Configurable numerical solutions of stochastic models

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Vörös András
Department of Measurement and Information Systems

Ensuring the correctness of critical systems – such as safety-critical, distributed and cloud applications – requires the rigorous analysis of the functional and extra-functional properties of the system. A large class of typical quantitative questions regarding dependability and performability are usually addressed by stochastic analysis.

Recent critical systems are often distributed/asynchronous, leading to the well-known phenomenon of \emph{state space explosion}. The size and complexity of such systems often prevents the success of the analysis due to the high sensitivity to the number of possible behaviors. In addition, temporal characteristics of the components can easily lead to huge computational overhead.

Calculation of dependability and performability measures can be reduced to steady-state and transient solutions of Markovian models. Various approaches are known in the literature for these problems differing in the representation of the stochastic behavior of the models or in the applied numerical algorithms. The efficiency of these approaches are influenced by various characteristics of the models, therefore no single best approach is known.

In this thesis we present numerical solution algorithms for the steady state and transient analysis of Markovian models. Various algorithms were implemented with configurable data structure and linear algebra operations.

Our framework provides configurable stochastic analysis: an approach is introduced to combine different matrix representations of stochastic behaviors with numerical solution algorithms for steady-state, transient, mean-time-to-first-failure and sensitivity problems.

The goal of our work is to introduce a framework that facilitates the analysis of complex, stochastic systems by combining the advantages of compact matrix representations and various numerical algorithms. The analysis tool is integrated into the PetriDotNet modeling application.

Benchmarks and industrial case studies are used to evaluate the applicability of our approach.


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