P\(^3\)-Folder: Optimal Model Simplification for Improving Accuracy in Process Performance Prediction

  • Arik Senderovich
  • Alexander Shleyfman
  • Matthias WeidlichEmail author
  • Avigdor Gal
  • Avishai Mandelbaum
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9850)


Operational process models such as generalised stochastic Petri nets (GSPNs) are useful when answering performance queries on business processes (e.g. ‘how long will it take for a case to finish?’). Recently, methods for process mining have been developed to discover and enrich operational models based on a log of recorded executions of processes, which enables evidence-based process analysis. To avoid a bias due to infrequent execution paths, discovery algorithms strive for a balance between over-fitting and under-fitting regarding the originating log. However, state-of-the-art discovery algorithms address this balance solely for the control-flow dimension, neglecting possible over-fitting in terms of performance annotations. In this work, we thus offer a technique for performance-driven model reduction of GSPNs, using structural simplification rules. Each rule induces an error in performance estimates with respect to the original model. However, we show that this error is bounded and that the reduction in model parameters incurred by the simplification rules increases the accuracy of process performance prediction. We further show how to find an optimal sequence of applying simplification rules to obtain a minimal model under a given error budget for the performance estimates. We evaluate the approach with a real-world case in the healthcare domain, showing that model simplification indeed yields significant improvements in time prediction accuracy.



This work was partially supported by the German Research Foundation (DFG), grant WE 4891/1-1.


