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We study time-bounded reachability in continuous-time Markov decisionprocesses for time-abstract scheduler classes. Such reachability problems playa paramount role in dependability analysis and the modelling of manufacturingand queueing systems. Consequently, their analysis has been studiedintensively, and techniques for the approximation of optimal control are wellunderstood. From a mathematical point of view, however, the question ofapproximation is secondary compared to the fundamental question whether or notoptimal control exists.  We demonstrate the existence of optimal schedulers for the time-abstractscheduler classes for all CTMDPs. Our proof is constructive: We show how tocompute optimal time-abstract strategies with finite memory. It turns out thatthese optimal schedulers have an amazingly simple structure - they converge toan 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: Weshow that both players have a likewise simple optimal strategy in these moregeneral structures.

Optimal Time-Abstract Schedulers for CTMDPs and Markov Games