Skip to main content

Precise Parameter Synthesis for Generalised Stochastic Petri Nets with Interval Parameters

  • Conference paper
  • First Online:
  • 1323 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10672))

Abstract

We consider the problem of synthesising parameters affecting transition rates and probabilities in generalised Stochastic Petri Nets (GSPNs). Given a time-bounded property expressed as a probabilisitic temporal logic formula, our method allows computing the parameters values for which the probability of satisfying the property meets a given bound, or is optimised. We develop algorithms based on reducing the parameter synthesis problem for GSPNs to the corresponding problem for continuous-time Markov Chains (CTMCs), for which we can leverage existing synthesis algorithms, while retaining the modelling capabilities and expressive power of GSPNs. We evaluate the usefulness of our approach by synthesising parameters for two case studies.

This work has been supported by the Czech Grant Agency grant No. GA16-24707Y and the IT4Innovations Excellence in Science project No. LQ1602.

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

Buying options

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 EPUB and 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

Learn about institutional subscriptions

References

  1. Al-Jaar, R.Y., Desrochers, A.A.: Performance evaluation of automated manufacturing systems using generalized stochastic petri nets. IEEE Trans. Robot. Autom. 6(6), 621–639 (1990)

    Article  Google Scholar 

  2. Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Verifying continuous time Markov chains. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 269–276. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-61474-5_75

    Chapter  Google Scholar 

  3. Baier, C., et al.: Model checking for performability. Math. Struct. Comput. Sci. 23(4), 751–795 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  4. Balbo, G.: Introduction to generalized stochastic Petri nets. In: Bernardo, M., Hillston, J. (eds.) SFM 2007. LNCS, vol. 4486, pp. 83–131. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72522-0_3

    Chapter  Google Scholar 

  5. Češka, M., et al.: Precise parameter synthesis for stochastic biochemical systems. Acta Informatica 54(6), 589–623 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  6. Češka, M., Pilař, P., Paoletti, N., Brim, L., Kwiatkowska, M.: PRISM-PSY: precise GPU-accelerated parameter synthesis for stochastic systems. In: Chechik, M., Raskin, J.-F. (eds.) TACAS 2016. LNCS, vol. 9636, pp. 367–384. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49674-9_21

    Google Scholar 

  7. Ghemawat, S., Gobioff, H., Leung, S.-T.: The Google file system. In: Proceedings of the SOSP 2003, pp. 29–43. ACM (2003)

    Google Scholar 

  8. Goss, P.J.E., Peccoud, J.: Quantitative modeling of stochastic systems in molecular biology by using stochastic petri nets. PNAS 95(12), 6750–6755 (1998)

    Article  Google Scholar 

  9. Heiner, M., Gilbert, D., Donaldson, R.: Petri nets for systems and synthetic biology. In: Bernardo, M., Degano, P., Zavattaro, G. (eds.) SFM 2008. LNCS, vol. 5016, pp. 215–264. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-68894-5_7

    Chapter  Google Scholar 

  10. Huang, C., Ferrell, J.: Ultrasensitivity in the mitogen-activated protein kinase cascade. Proc. Natl. Acad. Sci. 93, 10078–10083 (1996)

    Article  Google Scholar 

  11. Kwiatkowska, M., Norman, G., Parker, D.: Stochastic model checking. In: Bernardo, M., Hillston, J. (eds.) SFM 2007. LNCS, vol. 4486, pp. 220–270. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72522-0_6

    Chapter  Google Scholar 

  12. Marsan, M.A., et al.: Modelling with Generalized Stochastic Petri Nets. Wiley, Hoboken (1994)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Milan Češka Jr. .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Češka, M., Češka, M., Paoletti, N. (2018). Precise Parameter Synthesis for Generalised Stochastic Petri Nets with Interval Parameters. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2017. EUROCAST 2017. Lecture Notes in Computer Science(), vol 10672. Springer, Cham. https://doi.org/10.1007/978-3-319-74727-9_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-74727-9_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-74726-2

  • Online ISBN: 978-3-319-74727-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics