Configurable numerical analysis for stochastic systems

Abstract

Abstract-Stochastic aspects of complex systems require more and more involved analysis approaches. Answering reachability and related analysis questions can often be reduced to steadystate, transient, reward or sensitivity value analysis of stochastic models. In this paper we introduce a configurable stochastic analysis framework which supports the user to combine explicit, symbolic and numerical algorithms to efficiently compute the measures of stochastic models. Beyond the well-known algorithms from the field, we also developed an experimental version of an Induced Dimensionality Reduction Stabilized numerical solver to compute steady-state probabilities of Markovian models. As far as we know, this is the first attempt to exploit this algorithm in stochastic analysis. We have conducted experiments on different combinations of the algorithms on various models to assess their advantages and disadvantages in the analysis. This information can be used by the user to choose the combination of algorithms being efficient solving the analysis problem.

Industrial applications of the PetriDotNet modelling and analysis tool

“…In addition, we compared the various configurations of the algorithms and we also experimented with the extended algorithm of IDR(s)STAB(ℓ). These findings were summarized in [49].…”

“…Thus, the run time and memory trade-off can be tuned according to the user's preference. However, despite our modifications to the algorithm in [49], convergence behaviour with CTMC generator matrices remained unsatisfactory, as their rank deficiency seems to pose an obstacle for the algorithm.…”