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Tweaking the Odds in Probabilistic Timed Automata

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Quantitative Evaluation of Systems (QEST 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12846))

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Abstract

We consider probabilistic timed automata (PTA) in which probabilities can be parameters, i.e. symbolic constants. They are useful to model randomised real-time systems where exact probabilities are unknown, or where the probability values should be optimised. We prove that existing techniques to transform probabilistic timed automata into equivalent finite-state Markov decision processes (MDPs) remain correct in the parametric setting, using a systematic proof pattern. We implemented two of these parameter-preserving transformations—using digital clocks and backwards reachability—in the Modest Toolset. Using Storm ’s parameter space partitioning approach, parameter values can be efficiently synthesized in the resulting parametric MDPs. We use several case studies from the literature of varying state and parameter space sizes to experimentally evaluate the performance and scalability of this novel analysis trajectory for parametric PTA.

This work was funded by DFG RTG 2236 “UnRAVeL”, DFG grant 433044889 PASIWY, NWO grant OCENW.KLEIN.311, and NWO VENI grant 639.021.754.

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Data Availability

The tools used and data generated in our experimental evaluation are archived at DOI 10.4121/14910426 [29].

Notes

  1. 1.

    Parameter regions should not be confused with the regions of clock valuations as in the classic region graph construction for a (P)TA.

  2. 2.

    Existential Theory of the Reals. ETR problems are between NP and PSPACE, and ETR-hard problems are as hard as finding the roots of a multi-variate polynomial.

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Authors and Affiliations

  1. University of Twente, Enschede, The Netherlands

    Arnd Hartmanns, Joost-Pieter Katoen & Bram Kohlen

  2. RWTH Aachen University, Aachen, Germany

    Joost-Pieter Katoen & Jip Spel

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  1. Arnd Hartmanns
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  2. Joost-Pieter Katoen
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  3. Bram Kohlen
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  4. Jip Spel
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Correspondence to Arnd Hartmanns .

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Editors and Affiliations

  1. University of Oxford, Oxford, UK

    Alessandro Abate

  2. Ca’ Foscari University of Venice, Venice, Italy

    Andrea Marin

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Hartmanns, A., Katoen, JP., Kohlen, B., Spel, J. (2021). Tweaking the Odds in Probabilistic Timed Automata. In: Abate, A., Marin, A. (eds) Quantitative Evaluation of Systems. QEST 2021. Lecture Notes in Computer Science(), vol 12846. Springer, Cham. https://doi.org/10.1007/978-3-030-85172-9_3

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