Hierarchies in colored GSPNs

  • Peter Buchholz
Full Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 691)


Hierarchies are integrated in the class of Generalized Colored Stochastic Petri Nets (GCSPNs). The use of hierarchies supports the specification of nets describing large real-world systems. Moreover, the new model class can be analysed extremely efficient according to qualitative and quantitative results. Techniques for quantitative analysis, qualitative analysis and subnet aggregation are introduced. The usability of the approach is shown by means of a non-trivial example from literature.


Flexible Manufacturing System Abstract View Color Domain Virtual Transition Underlying Markov Chain 
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  1. 1.
    Ajmone-Marsan, M.A., Balbo, G., Chiola, G., Conte, G., Donatelli, S., Franceschinis, G.: An Introduction to Generalized Stochastic Petri Nets. Microelectron. Reliab. 31, 4 (1991), 699–725.Google Scholar
  2. 2.
    Ammar, H.H., Islam, S.M.: Time Scale Decomposition of a Class of Generalized Stochastic Petri Net Models. IEEE Trans, on Software Eng., 15, 6 (1989), 809–820.Google Scholar
  3. 3.
    Balbo, G., Bruell, S.C., Ghanta, S.: Combining Queueing Networks and Generalized Stochastic Petri Nets for the Solution of Complex System Behavior. IEEE Trans. on Comp. 37, 10 (1988) 1251–1268.Google Scholar
  4. 4.
    Buchholz, P.: The Aggregation of Markovian Submodels in Isolation. Universität Dortmund, Fachbereich Informatik, Forschungsbericht 369, 1990.Google Scholar
  5. 5.
    Buchholz, P.: Numerical Solution Methods based on Structured Descriptions of Markovian Models. In G. Balbo, G. Serazzi (eds.): Computer Performance Evaluation, Modelling Techniques and Tools, North Holland 1992, pp. 251–267.Google Scholar
  6. 6.
    Buchholz, P.: Hierarchical Markovian Models-Symmetries and Aggregation-. Proc. of the Sixth International Conference on Modelling Tools and Techniques for Computer Performance Evaluation, Edinburgh, Scotland, UK, September 15–18, 1992, pp. 305–319.Google Scholar
  7. 7.
    Buchholz, P.: A Hierarchical View of GCSPNs and its Impact on Qualtitative and Quantitative Analysis. Journal of Parallel and Distributed Computing 15, 2 (1992), 207–224.Google Scholar
  8. 8.
    Chiola, G., Dutheillet, C, Franceschinis, G., Haddad, S.: Stochastic Well-Formed colored Nets and Multiprocessor modeling Application. In K. Jensen, G. Rozenberg (eds.): High-Level Petri Nets. Theory and Application, Springer 1991.Google Scholar
  9. 9.
    Chiola, G., Bruno, G., Demaria, T.: Introducing a color Formalism into Generalized Stochastic Petri Nets. Proc. of the 9th European Workshop on Application and Theory of Petri Nets, Venezia, Italy, 1988.Google Scholar
  10. 10.
    Chehaibar, G.: Use of Reentrant Nets in Modular Analysis of Colored Nets. In K. Jensen, G. Rozenberg (eds.): High-Level Petri Nets. Theory and Application, Springer 1991.Google Scholar
  11. 11.
    Ciardo, G., Trivedi, K.S.: Solution of Large GSPN Models. In G. Stewart (ed.): Numerical Solution of Markov Chains, Marcel Dekker 1991.Google Scholar
  12. 12.
    Davio, M.: Kronecker Products and Shuffle Algebra. IEEE Trans. on Comp. 30, 2 (1981), 116–125.Google Scholar
  13. 13.
    Donatelli, S.: Superposed Stochastic Automata: a class of Stochastic Petri nets amenable to parallel solution. Proc. of the Fourth Int. Workshop on Petri Nets and Performance Models, Melbourne, 1991.Google Scholar
  14. 14.
    Fehling, R.: A Concept of Hierarchical Petri Nets with Building Blocks. Proc. of the 12th. Int. Conf. on Application and Theory of Petri Nets, Gjern, Denmark, June 1991.Google Scholar
  15. 15.
    Haddad, M.S.: A Reduction Theory for colored Nets. In G. Rozenberg (ed.): Advances in Petri Nets, Lecture Notes in Computer Sciences, vol. 424, Springer 1990, pp. 209–235.Google Scholar
  16. 16.
    Huber, P., Jensen, K., Shapiro, R.M.: Hierarchies in colored Petri Nets. In G. Rozenberg (ed.): Advances in Petri Nets, Lecture Notes in Computer Sciences, vol. 483, Springer 1990, pp. 313–341.Google Scholar
  17. 17.
    Krieger, U., Müller-Clostermann, B., Sczittnick, M.: Modeling and Analysis of Communication Systems Based on Computational Methods for Markov Chains. IEEE J. on Selected Areas in Communication 8, 9 (1990), 1630–1648.Google Scholar
  18. 18.
    Reibman, A., Trivedi, K.S.: Numerical Transient Analysis of Markov Models. Comput. Opns. Res. 15, 1 (1988), 19–36.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Peter Buchholz
    • 1
  1. 1.Informatik IVUniversität DortmundDortmund 50Germany

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