Skip to main content
SpringerLink
Log in

Automated Rare Event Simulation for Stochastic Petri Nets

  • Conference paper
Quantitative Evaluation of Systems (QEST 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8054))

Included in the following conference series:

Abstract

We introduce an automated approach for applying rare event simulation to stochastic Petri net (SPN) models of highly reliable systems. Rare event simulation can be much faster than standard simulation because it is able to exploit information about the typical behaviour of the system. Previously, such information came from heuristics, human insight, or analysis on the full state space. We present a formal algorithm that obtains the required information from the high-level SPN-description, without generating the full state space. Essentially, our algorithm reduces the state space of the model into a (much smaller) graph in which each node represents a set of states for which the most likely path to failure has the same form. We empirically demonstrate the efficiency of the method with two case studies.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ajmone Marsan, M., Balbo, G., Donatelli, S., Franceschinis, G., Conte, G.: Modelling with generalized stochastic Petri nets. John Wiley & Sons, Inc. (1994)

    Google Scholar 

  2. Baier, C., D’Argenio, P., Groesser, M.: Partial order reduction for probabilistic branching time. Electronic Notes in Theoretical Computer Science (2006)

    Google Scholar 

  3. Baier, C., Katoen, J.P.: Principles of model checking. MIT Press (2008)

    Google Scholar 

  4. Blum, A.M., Goyal, A., Heidelberger, P., Lavenberg, S.S., Nakayama, M.K., Shahabuddin, P.: Modeling and analysis of system dependability using the system availability estimator. In: Twenty-Fourth International Symposium on Fault-Tolerant Computing, pp. 137–141. IEEE (1994)

    Google Scholar 

  5. Carrasco, J.A.: Failure distance based simulation of repairable fault-tolerant systems. In: Proceedings of the 5th International Conference on Modeling Techniques and Tools for Computer Performance Evaluation, pp. 351–365 (1992)

    Google Scholar 

  6. Clark, G., Courtney, T., Daly, D., Deavours, D., Derisavi, S., Doyle, J.M., Sanders, W.H., Webster, P.: The Möbius modeling tool. In: Proceedings of the 9th International Workshop on Petri Nets and Performance Models. IEEE (2001)

    Google Scholar 

  7. Devetsikiotis, M., Townsend, J.K.: An algorithmic approach to the optimization of importance sampling parameters in digital communication system simulation. IEEE Transactions on Communications 41(10), 1464–1473 (1993)

    Article  MATH  Google Scholar 

  8. Glasserman, P., Heidelberger, P., Shahabuddin, P., Zajic, T.: Multilevel splitting for estimating rare event probabilities. Operations Research 47(4), 585–600 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  9. Han, T., Katoen, J.-P.: Counterexamples in probabilistic model checking. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 72–86. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  10. Heidelberger, P.: Fast simulation of rare events in queueing and reliability models. In: Donatiello, L., Nelson, R. (eds.) SIGMETRICS 1993 and Performance 1993. LNCS, vol. 729, pp. 165–202. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  11. Jegourel, C., Legay, A., Sedwards, S.: Cross-entropy optimisation of importance sampling parameters for statistical model checking. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 327–342. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  12. Jegourel, C., Legay, A., Sedwards, S.: A platform for high performance statistical model checking – PLASMA. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 498–503. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  13. Júlvez, J.: Basic qualitative properties of Petri nets with multi-guarded transitions. In: American Control Conference, ACC 2009. IEEE (2009)

    Google Scholar 

  14. Kelling, C.: A framework for rare event simulation of stochastic Petri nets using “RESTART”. In: Proceedings of the 28th Winter Simulation Conference, pp. 317–324. IEEE Computer Society (1996)

    Google Scholar 

  15. Kwiatkowska, M., Norman, G., Parker, D.: PRISM: Probabilistic symbolic model checker. In: Field, T., Harrison, P.G., Bradley, J., Harder, U. (eds.) TOOLS 2002. LNCS, vol. 2324, pp. 200–204. Springer, Heidelberg (2002)

