Abstract
Generalized Stochastic Petri Nets (GSPNs) are an established tool for representing and analyzing concurrency, timing, synchronization, precedence, and priority in processes. GSPNs emerged in the 1980s as the de facto standard for modeling stochastic processes using Petri nets, supported by tools such as GreatSPN. However, traditional applications of this technology assume that GSPNs are created manually. Given the widespread availability of event data in information systems, this seems sub-optimal. This explains the uptake of process mining, which starts from event data instead of manually created process models. There are dozens of techniques to discover basic (i.e., non-stochastic) Petri nets given an event log. However, there is an increasing interest in not just discovering control flow, but also learning the stochastic behavior based on event data. Therefore, we take GSPNs as the target representation for process discovery. Since there are numerous techniques to discover the control flow, we focus on the extensions provided by GSPNs. These include priorities, blocking, probabilities, and rates. In this paper, we sketch a concrete approach to discover probabilities and rates from event data. This is done by translating to GSPNs to Markov chains to which parameter synthesis is applied. Since priorities and blocking can be added without limiting GSPN-based performance analysis, we advocate the development of control-flow discovery techniques incorporating these features. Having GSPNs learned from event data, we can support more forward-looking forms of process mining.
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Notes
- 1.
Note that \(S_v \cap S_t = \emptyset \), \(M_{ final } \not \in S_v\), \(M_{ final } \not \in S_t\), and \(S = S_v \cup S_t \cup \{M_{ final }\}\).
References
van der Aalst, W.: Process Mining. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49851-4
van der Aalst, W.M.P., Carmona, J. (eds.): Process Mining Handbook. LNCS, vol. 448. Springer, Cham (2022)
van der Aalst, W.M.P., van Hee, K.M., Reijers, H.A.: Analysis of discrete-time stochastic petri nets. Stat. Neerl. 54(2), 237–255 (2000)
van der Aalst, W.M.P., Rubin, V., Verbeek, H.M.W., 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)
van der Aalst, W.M.P., Weijters, A.J.M.M., Maruster, L.: Workflow Mining: Discovering Process Models from Event Logs. QUT Technical report, FIT-TR-2003-03, Queensland University of Technology, Brisbane (2003). (Accepted for publication in IEEE Transactions on Knowledge and Data Engineering)
Ajmone Marsan, M., Balbo, G., Conte, G., Donatelli, S., Franceschinis, G.: Modelling with Generalized Stochastic Petri Nets. Wiley (1995)
Alkhammash, H., Polyvyanyy, A., Moffat, A.: Stochastic directly-follows process discovery using grammatical inference. In: Guizzardi, G., Santoro, F., Mouratidis, H., Soffer, P. (eds.) CAiSE 2024, pp. 87–103. Springer, Cham (2024). https://doi.org/10.1007/978-3-031-61057-8_6
Alkhammash, H., Polyvyanyy, A., Moffat, A., GarcÃa-Bañuelos, L.: Entropic relevance: a mechanism for measuring stochastic process models discovered from event data. Inf. Syst. 107, 101922 (2022)
Amparore, E.G., Balbo, G., Beccuti, M., Donatelli, S., Franceschinis, G.: 30 Years of GreatSPN. In: Fiondella, L., Puliafito, A. (eds.) Principles of Performance and Reliability Modeling and Evaluation. SSRE, pp. 227–254. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-30599-8_9
Augusto, A., et al.: Automated discovery of process models from event logs: review and benchmark. IEEE Trans. Knowl. Data Eng. 31(4), 686–705 (2019)
Augusto, A., Conforti, R., Marlon, M., La Rosa, M., Polyvyanyy, A.: Split miner: automated discovery of accurate and simple business process models from event logs. Knowl. Inf. Syst. 59(2), 251–284 (2019)
