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A Semantics for Every GSPN

  • Conference paper
Application and Theory of Petri Nets and Concurrency (PETRI NETS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7927))

Abstract

Generalised Stochastic Petri Nets (GSPNs) are a popular modelling formalism for performance and dependability analysis. Their semantics is traditionally associated to continuous-time Markov chains (CTMCs), enabling the use of standard CTMC analysis algorithms and software tools. Due to ambiguities in the semantic interpretation of confused GSPNs, this analysis strand is however restricted to nets that do not exhibit non-determinism, the so-called well-defined nets. This paper defines a simple semantics for every GSPN. No restrictions are imposed on the presence of confusions. Immediate transitions may be weighted but are not required to be. Cycles of immediate transitions are admitted too. The semantics is defined using a non-deterministic variant of CTMCs, referred to as Markov automata. We prove that for well-defined bounded nets, our semantics is weak bisimulation equivalent to the existing CTMC semantics. Finally, we briefly indicate how every bounded GSPN can be quantitatively assessed.

This work is supported by the EU FP7 Programme under grant agreement no. 295261 (MEALS) and 318490 (SENSATION), by the DFG as part of the SFB/TR 14 AVACS, and by DFG/NWO bilateral research programme ROCKS.

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References

  1. Ajmone Marsan, M., Balbo, G., Chiola, G., Conte, G.: Generalized stochastic Petri nets revisited: Random switches and priorities. In: Petri Nets and Performance Models (PNPM), pp. 44–53. IEEE CS Press (1987)

    Google Scholar 

  2. Ajmone Marsan, M., Balbo, G., Chiola, G., Conte, G., Donatelli, S., Franceschinis, G.: An introduction to Generalized Stochastic Petri Nets. Microel. and Rel. 31(4), 699–725 (1991)

    Article  Google Scholar 

  3. Ajmone Marsan, M., Balbo, G., Conte, G., Donatelli, S., Franceschinis, G.: Modelling with Generalized Stochastic Petri Nets. John Wiley & Sons (1995)

    Google Scholar 

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

    Article  Google Scholar 

  5. Baier, C., Katoen, J.-P.: Principles of Model Checking. MIT Press (2008)

    Google Scholar 

  6. Baier, C., Katoen, J.-P., Hermanns, H., Wolf, V.: Comparative branching-time semantics for Markov chains. Inf. Comput 200(2), 149–214 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Balbo, G.: Introduction to stochastic Petri nets. In: Brinksma, E., Hermanns, H., Katoen, J.-P. (eds.) FMPA 2000, LNCS, vol. 2090, pp. 84–155. Springer, Heidelberg (2001)

    Google Scholar 

  8. 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)

    Chapter  Google Scholar 

  9. Bause, F.: No way out ∞ The timeless trap. Petri Net Newsletter 37, 4–8 (1990)

    Google Scholar 

  10. Bertsekas, D.P., Tsitsiklis, J.N.: An analysis of stochastic shortest path problems. Mathematics of Operations Research 16(3), 580–595 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  11. Buchholz, P.: Exact and ordinary lumpability in finite Markov chains. J. Applied Probability 31, 59–75 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  12. Chiola, G., Donatelli, S., Franceschinis, G.: GSPNs versus SPNs: What is the actual role of immediate transitions? In: Petri Nets and Performance Models (PNPM), pp. 20–31. IEEE CS Press (1991)

    Google Scholar 

  13. Chiola, G., Ajmone Marsan, M., Balbo, G., Conte, G.: Generalized stochastic Petri nets: A definition at the net level and its implications. IEEE TSE 19(2), 89–107 (1993)

    Google Scholar 

  14. Ciardo, G., Zijal, R.: Well-defined stochastic Petri nets. In: MASCOTS, pp. 278–284 (1996)

    Google Scholar 

  15. Deavours, D.D., Sanders, W.H.: An efficient well-specified check. In: Petri Nets and Performance Models (PNPM), pp. 124–133. IEEE CS Press (1999)

