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Polynomial Analysis Algorithms for Free Choice Probabilistic Workflow Nets

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Quantitative Evaluation of Systems (QEST 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9826))

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Abstract

We study Probabilistic Workflow Nets (PWNs), a model extending van der Aalst’s workflow nets with probabilities. We give a semantics for PWNs in terms of Markov Decision Processes and introduce a reward model. Using a result by Varacca and Nielsen, we show that the expected reward of a complete execution of the PWN is independent of the scheduler. Extending previous work on reduction of non-probabilistic workflow nets, we present reduction rules that preserve the expected reward. The rules lead to a polynomial-time algorithm in the size of the PWN (not of the Markov decision process) for the computation of the expected reward. In contrast, since the Markov decision process of PWN can be exponentially larger than the PWN itself, all algorithms based on constructing the Markov decision process require exponential time. We report on a sample implementation and its performance on a collection of benchmarks.

This work was funded by the DFG Project “Negotiations: A Model for Tractable Concurrency”.

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Notes

  1. 1.

    In [6] clusters are defined in a slightly different way.

  2. 2.

    In [20], enabled conflict sets are called actions, and markings are called cases.

  3. 3.

    Stated as Theorem 2, the original paper gives this theorem with \(S_1'\) and \(S_2'\) being (non-partial) schedulers. However, in the paper equivalence is only defined for partial schedulers and the schedulers constructed in the proof are also partial.

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Acknowledgments

We thank the anonymous referees for their comments, and especially the one who helped us correct a mistake in Lemmas 2 and 3.

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Authors and Affiliations

  1. Technische Universität München, Munich, Germany

    Javier Esparza & Philipp Hoffmann

  2. National University of Singapore, Singapore, Singapore

    Ratul Saha

Authors
  1. Javier Esparza
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  2. Philipp Hoffmann
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  3. Ratul Saha
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Corresponding author

Correspondence to Philipp Hoffmann .

Editor information

Editors and Affiliations

  1. University of Illinois , Urbana, Illinois, USA

    Gul Agha

  2. University of Antwerp , Antwerp, Belgium

    Benny Van Houdt

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Esparza, J., Hoffmann, P., Saha, R. (2016). Polynomial Analysis Algorithms for Free Choice Probabilistic Workflow Nets. In: Agha, G., Van Houdt, B. (eds) Quantitative Evaluation of Systems. QEST 2016. Lecture Notes in Computer Science(), vol 9826. Springer, Cham. https://doi.org/10.1007/978-3-319-43425-4_6

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  • DOI: https://doi.org/10.1007/978-3-319-43425-4_6

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-43425-4

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