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Optimizing Performance of Continuous-Time Stochastic Systems Using Timeout Synthesis

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Quantitative Evaluation of Systems (QEST 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9259))

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Abstract

We consider parametric version of fixed-delay continuous-time Markov chains (or equivalently deterministic and stochastic Petri nets, DSPN) where fixed-delay transitions are specified by parameters, rather than concrete values. Our goal is to synthesize values of these parameters that, for a given cost function, minimise expected total cost incurred before reaching a given set of target states. We show that under mild assumptions, optimal values of parameters can be effectively approximated using translation to a Markov decision process (MDP) whose actions correspond to discretized values of these parameters. To this end we identify and overcome several interesting phenomena arising in systems with fixed delays.

The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement \(\text {n}^\circ \) [291734]. This work is partly supported by the German Research Council (DFG) as part of the Transregional Collaborative Research Center AVACS (SFB/TR 14), by the EU 7th Framework Programme under grant agreement no. 295261 (MEALS) and 318490 (SENSATION), by the Czech Science Foundation, grant No. 15-17564S, and by the CAS/SAFEA International Partnership Program for Creative Research Teams.

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Notes

  1. 1.

    More precisely, all but the largest probability in \(T(s,\mathbf {d})\) are rounded up, the largest probability is suitably rounded down so that the resulting vector adds up to 1.

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Brázdil, T., Korenčiak, Ľ., Krčál, J., Novotný, P., Řehák, V. (2015). Optimizing Performance of Continuous-Time Stochastic Systems Using Timeout Synthesis. In: Campos, J., Haverkort, B. (eds) Quantitative Evaluation of Systems. QEST 2015. Lecture Notes in Computer Science(), vol 9259. Springer, Cham. https://doi.org/10.1007/978-3-319-22264-6_10

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