Polynomial analysis algorithms for free choice Probabilistic Workflow Nets

We introduce Probabilistic Workflow Nets (PWNs), a model extending confusion-free workflow Petri nets with probabilities. We give PWNs a semantics in terms of Markov Decision Processes (MDPs) and introduce a reward model. We show that the expected reward of a complete execution of a PWN is independent of the scheduler used to resolve the nondeterminism of the MDP, which allows one to choose a suitable scheduler for its computation. However, this feature does not lead to a polynomial algorithm, and in fact we prove that deciding whether the expected reward exceeds a given threshold is PSPACE-hard. To alleviate this high computational cost, we extend previous work on property preserving reductions of non-probabilistic workflow nets. We introduce reduction rules for PWNs, and prove that they preserve the expected reward. The rules allow us to simplify the workflow before constructing its MDP. We then consider the subclass of free-choice PWNs, whose non-probabilistic counterpart has been extensively studied. Using a previous result on the power of the rules for this class, published by us in FASE'16, we derive a polynomial-time algorithm in the size of the PWN for the computation of the expected reward. In contrast, algorithms based on constructing the MDP require exponential time. We report on a sample implementation of the reduction algorithm and on its performance on a collection of benchmarks. Finally, we present two extensions of our work. First, we show that our reduction rules can also be used to compute the expected reward parametrically, that is, as a function of parameters related to the probabilities and rewards of the transitions. Second, we discuss the extension of PWNs to workflow nets that are not confusion-free, and show that some of our results still hold. (c) 2017 Elsevier B.V. All rights reserved.