Skip to main content
SpringerLink
Log in

Analysis of Non-Markovian Systems in GreatSPN

  • Conference paper
  • First Online:
New Frontiers in Quantitative Methods in Informatics (InfQ 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 825))

Included in the following conference series:

  • 241 Accesses

Abstract

Markov Regenerative Processes (MRgP) with enabling restriction allow to model stochastic processes where the firing distribution of some events may be specified by a non-Markovian Probability Distribution Function, provided that at most one of these events is enabled in any state of the process. The GreatSPN framework is a collection of tools for the modeling and analysis of systems specified as Stochastic Petri Nets. The paper describes the new features of the MRgP solver of GreatSPN to deal with MRgP processes. The solver supports a rich language for the specification of non-Markovian events, and different solution techniques (explicit, matrix-free, component-based) for the MRgP analysis. The potentiality of the tools are shown on a few examples.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Institutional subscriptions

Similar content being viewed by others

References

  1. Ajmone Marsan, M., Chiola, G.: On Petri nets with deterministic and exponentially distributed firing times. In: Rozenberg, G. (ed.) APN 1986. LNCS, vol. 266, pp. 132–145. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-18086-9_23

    Chapter  Google Scholar 

  2. Ajmone Marsan, M., Conte, G., Balbo, G.: A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems. ACM Trans. Comput. Syst. 2, 93–122 (1984)

    Article  Google Scholar 

  3. Amparore, E.G.: The home of the new GreatSPN Graphical User Interface (2014). http://www.di.unito.it/~amparore/mc4cslta/editor.html

  4. Amparore, E.G., Buchholz, P., Donatelli, S.: A structured solution approach for Markov regenerative processes. In: Norman, G., Sanders, W. (eds.) QEST 2014. LNCS, vol. 8657, pp. 9–24. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10696-0_3

    Chapter  Google Scholar 

  5. Amparore, E.G., Donatelli, S.: DSPN-Tool: a new DSPN and GSPN solver for GreatSPN. In: International Conference on Quantitative Evaluation of Systems, Los Alamitos, CA, USA, pp. 79–80. IEEE Computer Society (2010)

    Google Scholar 

  6. Amparore, E.G., Donatelli, S.: Revisiting the matrix-free solution of Markov regenerative processes. Numer. Linear Algebr. Appl. Spec. Issue Numer. Solut. Markov Chains 18, 1067–1083 (2011)

    Article  MathSciNet  Google Scholar 

  7. Amparore, E.G., Donatelli, S.: A component-based solution for reducible Markov regenerative processes. Perform. Eval. 70(6), 400–422 (2013)

    Article  Google Scholar 

  8. Amparore, E.G., Donatelli, S.: alphaFactory: a tool for generating the alpha factors of general distributions. In: Bertrand, N., Bortolussi, L. (eds.) QEST 2017. LNCS, vol. 10503, pp. 36–51. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66335-7_3

    Chapter  Google Scholar 

  9. Bobbio, A., Puliafito, A., Scarpa, M., Telek, M.: WebSPN: non-Markovian stochastic Petri net tool. In: 18th Conference on Application and Theory of Petri Nets (1997)

    Google Scholar 

  10. Bodenstein, C., Zimmermann, A.: TimeNET optimization environment: batch simulation and heuristic optimization of SCPNs with TimeNET 4.2. In: 8th International Conference on Performance Evaluation Methodologies and Tools, pp. 129–133. ICST (2014)

    Google Scholar 

  11. Bucci, G., Carnevali, L., Ridi, L., Vicario, E.: Oris: a tool for modeling, verification and evaluation of real-time systems. Int. J. Softw. Tools Technol. Transfer 12(5), 391–403 (2010)

    Article  Google Scholar 

  12. Carnevali, L., Ridi, L., Vicario, E.: A framework for simulation and symbolic state space analysis of non-Markovian models. In: Flammini, F., Bologna, S., Vittorini, V. (eds.) SAFECOMP 2011. LNCS, vol. 6894, pp. 409–422. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-24270-0_30