Bergenthum, R., Desel, J., Lorenz, R., Mauser, S.: Process mining based on regions of languages. In: Alonso, G., Dadam, P., Rosemann, M. (eds.) International Conference on Business Process Management (BPM 2007). LNCS, vol. 4714, pp. 375–383. Springer, Berlin (2007). https://doi.org/10.1007/978-3-540-75183-0_27
Burke, A., Leemans, S.J.J., Wynn, M.T.: Stochastic process discovery by weight estimation. In: Leemans, S., Leopold, H. (eds.) ICPM 2020. LNBIP, vol. 406, pp. 260–272. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-72693-5_20
Burke, A., Leemans, S.J.J., Wynn, M.T.: Discovering stochastic process models by reduction and abstraction. In: Buchs, D., Carmona, J. (eds.) PETRI NETS 2021. LNCS, vol. 12734, pp. 312–336. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-76983-3_16
Burke, A.T., Leemans, S.J.J., Wynn, M.T., van der Aalst, W.M.P., ter Hofstede, A.H.M.: Stochastic process model-log quality dimensions: an experimental study. In: Burattin, A., Polyvyanyy, A., Weber, B., (eds.) International Conference on Process Mining (ICPM 2022), pp. 80–87. IEEE (2022)
Busi, N., Pinna, G.M.: Synthesis of nets with inhibitor arcs. In: Mazurkiewicz, A., Winkowski, J. (eds.) CONCUR 1997. LNCS, vol. 1243, pp. 151–165. Springer, Heidelberg (1997). https://doi.org/10.1007/3-540-63141-0_11
Campos, J., Marsan, M.A., Balbo, G., Conte, G.: Generalized stochastic petri nets: a definition at the net level and its implications. IEEE Trans. Softw. Eng. 19(2), 89–107 (1993)
Carmona, J., Cortadella, J., Kishinevsky, M.: A region-based algorithm for discovering petri nets from event logs. In: Dumas, M., Reichert, M., Shan, M.-C. (eds.) BPM 2008. LNCS, vol. 5240, pp. 358–373. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85758-7_26
Dehnert, C., et al.: Parameter synthesis for probabilistic systems. In: MBMV, pp. 72–74. Albert-Ludwigs-Universität Freiburg (2016)
Devillers, R., Tredup, R.: Synthesis of inhibitor-reset petri nets: algorithmic and complexity issues. In: Bernardinello, L., Petrucci, L. (eds.) PETRI NETS 2022, pp. 213–235. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-06653-5_12
Eisentraut, C., Hermanns, H., Katoen, J.-P., Zhang, L.: A semantics for every GSPN. In: Colom, J.-M., Desel, J. (eds.) PETRI NETS 2013. LNCS, vol. 7927, pp. 90–109. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38697-8_6
Florin, G., Natkin, S.: Evaluation based upon stochastic petri nets of the maximum throughput of a full duplex protocol. In: Girault, C., Reisig, W. (eds.) Application and Theory of Petri Nets: Selected Papers from the First and the Second European Workshop on Application and Theory of Petri Nets Strasbourg, 23–26 September 1980 Bad Honnef, 28–30 September 1981, pp. 280–288. Springer, Heidelberg (1982). https://doi.org/10.1007/978-3-642-68353-4_45
Haas, P.J.: Stochastic Petri Nets: Modelling, Stability. Simulation. Springer Series in Operations Research. Springer, Berlin (2002)
Junges, S., Katoen, J.-P., Stoelinga, M., Volk, M.: One net fits all. In: Khomenko, V., Roux, O.H. (eds.) PETRI NETS 2018. LNCS, vol. 10877, pp. 272–293. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-91268-4_14
Katoen, J.P.: GSPNs revisited: simple semantics and new analysis algorithms. In: Brandt, J., Heljanko, K. (eds.) 12th International Conference on Application of Concurrency to System Design (ACSD 2012), pp. 6–11. IEEE Computer Society (2012)
Leemans, S.J.J., van der Aalst, W.M.P., Brockhoff, T., Polyvyanyy, A.: Stochastic process mining: earth movers’ stochastic conformance. Inf. Syst. 102, 101724 (2021)
Leemans, S.J.J., Fahland, D., van der Aalst, W.M.P.: Discovering block-structured process models from event logs - a constructive approach. In: Colom, J.-M., Desel, J. (eds.) PETRI NETS 2013. LNCS, vol. 7927, pp. 311–329. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38697-8_17
Leemans, S.J.J., Fahland, D., van der Aalst, W.M.P.: Discovering block-structured process models from event logs containing infrequent behaviour. In: Lohmann, N., Song, M., Wohed, P. (eds.) BPM 2013. LNBIP, vol. 171, pp. 66–78. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-06257-0_6
