Delayed Nondeterminism in Continuous-Time Markov Decision Processes

  • Authors:

  • Martin R. Neuhäußer;Mariëlle Stoelinga;Joost-Pieter Katoen

  • Affiliations:

  • MOVES Group, RWTH Aachen University, Germany and FMT Group, University of Twente, The Netherlands;FMT Group, University of Twente, The Netherlands;MOVES Group, RWTH Aachen University, Germany and FMT Group, University of Twente, The Netherlands

  • Venue:
  • FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
  • Year:
  • 2009

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Abstract

Schedulers in randomly timed games can be classified as to whether they use timing information or not. We consider continuous-time Markov decision processes (CTMDPs) and define a hierarchy of positional (P) and history-dependent (H) schedulers which induce strictly tighter bounds on quantitative properties on CTMDPs. This classification into time abstract (TA), total time (TT) and fully time-dependent (T) schedulers is mainly based on the kind of timing details that the schedulers may exploit. We investigate when the resolution of nondeterminism may be deferred. In particular, we show that TTP and TAP schedulers allow for delaying nondeterminism for all measures, whereas this does neither hold for TP nor for any TAH scheduler. The core of our study is a transformation on CTMDPs which unifies the speed of outgoing transitions per state.