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May I Take Your Order?

On the Interplay Between Time and Order in Process Mining

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Business Process Management Workshops (BPM 2021)

Part of the book series: Lecture Notes in Business Information Processing ((LNBIP,volume 436))

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Abstract

Process mining starts from event data. The ordering of events is vital for the discovery of process models. However, the timestamps of events may be unreliable or imprecise. To further complicate matters, also causally unrelated events may be ordered in time. The fact that one event is followed by another does not imply that the former causes the latter. This paper explores the relationship between time and order. Moreover, it describes an approach to preprocess event data having timestamp-related problems. This approach avoids using accidental or unreliable orders and timestamps, creates partial orders to capture uncertainty, and allows for exploiting domain knowledge to (re)order events. Optionally, the approach also generates interleavings to be able to use existing process mining techniques that cannot handle partially ordered event data. The approach has been implemented using ProM and can be applied to any event log.

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Notes

  1. 1.

    We use the shorthand \(\pi _n(e) = \pi (e)(n)\). Note that \(\pi _{ case }(e)\), \(\pi _{ act }(e)\), and \(\pi _{ time }(e)\) denote the case, activity, and timestamp of an event \(e \in E\).

  2. 2.

    For any \(e,e_1,e_2,e_3 \in E\): \(e \nprec _o e\) (irreflexivity), if \(e_1 \prec _o e_2\) and \(e_2 \prec _o e_3\), then \(e_1 \prec _o e_3\) (transitivity), and if \(e_1 \prec _o e_2\), then \(e_2 \nprec _o e_1\) (asymmetry).

  3. 3.

    Recall that negative transitivity means that if \(e_1 \nprec _t e_2\) and \(e_2 \nprec _t e_3\), then \(e_1 \nprec _t e_3\). In a strict weak ordering, incomparability is transitive, i.e., \(e_1 \sim _t e_2 \ \wedge \ e_2 \sim _t e_3 \Rightarrow e_1 \sim _t e_3\).

  4. 4.

    Road Traffic Fine Management Process, 4TU.ResearchData, https://doi.org/10.4121/uuid:270fd440-1057-4fb9-89a9-b699b47990f5.

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Acknowledgments

We thank the Alexander von Humboldt (AvH) Stiftung and the NHR Center for Computational Engineering Sciences (NHR4CES) for supporting our research.

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Authors and Affiliations

  1. Process and Data Science (Informatik 9), RWTH Aachen University, Aachen, Germany

    Wil M. P. van der Aalst & Luis Santos

  2. Fraunhofer-Institut für Angewandte Informationstechnik (FIT), Sankt Augustin, Germany

    Wil M. P. van der Aalst

Authors
  1. Wil M. P. van der Aalst
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  2. Luis Santos
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Correspondence to Wil M. P. van der Aalst .

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Editors and Affiliations

  1. Sapienza University of Rome, Rome, Italy

    Andrea Marrella

  2. University of St. Gallen, St. Gallen, Switzerland

    Barbara Weber

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van der Aalst, W.M.P., Santos, L. (2022). May I Take Your Order?. In: Marrella, A., Weber, B. (eds) Business Process Management Workshops. BPM 2021. Lecture Notes in Business Information Processing, vol 436. Springer, Cham. https://doi.org/10.1007/978-3-030-94343-1_8

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  • DOI: https://doi.org/10.1007/978-3-030-94343-1_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-94342-4

  • Online ISBN: 978-3-030-94343-1

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