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Extension of Petri Nets for Representing and Reasoning with Tasks with Imprecise Durations

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Abstract

This paper presents an extension of Petri net framework with imprecise temporal properties. We use possibility theory to represent imprecise time by time-stamping tokens and assigning durations to firing of the transitions. A method for approximation of an arbitrary temporal distribution with a set of possibilistic intervals is used to introduce the composition operation for two possibilistic temporal distributions. We developed a method to determining an effective enabling time of a transition with incoming tokens with possibilistic distributions. The utility of the proposed theory is illustrated using an example of an automated manufacturing system. The proposed approach is novel and has a broad utility beyond a timed Petri network and its applications.

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References

  1. J. Allen, “Maintaining knowledge about temporal intervals,” Communications of the ACM, vol. 26 pp. 832–843, 1983.

    Article  Google Scholar 

  2. I. Bestuzheva and V. Rudnev, “Timed Petri nets: Classification and comparative analysis,” Automation and Remote Control, vol. 51, no.10, pp. 1308–1318, 1990, Consultants Bureau, New York.

    Google Scholar 

  3. C. Brown and D. Gurr, “Temporal logic and categories of petri nets,” in Automata, Languages and Programming, edited by A. Lingass and R. Karlsson, Springer-Verlag: New York, pp. 570–581, 1993.

    Google Scholar 

  4. J. Carlier and P. Chretienne, “Timed petri net schedules,” in Advances in Petri Nets, edited by G. Rozenberg, Springer-Verlag: New York pp. 642–666, 1988.

    Google Scholar 

  5. J. Cardoso and H. Camargo, editors, Fuzziness in Petri Nets, Physica Verlag: New York, NY, 1999.

  6. J. Cardoso, R. Valette, and D. Dubois, “Fuzzy Petri nets: An overview,” in Proceedings of the 13th IFAC World Congress, edited by G. Rosenberg, San Francisco CA, 30 June–5 July 1996, pp. 443–448.

  7. J. Cardoso, R. Valette, and D. Dubois, “Possibilistic Petri nets,” IEEE transactions on Systems, Man and Cybernetics, Part B: Cybernetics, vol. 29, no. 5, pp. 573–582, 1999.

  8. J. Coolahan and N. Roussopoulos, “Timing requirements for time-driven systems using augmented petrinets,” IEEE Transactions on Software Engineering, vol. 9, no. 5, pp. 603–616, 1983.

    Google Scholar 

  9. R. Dechter, I. Meiri, and J. Pearl, “Temporal constraint networks,” Artificial Intelligence, vol. 49, pp. 61–95, 1991.

    Article  MathSciNet  Google Scholar 

  10. M. Diaz and P. Senac, “Time stream petri nets: A model for timed multimedia information,” in Application and Theory of Petri Nets-94, edited by R. Valette, Springer-Verlag: New York, 1994, pp. 219–238.

    Google Scholar 

  11. D. Dubois and H. Prade, Possibility Theory, Plenum Press: New York, 1988.

  12. D. Dubois and H. Prade, “Processing fuzzy temporal knowledge,” IEEE Transactions on Systems, Man and Cybernetics, vol. 19, no. 4, pp. 729–744, 1989.

    Google Scholar 

  13. D. Dubois, J. Lang, and H. Prade, “Timed possibilistic logic,” Fundamenta Informaticae, vol. 15, nos. 3/4, pp. 211–234, 1991.

    Google Scholar 

  14. D. Dubois and H. Prade, “Processing fuzzy temporal knowledge,” IEEE Transactions on Systems, Man and Cybernetics, vol. 19, no. 4, pp. 729–744, 1989.

    Google Scholar 

  15. M. Felder, and A. Morzenti, “A temporal logic approach to implementation and refinement of timed petrinets,” in Proceedings of 1st international conference on Temporal Logic ICTL-94, edited by, D. Gabbay, Bonn, Germany, July 11–14, Springer-Verlag, New York, pp. 365–381, 1994.

  16. P. Fortemps, “Jobshop scheduling with imprecise durations: A fuzzy approach,” IEEE Transactions on Fuzzy Systems, vol. 5, no. 4, pp. 557–569, 1997.

    Article  Google Scholar 

  17. C. Ghezzi, D. Mandrioli, S. Morasca, and P. Mauro, “A general way to put time into petri nets,” ACM SIGSOFT Engineering Notes, vol. 14, no. 3, pp. 60–67, 1989.

    Article  Google Scholar 

  18. L. Godo and L. Vila, “Possibilistic temporal reasoning based on fuzzy temporal constraints,” in Proceedings of IJCAI-95, edited by C. Mellish, Montreal, Canada, 20–25 August, Morgan Kaufmann: San Francisco, CA, pp. 1916–1922, 1995.

  19. H. Hanisch, “Analysis of place/transition nets with timed arcs and its application to batch process control,” in Application and Theory of Petri Nets-93, edited by M. Marsan, Springer-Verlag, pp. 282–299, 1993.

  20. E. Kindler and T. Vesper, “ESTL: A temporal logic for events and states,” in Application and Theory of Petri Nets-98, edited by J. Desel and M. Silva, Springer-Verlag: New York, pp. 365–384, 1998.

    Google Scholar 

  21. L. Kunzle, R. Valette, and B. Pradin-Chezalviel, “Temporal reasoning in fuzzy time petri nets,” in Fuzziness in Petri Nets, edited by J. Cardoso and H. Camargo, Physica Verlag: New York, NY, pp. 146–173, 1999.

    Google Scholar 

  22. S. Kurkovsky, “Possibilistic temporal propagation, Ph.D. dissertation,” University of Southwestern Louisiana, 1999.

  23. J. Lee, K. Liu, and W. Chiang, “Modeling uncertainty reasoning with possibilistic petri nets,” IEEE Transactions on Systems, Man, and Cybernetics. vol. 33, no. 2, pp. 214–224, 2003.

    Google Scholar 

  24. P. Merlin, and D. Farber, “Recoverability of communication protocols,” IEEE Transactions on Communications, vol. 24, no. 9, pp. 541–580, 1989.

    Google Scholar 

  25. D. Milutinovic, and P. Lima, “Petri net models of robotic tasks,” in Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Washington DC, vol. 4, pp. 4059–4064, 2002.

  26. C. Petri, “Kommunikation mit Automaten, Ph.D. dissertation,” Technische Universitat Darmstadt, Germany, 1962.

  27. A. Raposo et al., “Using fuzzy petri nets to coordinate collaborative activities,” in Proceedings of the Joint 9th International Fuzzy Systems Association World Congress and 20th North American Fuzzy Information Processing Society International Conference. Vancouver, Canada. IEEE Press, 2001, pp. 1494–1499.

  28. M. Tanabe, “Timed petri nets and temporal linear logic,” in Application and Theory of Petri Nets-97, edited by P. Azema, G. Balbo, Springer-Verlag: New York, pp. 156–174, 1997.

    Google Scholar 

  29. M. Woo, N. Qazi, and A. Ghafoor, “A synchronization framework for communication of pre-orchestrated multimedia information,” IEEE Networks, vol. 8, no. 1, 52–61, 1994.

    Article  Google Scholar 

  30. Y. Yao, “A petri net model for temporal knowledge representation and reasoning,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 24, no. 9, pp. 1374–1382, 1994.

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Columbus State University, U.S.A.

    Stanislav Kurkovsky

  2. Intelligent System Laboratory, Center for Advanced Computer Studies, University of Louisiana at Lafayette, U.S.A.

    Rasiah Loganantharaj

Authors
  1. Stanislav Kurkovsky
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  2. Rasiah Loganantharaj
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Correspondence to Stanislav Kurkovsky.

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Kurkovsky, S., Loganantharaj, R. Extension of Petri Nets for Representing and Reasoning with Tasks with Imprecise Durations. Appl Intell 23, 97–108 (2005). https://doi.org/10.1007/s10489-005-3415-8

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