    Google Scholar 

  16. Deng, Y., van Glabbeek, R., Hennessy, M., Morgan, C.: Testing finitary probabilistic processes. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 274–288. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  17. Desharnais, J., Gupta, V., Jagadeesan, R., Panangaden, P.: Weak bisimulation is sound and complete for PCTL*. Inf. Comput. 208(2), 203–219 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  18. Hillston, J.: A Compositional Approach to Performance Modelling. PhD thesis, University of Edinburgh (1994)

    Google Scholar 

  19. Eisentraut, C., Hermanns, H., Zhang, L.: Concurrency and composition in a stochastic world. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010. LNCS, vol. 6269, pp. 21–39. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  20. Eisentraut, C., Hermanns, H., Zhang, L.: On probabilistic automata in continuous time. In: LICS, pp. 342–351. IEEE (2010)

    Google Scholar 

  21. Guck, D., Han, T., Katoen, J.-P., Neuhäußer, M.R.: Quantitative timed analysis of interactive markov chains. In: Goodloe, A.E., Person, S. (eds.) NFM 2012. LNCS, vol. 7226, pp. 8–23. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  22. Hermanns, H. (ed.): Interactive Markov Chains. LNCS, vol. 2428. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  23. Hatefi, H., Hermanns, H.: Model Checking Algorithms for Markov Automata. ECEASST 53, 1–15 (2012)

    Google Scholar 

  24. Hermanns, H., Herzog, U., Mertsiotakis, V., Rettelbach, M.: Exploiting stochastic process algebra achievements for Generalized Stochastic Petri Nets. In: Petri Nets and Performance Models (PNPM), pp. 183–192. IEEE CS Press (1997)

    Google Scholar 

  25. Katoen, J.-P.: GSPNs revisited: Simple semantics and new analysis algorithms. In: ACSD, pp. 6–11. IEEE (2012)

    Google Scholar 

  26. Kemeny, J.G., Snell, J.L., Knapp, A.W.: Denumerable Markov Chains, 2nd edn. Springer (1976)

    Google Scholar 

  27. Lohrey, M., D’Argenio, P.R., Hermanns, H.: Axiomatising divergence. Inf. Comput. 203(2), 115–144 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  28. Meyer, J.F., Movaghar, A., Sanders, W.H.: Stochastic activity networks: Structure, behavior, and application. In: Petri Nets and Performance Models (PNPM), pp. 106–115. IEEE CS Press (1985)

    Google Scholar 

  29. Milner, R.: Communication and Concurrency. Prentice-Hall (1989)

    Google Scholar 

  30. 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)

    Google Scholar 

  31. Segala, R.: Modeling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, Laboratory for Computer Science, Massachusetts Institute of Technology (1995)

    Google Scholar 

  32. Teruel, E., Franceschinis, G., De Pierro, M.: Well-defined Generalized Stochastic Petri Nets: A net-level method to specify priorities. IEEE TSE 29(11), 962–973 (2003)

    Google Scholar 

  33. Timmer, M., Katoen, J.-P., van de Pol, J., Stoelinga, M.I.A.: Efficient modelling and generation of markov automata. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 364–379. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  34. Zhang, L., Neuhäußer, M.R.: Model checking interactive Markov chains. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 53–68. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Science, Saarland University, Germany

    Christian Eisentraut & Holger Hermanns

  2. Department of Computer Science, RWTH Aachen University, Germany

    Joost-Pieter Katoen

  3. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, China

    Lijun Zhang

Authors
  1. Christian Eisentraut
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  2. Holger Hermanns
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  3. Joost-Pieter Katoen
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  4. Lijun Zhang
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Editor information

Editors and Affiliations

  1. Departamento de Informática e Ingeniería de Sistemas, Universidad de Zaragoza, María de Luna, 1, 50018, Zaragoza, Spain

    José-Manuel Colom

  2. Fernuniversität Hagen, IZ, Universitätsstraße 1, 58097, Hagen, Germany

    Jörg Desel

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Eisentraut, C., Hermanns, H., Katoen, JP., Zhang, L. (2013). A Semantics for Every GSPN. In: Colom, JM., Desel, J. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2013. Lecture Notes in Computer Science, vol 7927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38697-8_6

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  • DOI: https://doi.org/10.1007/978-3-642-38697-8_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38696-1

  • Online ISBN: 978-3-642-38697-8

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