  1. 1.
    Dumas, M., Rosa, M.L., Mendling, J., Reijers, H.A.: Fundamentals of Business Process Management. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  2. 2.
    Rogge-Solti, A., Weske, M.: Prediction of remaining service execution time using stochastic petri nets with arbitrary firing delays. In: Basu, S., Pautasso, C., Zhang, L., Fu, X. (eds.) ICSOC 2013. LNCS, vol. 8274, pp. 389–403. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  3. 3.
    Senderovich, A., Weidlich, M., Gal, A., Mandelbaum, A.: Queue mining – predicting delays in service processes. In: Jarke, M., Mylopoulos, J., Quix, C., Rolland, C., Manolopoulos, Y., Mouratidis, H., Horkoff, J. (eds.) CAiSE 2014. LNCS, vol. 8484, pp. 42–57. Springer, Heidelberg (2014)Google Scholar
  4. 4.
    van der Aalst, W.M.P.: Process Mining: Discovery, Conformance and Enhancement of Business Processes. Springer, Heidelberg (2011)CrossRefzbMATHGoogle Scholar
  5. 5.
    van der Aalst, W.M.P., Rubin, V., Verbeek, H., van Dongen, B.F., Kindler, E., Günther, C.W.: Process mining: a two-step approach to balance between underfitting and overfitting. Softw. Syst. Model. 9(1), 87–111 (2010)CrossRefGoogle Scholar
  6. 6.
    Buijs, J.C.A.M., van Dongen, B.F., van der Aalst, W.M.P.: On the role of fitness, precision, generalization and simplicity in process discovery. In: Meersman, R., Panetto, H., Dillon, T., Rinderle-Ma, S., Dadam, P., Zhou, X., Pearson, S., Ferscha, A., Bergamaschi, S., Cruz, I.F. (eds.) OTM 2012, Part I. LNCS, vol. 7565, pp. 305–322. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  7. 7.
    van Zelst, S.J., van Dongen, B.F., van der Aalst, W.M.P.: Avoiding over-fitting in ILP-based process discovery. In: Motahari-Nezhad, H.R., Recker, J., Weidlich, M. (eds.) BPM. LNCS, vol. 9253, pp. 163–171. Springer, Heidelberg (2015)Google Scholar
  8. 8.
    Senderovich, A., Rogge-Solti, A., Gal, A., Mendling, J., Mandelbaum, A., Kadish, S., Bunnell, C.A.: Data-driven performance analysis of scheduled processes. In: Motahari-Nezhad, H.R., Recker, J., Weidlich, M. (eds.) BPM. LNCS, vol. 9253, pp. 35–52. Springer, Heidelberg (2015)Google Scholar
  9. 9.
    van der Aalst, W.M.P., Schonenberg, M., Song, M.: Time prediction based on process mining. Inf. Syst. 36(2), 450–475 (2011)CrossRefGoogle Scholar
  10. 10.
    de Leoni, M., van der Aalst, W.M., Dees, M.: A general process mining framework for correlating, predicting and clustering dynamic behavior based on event logs. Inf. Syst. 56, 235–257 (2016)CrossRefGoogle Scholar
  11. 11.
    Leontjeva, A., Conforti, R., Di Francescomarino, C., Dumas, M., Maggi, F.M.: Complex symbolic sequence encodings for predictive monitoring of business processes. In: Motahari-Nezhad, H.R., Recker, J., Weidlich, M. (eds.) BPM, vol. 9253, pp. 297–313. Springer, Heidelberg (2015)Google Scholar
  12. 12.
    Rogge-Solti, A., van der Aalst, W.M., Weske, M.: Discovering stochastic petri nets with arbitrary delay distributions from event logs. In: Lohmann, N., Song, M., Wohed, P. (eds.) BPM 2013, vol. 171, pp. 15–27. Springer, Heidelberg (2013)Google Scholar
  13. 13.
    Rozinat, A., Mans, R., Song, M., van der Aalst, W.M.P.: Discovering simulation models. Inf. Syst. 34(3), 305–327 (2009)CrossRefGoogle Scholar
  14. 14.
    Leemans, S.J., Fahland, D., van der Aalst, W.M.: Discovering block-structured process models from event logs containing infrequent behaviour. In: Lohmann, N., Song, M., Wohed, P. (eds.) BPM Workshops, vol. 171, pp. 66–78. Springer, Heidelberg (2014)Google Scholar
  15. 15.
    Marsan, M.A., Balbo, G., Conte, G., Donatelli, S., Franceschinis, G.: Modelling with Generalized Stochastic Petri Nets. Wiley, Hoboken (1994)zbMATHGoogle Scholar
  16. 16.
    Bolch, G., Greiner, S., de Meer, H., Trivedi, K.S.: Queueing Networks and Markov Chains - Modeling and Performance Evaluation with Computer Science Applications. Wiley, Hoboken (2006)CrossRefzbMATHGoogle Scholar
  17. 17.
    Whitt, W.: The queueing network analyzer. Bell Syst. Tech. J. 62(9), 2779–2815 (1983)CrossRefGoogle Scholar
  18. 18.
    van der Aalst, W.M., Ter Hofstede, A.H., Kiepuszewski, B., Barros, A.P.: Workflow patterns. Distrib. Parallel Databases 14(1), 5–51 (2003)CrossRefGoogle Scholar
  19. 19.
    Hall, R.W.: Queueing methods for services and manufacturing (1990)Google Scholar
  20. 20.
    Balsamo, S., Marin, A.: Composition of product-form generalized stochastic petri nets: a modular approach. In: Proceedings of the ESM, pp. 26–28 (2009)Google Scholar
  21. 21.
    Vanhatalo, J., Völzer, H., Koehler, J.: The refined process structure tree. Data Knowl. Eng. (DKE) 68(9), 793–818 (2009)CrossRefGoogle Scholar
  22. 22.
    Polyvyanyy, A., Vanhatalo, J., Völzer, H.: Simplified computation and generalization of the refined process structure tree. In: Bravetti, M. (ed.) WS-FM 2010. LNCS, vol. 6551, pp. 25–41. Springer, Heidelberg (2011)Google Scholar
  23. 23.
    Shaw, D.X., Cho, G.: The critical-item, upper bounds, and a branch-and-bound algorithm for the tree knapsack problem. Networks 31(4), 205–216 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning. Springer Series in Statistics. Springer New York Inc., New York (2001)CrossRefzbMATHGoogle Scholar
  25. 25.
    Smirnov, S., Reijers, H.A., Weske, M., Nugteren, T.: Business process model abstraction: a definition, catalog, and survey. Distrib. Parallel Databases 30(1), 63–99 (2012)CrossRefGoogle Scholar
  26. 26.
    Resnick, S.I.: Adventures in Stochastic Processes. Springer Science & Business Media, New York (2013)zbMATHGoogle Scholar
  27. 27.
    Günther, C.W., van der Aalst, W.M.P.: Fuzzy mining – adaptive process simplification based on multi-perspective metrics. In: Alonso, G., Dadam, P., Rosemann, M. (eds.) BPM 2007. LNCS, vol. 4714, pp. 328–343. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  28. 28.
    Mafazi, S., Grossmann, G., Mayer, W., Schrefl, M., Stumptner, M.: Consistent abstraction of business processes based on constraints. J. Data Semant. 4(1), 59–78 (2014)CrossRefGoogle Scholar
  29. 29.
    Zerguini, L.: On the estimation of the response time of the business process. In: 17th UK Performance Engineering Workshop, University of Leeds. Citeseer (2001)Google Scholar
  30. 30.
    Zerguini, L., van Hee, K.M.: A new reduction method for the analysis of large workflow models. In: Promise, pp. 188–201 (2002)Google Scholar
  31. 31.
    Balbo, G., Bruell, S.C., Ghanta, S.: Combining queueing networks and generalized stochastic petri nets for the solution of complex models of system behavior. IEEE Trans. Comput. 37(10), 1251–1268 (1988)CrossRefzbMATHGoogle Scholar
  32. 32.
    Ciardo, G., Trivedi, K.S.: A decomposition approach for stochastic petri net models. In: Petri Nets and Performance Models, pp. 74–83. IEEE (1991)Google Scholar
  33. 33.
    Woodside, C.M., Li, Y.: Performance petri net analysis of communications protocol software by delay-equivalent aggregation. In: Petri Nets and Performance Models, pp. 64–73. IEEE (1991)Google Scholar
  34. 34.
    Freiheit, J., Billington, J.: New developments in closed-form computation for GSPN aggregation. In: Dong, J.S., Woodcock, J. (eds.) ICFEM 2003. LNCS, vol. 2885, pp. 471–490. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  35. 35.
    Fahland, D., Van Der Aalst, W.M.P.: Simplifying discovered process models in a controlled manner. Inf. Syst. 38(4), 585–605 (2013)CrossRefGoogle Scholar
  36. 36.
    Gurobi Optimization Inc: Gurobi Optimizer Reference Manual (2015).

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Arik Senderovich
    • 1
  • Alexander Shleyfman
    • 1
  • Matthias Weidlich
    • 2
    Email author
  • Avigdor Gal
    • 1
  • Avishai Mandelbaum
    • 1
  1. 1.Technion–Israel Institute of TechnologyHaifaIsrael
  2. 2.Humboldt-Universität zu BerlinBerlinGermany

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