    Chapter  Google Scholar 

  13. Chiola, G., Dutheillet, C., Franceschinis, G., Haddad, S.: Stochastic well-formed colored nets and symmetric modeling applications. IEEE Trans. Comput. 42(11), 1343–1360 (1993)

    Article  Google Scholar 

  14. Choi, H., Kulkarni, V.G., Trivedi, K.S.: Markov regenerative stochastic Petri nets. Perform. Eval. 20(1–3), 337–357 (1994)

    Article  MathSciNet  Google Scholar 

  15. Dingle, N.J., Harrison, P.G., Knottenbelt, W.J.: Response time densities in generalised stochastic Petri nets. In: Workshop on Software and Performance, pp. 46–54 (2002)

    Google Scholar 

  16. Donatelli, S., Haddad, S., Sproston, J.: Model checking timed and stochastic properties with CSL\(^\text{ TA }\). IEEE Trans. Softw. Eng. 35(2), 224–240 (2009)

    Article  Google Scholar 

  17. German, R.: Markov regenerative stochastic Petri nets with general execution policies: supplementary variable analysis and a prototype tool. Perform. Eval. 39(1–4), 165–188 (2000)

    Article  Google Scholar 

  18. German, R.: Performance Analysis of Communication Systems with Non-Markovian Stochastic Petri Nets. Wiley, New York (2000)

    MATH  Google Scholar 

  19. German, R.: Iterative analysis of Markov regenerative models. Perform. Eval. 44, 51–72 (2001)

    Article  Google Scholar 

  20. Grassmann, W.: Transient solutions in Markovian queueing systems. Comput. Oper. Res. 4(1), 47–53 (1977)

    Article  Google Scholar 

  21. Lindemann, C.: Performance Modelling with Deterministic and Stochastic Petri Nets. Wiley, New York (1998)

    MATH  Google Scholar 

  22. Longo, F., Scarpa, M.: Two-layer symbolic representation for stochastic models with Phase-type distributed events. Int. J. Syst. Sci. 46(9), 1540–1571 (2015)

    Article  MathSciNet  Google Scholar 

  23. Mura, I., Bondavalli, A., Zang, X., Trivedi, K.S.: Dependability modeling and evaluation of phased mission systems: a DSPN approach. In: International Conference on Dependable Computing for Critical Applications (DCCA), pp. 299–318. IEEE (1999)

    Google Scholar 

  24. Mura, I., Bondavalli, A.: Markov regenerative stochastic Petri nets to model and evaluate the dependability of phased mission systems dependability. IEEE Trans. Comput. 50(12), 1337–1351 (2001)

    Article  Google Scholar 

  25. Zimmermann, A.: Modelling and performance evaluation with TimeNET 4.4. In: Bertrand, N., Bortolussi, L. (eds.) QEST 2017. LNCS, vol. 10503, pp. 300–303. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66335-7_19

    Chapter  Google Scholar 

  26. 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). https://doi.org/10.1007/3-540-46429-8_14

    Chapter  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università di Torino, Turin, Italy

    Elvio Gilberto Amparore & Susanna Donatelli

Authors
  1. Elvio Gilberto Amparore
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Susanna Donatelli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Elvio Gilberto Amparore .

Editor information

Editors and Affiliations

  1. Ca’ Foscari University of Venice, Venice, Italy

    Simonetta Balsamo

  2. Ca’ Foscari University of Venice, Venice, Italy

    Andrea Marin

  3. University of Florence, Florence, Italy

    Enrico Vicario

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Amparore, E.G., Donatelli, S. (2018). Analysis of Non-Markovian Systems in GreatSPN. In: Balsamo, S., Marin, A., Vicario, E. (eds) New Frontiers in Quantitative Methods in Informatics. InfQ 2017. Communications in Computer and Information Science, vol 825. Springer, Cham. https://doi.org/10.1007/978-3-319-91632-3_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-91632-3_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91631-6

  • Online ISBN: 978-3-319-91632-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation