As Soon as Probable: Optimal Scheduling under Stochastic Uncertainty

In this paper we continue our investigation of stochastic (and hence dynamic) variants of classical scheduling problems. Such problems can be modeled as duration probabilistic automata (DPA), a well-structured class of acyclic timed automata where temporal uncertainty is interpreted as a bounded uniform distribution of task durations [18]. In [12] we have developed a framework for computing the expected performance of a given scheduling policy. In the present paper we move from analysis to controller synthesis and develop a dynamic-programming style procedure for automatically synthesizing (or approximating) expected time optimal schedulers, using an iterative computation of a stochastic time-to-go function over the state and clock space of the automaton.

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