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May I Take Your Order?

On the Interplay Between Time and Order in Process Mining

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


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.


  • Process mining
  • Event data
  • Partial orders
  • Uncertainty

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  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,


  1. van der Aa, H., Leopold, H., Weidlich, M.: Partial order resolution of event logs for process conformance checking. Decis. Support Syst. 136, 113347 (2020)

    CrossRef  Google Scholar 

  2. van der Aalst, W.M.P.: Process Mining: Data Science in Action. Springer, Heidelberg (2016).

    CrossRef  Google Scholar 

  3. Andrews, R., van Dun, C.G.J., Wynn, M.T., Kratsch, W., Röglinger, M.K.E., ter Hofstede, A.H.M.: Quality-informed semi-automated event log generation for process mining. Decis. Support Syst. 132, 113265 (2020)

    CrossRef  Google Scholar 

  4. Bergenthum, R., Desel, J., Mauser, S., Lorenz, R.: Synthesis of petri nets from term based representations of infinite partial languages. Fund. Inform. 95(1), 187–217 (2009)

    Google Scholar 

  5. Carmona, J., van Dongen, B., Solti, A., Weidlich, M.: Conformance Checking: Relating Processes and Models. Springer, Cham (2018).

    CrossRef  Google Scholar 

  6. Conforti, R., La Rosa, M., ter Hofstede, A.H.M., Augusto, A.: Automatic repair of same-timestamp errors in business process event logs. In: Fahland, D., Ghidini, C., Becker, J., Dumas, M. (eds.) BPM 2020. LNCS, vol. 12168, pp. 327–345. Springer, Cham (2020).

    CrossRef  Google Scholar 

  7. Desel, J.: Validation of process models by construction of process nets. In: van der Aalst, W., Desel, J., Oberweis, A. (eds.) Business Process Management. LNCS, vol. 1806, pp. 110–128. Springer, Heidelberg (2000).

    CrossRef  Google Scholar 

  8. van Dongen, B.F., Desel, J., van der Aalst, W.M.P.: Aggregating causal runs into workflow nets. In: Jensen, K., van der Aalst, W.M., Ajmone Marsan, M., Franceschinis, G., Kleijn, J., Kristensen, L.M. (eds.) Transactions on Petri Nets and Other Models of Concurrency VI. LNCS, vol. 7400, pp. 334–363. Springer, Heidelberg (2012).

    CrossRef  Google Scholar 

  9. Lu, X., Fahland, D., van der Aalst, W.M.P.: Conformance checking based on partially ordered event data. In: Fournier, F., Mendling, J. (eds.) BPM 2014. LNBIP, vol. 202, pp. 75–88. Springer, Cham (2015).

    CrossRef  Google Scholar 

  10. Mans, R., van der Aalst, W.M.P., Vanwersch, R.: Process Mining in Healthcare: Evaluating and Exploiting Operational Healthcare Processes. Springer Briefs in Business Process Management, Springer, Cham (2015).

    CrossRef  Google Scholar 

  11. Martin, N.: Data quality in process mining. In: Fernandez-Llatas, C. (ed.) Interactive Process Mining in Healthcare. Health Informatics, pp. 53–79. Springer, Cham (2021).

    CrossRef  Google Scholar 

  12. Pegoraro, M., van der Aalst, W.M.P.: Mining uncertain event data in process mining. In: Carmona, J., Jans, M., La Rosa, M. (eds.) International Conference on Process Mining (ICPM 2019), Aachen, Germany, pp. 89–96. IEEE Computer Society (2019)

    Google Scholar 

  13. Pegoraro, M., Uysal, M.S., van der Aalst, W.M.P.: Efficient construction of behavior graphs for uncertain event data. In: Abramowicz, W., Klein, G. (eds.) BIS 2020. LNBIP, vol. 389, pp. 76–88. Springer, Cham (2020).

    CrossRef  Google Scholar 

  14. Reinkemeyer, L.: Process Mining in Action: Principles, Use Cases and Outlook. Springer, Cham (2020).

    CrossRef  Google Scholar 

  15. Suriadi, S., Andrews, R., ter Hofstede, A.H.M., Wynn, M.T.: Event log imperfection patterns for process mining: towards a systematic approach to cleaning event logs. Inf. Syst. 64, 132–150 (2017)

    CrossRef  Google Scholar 

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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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Correspondence to Wil M. P. van der Aalst .

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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.

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