Delayed Nondeterminism in Continuous-Time Markov Decision Processes

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 historydependent (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.