The Complexity of Deadline Analysis for Workflow Graphs with Multiple Resources

  • Mirela Botezatu
  • Hagen Völzer
  • Lothar Thiele
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9850)


We study whether the executions of a time-annotated sound workflow graph (WFG) meet a given deadline when an unbounded number of resources (i.e., executing agents) is available. We present polynomial-time algorithms and NP-hardness results for different cases. In particular, we show that it can be decided in polynomial time whether some executions of a sound workflow graph meet the deadline. For acyclic sound workflow graphs, it can be decided in linear time whether some or all executions meet the deadline. Furthermore, we show that it is NP-hard to compute the expected duration of a sound workflow graph for unbounded resources, which is contrasting the earlier result that the expected duration of a workflow graph executed by a single resource can be computed in cubic time. We also propose an algorithm for computing the maximum concurrency of the workflow graph, which helps to determine the optimal number of resources needed to execute the workflow graph.


Maximum Degree Regular Graph Minimum Duration Outgoing Edge Incoming Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    van der Aalst, W.M.P., Hirnschall, A., Verbeek, H.M.W.E.: An alternative way to analyze workflow graphs. In: Pidduck, A.B., Mylopoulos, J., Woo, C.C., Ozsu, M.T. (eds.) CAiSE 2002. LNCS, vol. 2348, pp. 535–552. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Bellman, R.: On a routing problem. Q. Appl. Math. 16, 87–90 (1958)MATHGoogle Scholar
  3. 3.
    Botezatu, M., Völzer, H., Thiele, L.: The complexity of deadline analysis for workflow graphs with a single resource. In: Proceedings of the 20th IEEE ICECCS Conference, December 2015Google Scholar
  4. 4.
    Botezatu, M., Völzer, H., Thiele, L.: The complexity of deadline analysis for workflow graphs with multiple resources. Technical report RZ3896, IBM (2016)Google Scholar
  5. 5.
    Desel, J., Esparza, J.: Free Choice Petri Nets. Cambridge University Press, New York (1995)CrossRefMATHGoogle Scholar
  6. 6.
    Favre, C., Fahland, D., Völzer, H.: The relationship between workflow graphs and free-choice workflow nets. Inf. Syst. 47, 197–219 (2015)CrossRefGoogle Scholar
  7. 7.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1979)MATHGoogle Scholar
  8. 8.
    Gaujal, B., Haar, S., Mairesse, J.: Blocking a transition in a free choice net and what it tells about its throughput. J. Comput. Syst. Sci. 66(3), 515–548 (2003)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Hansson, H., Jonsson, B.: A framework for reasoning about time and reliability. In: Proceedings of the Real Time Systems Symposium, 1989, pp. 102–111, December 1989Google Scholar
  10. 10.
    Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: verification of probabilistic real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Mili, H., Tremblay, G., Jaoude, G., Lefebvre, É., Elabed, L., El Boussaidi, G.: Business process modeling languages: sorting through the alphabet soup. ACM Comput. Surv. 43(1), 4:1–4:56 (2010)CrossRefGoogle Scholar
  12. 12.
    Murata, T.: Petri nets: properties, analysis and applications. Proc. IEEE 77(4), 541–580 (1989)CrossRefGoogle Scholar
  13. 13.
    Popova-Zeugmann, L., Heiner, M.: Worst-case analysis of concurrent systems with duration interval petri nets. In: BTU COTTBUS, pp. 162–179 (1996)Google Scholar
  14. 14.
    Vanhatalo, J., Völzer, H., Koehler, J.: The refined process structure tree. Data Knowl. Eng. 68(9), 793–818 (2009)CrossRefGoogle Scholar
  15. 15.
    Vanhatalo, J., Völzer, H., Leymann, F.: Faster and more focused control-flow analysis for business process models through SESE decomposition. In: Krämer, B.J., Lin, K.-J., Narasimhan, P. (eds.) ICSOC 2007. LNCS, vol. 4749, pp. 43–55. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  16. 16.
    Varacca, D., Völzer, H., Winskel, G.: Probabilistic event structures and domains. Theor. Comput. Sci. 358(2–3), 173–199 (2006)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Völzer, H.: Randomized non-sequential processes. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 184–201. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  18. 18.
    Wan, M., Ciardo, G.: Symbolic reachability analysis of integer timed Petri nets. In: Nielsen, M., Kučera, A., Miltersen, P.B., Palamidessi, C., Tůma, P., Valencia, F. (eds.) SOFSEM 2009. LNCS, vol. 5404, pp. 595–608. Springer, Heidelberg (2009)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Mirela Botezatu
    • 1
    • 2
  • Hagen Völzer
    • 1
  • Lothar Thiele
    • 2
  1. 1.IBM ResearchZürichSwitzerland
  2. 2.ETHZürichSwitzerland

Personalised recommendations