Leemans, S.J.J., Fahland, D., van der Aalst, W.M.P.: Scalable process discovery and conformance checking. Softw. Syst. Model. 17(2), 599–631 (2018)
Leemans, S.J.J., Li, T., Montali, M., Polyvyanyy, A.: Stochastic process discovery: can it be done optimally? In: Guizzardi, G., Santoro, F., Mouratidis, H., Soffer, P. (eds.) CAiSE 2024. LNCS, vol. 14663, pp. 36–52. Springer, Cham (2024). https://doi.org/10.1007/978-3-031-61057-8_3
Leemans, S.J.J., Mannel, L.L., Sidorova, N.: Significant stochastic dependencies in process models. Inf. Syst. 118, 102223 (2023)
Leemans, S.J.J., Syring, A.F., van der Aalst, W.M.P.: Earth movers’ stochastic conformance checking. In: Hildebrandt, T., van Dongen, B.F., Röglinger, M., Mendling, J. (eds.) BPM 2019. LNBIP, vol. 360, pp. 127–143. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26643-1_8
Mannel, L.L., van der Aalst, W.M.P.: Finding complex process-structures by exploiting the token-game. In: Donatelli, S., Haar, S. (eds.) PETRI NETS 2019. LNCS, vol. 11522, pp. 258–278. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-21571-2_15
Mannhardt, F., Leemans, S.J.J., Schwanen, C.T., de Leoni, M.: Modelling data-aware stochastic processes - discovery and conformance checking. In: Gomes, L., Lorenz, R. (eds.) PETRI NETS 2023. LNC, vol. 13929, pp. 77–98. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-33620-1_5
Mannhardt, F., de Leoni, M., Reijers, H.A., van der Aalst, W.M.P.: Balanced multi-perspective checking of process conformance. Computing 98(4), 407–437 (2016)
Ajmone Marsan, M., Balbo, G., Conte, G.: A class of generalised stochastic petri nets for the performance evaluation of multiprocessor systems. ACM Trans. Comput. Syst. 2(2), 93–122 (1984)
Merlin, P., Faber, D.J.: Recoverability of communication protocols. IEEE Trans. Commun. 24(9), 1036–1043 (1976)
Molloy, M.K.: On the Integration of Delay and Throughput Measures in Distributed Processing Models. PhD thesis, University of California, Los Angeles (1981)
Quatmann, T., Dehnert, C., Jansen, N., Junges, S., Katoen, J.-P.: Parameter synthesis for Markov models: faster than ever. In: Artho, C., Legay, A., Peled, D. (eds.) ATVA 2016. LNCS, vol. 9938, pp. 50–67. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46520-3_4
Ramchandani, C.: Performance Evaluation of Asynchronous Concurrent Systems by Timed Petri Nets. PhD thesis, Massachusetts Institute of Technology, Cambridge (1973)
Rogge-Solti, A., van der Aalst, W.M.P., Weske, M.: Discovering stochastic petri nets with arbitrary delay distributions from event logs. In: Lohmann, N., Song, M., Wohed, P. (eds.) BPM 2013. LNBIP, vol. 171, pp. 15–27. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-06257-0_2
Rozinat, A., Mans, R.S., Song, M., van der Aalst, W.M.P.: Discovering simulation models. Inf. Syst. 34(3), 305–327 (2009)
Salmani, B., Katoen, J.P.: Automatically finding the right probabilities in Bayesian networks. J. Artif. Intell. Res. 77, 1637–1696 (2023)
Solé, M., Carmona, J.: Process mining from a basis of state regions. In: Lilius, J., Penczek, W. (eds.) PETRI NETS 2010. LNCS, vol. 6128, pp. 226–245. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13675-7_14
Weijters, A.J.M.M., van der Aalst, W.M.P.: Rediscovering workflow models from event-based data using little thumb. Integrat. Comput.-Aided Eng. 10(2), 151–162 (2003)
van der Werf, J.M.E.M., van Dongen, B.F., Hurkens, C.A.J., Serebrenik, A.: Process discovery using integer linear programming. Fund. Inform. 94, 387–412 (2010)
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van der Aalst, W.M.P., Leemans, S.J.J. (2025). Learning Generalized Stochastic Petri Nets From Event Data. In: Jansen, N., et al. Principles of Verification: Cycling the Probabilistic Landscape . Lecture Notes in Computer Science, vol 15262. Springer, Cham. https://doi.org/10.1007/978-3-031-75778-5_1
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