Probabilistic planning problems are typically modeled as a Markov Decision Process (MDP). MDPs, while an otherwise expressive model, allow only for sequential, non-durative actions. This poses severe restrictions in modeling and solving a real world planning problem. We extend the MDP model to incorporate-1) simultaneous action execution, 2) durative actions, and 3) stochastic durations. We develop several algorithms to combat the computational explosion introduced by these features. The key theoretical ideas used in building these algorithms are - modeling a complex problem as an MDP in extended state/action space, pruning of irrelevant actions, sampling of relevant actions, using informed heuristics to guide the search, hybridizing different planners to achieve benefits of both, approximating the problem and replanning. Our empirical evaluation illuminates the different merits in using various algorithms, viz., optimality, empirical closeness to optimality, theoretical error bounds, and speed.
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