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

Christel BaierChristel Baier, Clemens DubslaffClemens Dubslaff, L'uboš KorenčiakL'uboš Korenčiak, Antonín kučeraAntonín kučera, Vojtěch ŘehákVojtěch Řehák

DOI Link

Christel Baier, Clemens Dubslaff, L'uboš Korenčiak, Antonín kučera, Vojtěch Řehák
Mean-Payoff Optimization in Continuous-Time Markov Chains with Parametric Alarms
ACM Transactions on Modeling and Computer Simulation, 29(4), 2019

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Bibtex

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 the subject of parameter synthesis. In this line, an algorithm is presented that solves the ε-optimal parameter synthesis problem for parametric ACTMCs with long-run average optimization objectives. The approach provided in this article is based on a reduction of the problem to finding long-run average optimal policies in semi-Markov decision processes (semi-MDPs) and sufficient discretization of the parameter (i.e., action) space. Since the set of actions in the discretized semi-MDP can be very large, a straightforward approach based on an 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. Soundness of the algorithm is established for parametric ACTMCs with alarm-event distributions that satisfy four mild assumptions, fulfilled by many kinds of distributions. Exemplifying proofs for the satisfaction of these requirements are provided for Dirac, uniform, exponential, Erlang, and Weibull distributions in particular. An experimental implementation shows that the symbolic technique substantially improves the efficiency of the synthesis algorithm and allows us to solve instances of realistic size.
Forschungsgruppe:Research Group: Algebraische und logische Grundlagen der InformatikAlgebraic and Logical Foundations of Computer Science

@article{BDKk{2019,
  author    = {Christel Baier and Clemens Dubslaff and 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},
  journal   = {ACM Transactions on Modeling and Computer Simulation},
  volume    = {29},
  number    = {4},
  publisher = {Association for Computing Machinery},
  year      = {2019},
  doi       = {10.1145/3310225}
}