    Google Scholar 

  16. Law, A., Kelton, W.: Simulation modeling and analysis. McGraw-Hill, New York (1991)

    Google Scholar 

  17. L’Ecuyer, P., Tuffin, B.: Approximating zero-variance importance sampling in a reliability setting. Annals of Operations Research 189(1), 277–297 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Miretskiy, D., Scheinhardt, W., Mandjes, M.: On efficiency of multilevel splitting. Communications in Statistics – Simulation and Computation 41(6), 890–904 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  19. Murata, T.: Petri nets: Properties, analysis and applications. Proceedings of the IEEE 77(4), 541–580 (1989)

    Article  Google Scholar 

  20. Nicola, V., Shahabuddin, P., Nakayama, M.: Techniques for fast simulation of models of highly dependable systems. IEEE Transactions on Reliability 50(3), 246–264 (2001)

    Article  Google Scholar 

  21. Obal, W., Sanders, W.: An environment for importance sampling based on stochastic activity networks. In: Proceedings of the 13th Symposium on Reliable Distributed Systems, pp. 64–73. IEEE (1994)

    Google Scholar 

  22. Ridder, A.: Importance sampling simulations of Markovian reliability systems using cross-entropy. Annals of Operations Research 134(1), 119–136 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  23. Rubinstein, R., Kroese, D.: The cross-entropy method: a unified approach to combinatorial optimization, Monte-Carlo simulation and machine learning. Springer (2004)

    Google Scholar 

  24. Sanders, W.H., Meyer, J.F.: Stochastic activity networks: Formal definitions and concepts. In: Brinksma, E., Hermanns, H., Katoen, J.-P. (eds.) FMPA 2000. LNCS, vol. 2090, pp. 315–343. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  25. Shahabuddin, P.: Importance sampling for the simulation of highly reliable Markovian systems. Management Science 40(3), 333–352 (1994)

    Article  MATH  Google Scholar 

  26. Tuffin, B., Trivedi, K.S.: Implementation of importance splitting techniques in stochastic Petri net package. In: Haverkort, B.R., Bohnenkamp, H.C., Smith, C.U. (eds.) TOOLS 2000. LNCS, vol. 1786, pp. 216–229. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  27. Villén-Altamirano, M., Villén-Altamirano, J.: RESTART: A method for accelerating rare event simulations. In: Queueing, Performance and Control in ATM, pp. 71–76. Elsevier Science Publishers (1991)

    Google Scholar 

  28. Zimmermann, A., Freiheit, J., German, R., Hommel, G.: Petri net modelling and performability evaluation with TimeNET 3.0. In: Haverkort, B.R., Bohnenkamp, H.C., Smith, C.U. (eds.) TOOLS 2000. LNCS, vol. 1786, pp. 188–202. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Telematics & Information Technology, University of Twente, Enschede, The Netherlands

    Daniël Reijsbergen, Pieter-Tjerk de Boer, Werner Scheinhardt & Boudewijn Haverkort

Authors
  1. Daniël Reijsbergen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pieter-Tjerk de Boer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Werner Scheinhardt
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Boudewijn Haverkort
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. AT&T Labs Research, 180 Park Avenue, Building 103, 07932, Florham Park, NJ, USA

    Kaustubh Joshi

  2. Institut für Technische Informatik, Universität der Bundeswehr München, Werner-Heisenberg Weg 39, 85577, Neubiberg, Germany

    Markus Siegle

  3. Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, Drienerlolaan 5, Zilverling Building, 7522 NB, Enschede, The Netherlands

    Mariëlle Stoelinga

  4. Facultad de Matemáticas, Astronomía y Física, Universidad Nacional de Córdoba – CONICET, Medina Allende s/n, X5000HUA, Córdoba, Argentina

    Pedro R. D’Argenio

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Reijsbergen, D., de Boer, PT., Scheinhardt, W., Haverkort, B. (2013). Automated Rare Event Simulation for Stochastic Petri Nets. In: Joshi, K., Siegle, M., Stoelinga, M., D’Argenio, P.R. (eds) Quantitative Evaluation of Systems. QEST 2013. Lecture Notes in Computer Science, vol 8054. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40196-1_31

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-40196-1_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40195-4

  • Online ISBN: 978-3-642-40196-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation