique of model checking, in which it is verified automatically whether a system satisfies a certain desired property. In order to describe formally probabilistic timed systems, we consider probabilistic extensions of timed automata, such as real-time probabilistic processes, probabilistic timed automata and continuous probabilistic timed automata, the underlying semantics of each of which is an infinite-state structure. For each formalism, we consider how the well-known region equivalence relation can be used to reduce the infinite state-space model into a finite-state system, which can then be used for model checking