Optimal Time-Abstract Schedulers for CTMDPs and Markov Games

Markus Rabe
(Saarland University)
Sven Schewe
(University of Liverpool)

We study time-bounded reachability in continuous-time Markov decision processes for time-abstract scheduler classes. Such reachability problems play a paramount role in dependability analysis and the modelling of manufacturing and queueing systems. Consequently, their analysis has been studied intensively, and techniques for the approximation of optimal control are well understood. From a mathematical point of view, however, the question of approximation is secondary compared to the fundamental question whether or not optimal control exists.

We demonstrate the existence of optimal schedulers for the time-abstract scheduler classes for all CTMDPs. Our proof is constructive: We show how to compute optimal time-abstract strategies with finite memory. It turns out that these optimal schedulers have an amazingly simple structure—they converge to an easy-to-compute memoryless scheduling policy after a finite number of steps.

Finally, we show that our argument can easily be lifted to Markov games: We show that both players have a likewise simple optimal strategy in these more general structures.

In Alessandra Di Pierro and Gethin Norman: Proceedings Eighth Workshop on Quantitative Aspects of Programming Languages (QAPL 2010), Paphos, Cyprus, 27-28th March 2010 , Electronic Proceedings in Theoretical Computer Science 28, pp. 144–158.
Published: 26th June 2010.

ArXived at: http://dx.doi.org/10.4204/EPTCS.28.10 bibtex PDF

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