Mean-Payoff Optimization in Continuous-Time Markov Chains with Parametric Alarms

Christel BaierChristel Baier, Clemens DubslaffClemens Dubslaff, Ľuboš KorenčiakĽuboš Korenčiak, Antonín KučeraAntonín Kučera, Vojtěch ŘehákVojtěch Řehák

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Christel Baier, Clemens Dubslaff, Ľuboš Korenčiak, Antonín Kučera, Vojtěch Řehák
Mean-Payoff Optimization in Continuous-Time Markov Chains with Parametric Alarms
Proc. of the 14th International Conference on Quantitative Evaluation of Systems (QEST), volume 10503 of Lecture Notes in Computer Science, 190--206, 2017. Springer

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KurzfassungAbstract
Continuous-time Markov chains with alarms (ACTMCs) allow for alarm events that can be non-exponentially distributed. Within parametric ACTMCs, the parameters of alarm-event distributions are not given explicitly and can be subject of parameter synthesis. An algorithm solving the -optimal parameter synthesis problem for parametric ACTMCs with long-run average optimization objectives is presented. Our approach is based on reduction of the problem to finding long-run average optimal strategies in semi-Markov decision processes (semi-MDPs) and sufficient discretization of parameter (i.e., action) space. Since the set of actions in the discretized semi-MDP can be very large, a straightforward approach based on explicit action-space construction fails to solve even simple instances of the problem. The presented algorithm uses an enhanced policy iteration on symbolic representations of the action space. The soundness of the algorithm is established for parametric ACTMCs with alarm-event distributions satisfying four mild assumptions that are shown to hold for uniform, Dirac, exponential, and Weibull distributions in particular, but are satisfied for many other distributions as well. An experimental implementation shows that the symbolic technique substantially improves the efficiency of the synthesis algorithm and allows to solve instances of realistic size.
Forschungsgruppe:Research Group: Algebraische und logische Grundlagen der InformatikAlgebraic and Logical Foundations of Computer Science

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-66335-7_12.

@inproceedings{BDKK{2017,
  author    = {Christel Baier and Clemens Dubslaff and {\v{L}}ubo{\v{s}}
               Koren{\v{c}}iak and Anton{\'{\i}}n Ku{\v{c}}era and Vojt{\v{e}}ch
               {\v{R}}eh{\'{a}}k},
  title     = {Mean-Payoff Optimization in Continuous-Time Markov Chains with
               Parametric Alarms},
  booktitle = {Proc. of the 14th International Conference on Quantitative
               Evaluation of Systems (QEST)},
  series    = {Lecture Notes in Computer Science},
  volume    = {10503},
  publisher = {Springer},
  year      = {2017},
  pages     = {190--206},
  doi       = {10.1007/978-3-319-66335-7_12}
}