Abstract
An efficient way to cope with the complexity in modelling a large-scale system consists in decomposing it into subsystems called modules, modelling each module using Petri nets and integrating these models together to obtain the model of the whole system. This paper addresses the liveness and boundedness analysis for a Petri net model with event graph modules (also called marked graphs). We prove that each event graph module can be replaced by a simple but still equivalent event graph model called minimal representation in which the internal transitions of the initial module are removed. We also prove some properties of general Petri nets which allow to simplify the liveness and boundedness analysis.
Preview
Unable to display preview. Download preview PDF.
References
T. Agerwala and Y. Choed-Amphai, “A Synthesis Rule for Concurrent Systems,” Proc. 15th Design Automation Conf., Las Vegas, pp. 305–311, June 1978
G. Berthlot, “Checking Properties of Nets using Transformation,” in Advances in Petri Nets 1985, G. Rozenberg (ed.), Lecture Notes in Computer Sience, Springer-Verlag, pp. 19–40, 1985
F. Commoner, A. Holt, S. Even and A. Pnueli, “Marked Directed Graphs,” J. of Computer and System Science, vol. 5, No. 5, pp. 511–523, 1971
G. Harhalakis, J.M. Proth, V.M. Savi, and X.L. Xie, “A Stepwise Specification of a Manufacturing System using Petri Nets,” Proc. 1991 IEEE International Conference on Systems, Man, and Cybernetics, Charlottesville, Virginia, October, 1991
L.E. Holloway and B.H. Krogh, “Synthesis of Feedback Control Logic for a Class of Controlled Petri Nets,” IEEE Trans. on Automatic Control, vol. AC-35, No. 5, pp 514–523, May 1990
G. Huet, “Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems,” J. of ACM, vol. 27, No. 4, pp. 797–821, October 1980
J.R. Jump and P.S. Thiagarajan, “On the Equivalence of Asynchronous Control Structure,” SIAM J. Comput., vol. 2, No. 2, pp. 67–87, June 1973
J. Koh, and F. DiCesare, “Transformation Methods for Generalized Petri Nets and Their Applications to Flexible Manufacturing Systems,” Proc. of IEEE Robotics and Automation, pp.534–539, Scottsdale, AZ, 1989
W.E. Kluge and K. Lautenbach, “The Orderly Resolution of Memory Access Conflict Among Competing Channel Processes,” IEEE Trans. on Computers, vol. C-31, No. 3, pp. 194–207, March 1982
B.H. Krogh and C.L. Beck, “Synthesis of Place/Transition Nets for Simulation and Control of Manufacturing Systems,” Proc. IFIP Symp. Large Scale Syst., Zurich, August 1986
L.H. Landweber and E.L. Robertson, “Properties of Conflict-Free and Persistent Petri Nets,” J. of ACM, vol. 25, No. 3, pp. 352–364, July 1978
K.H. Lee and J. Favrel, “Hierarchical Reduction Method for Analysis and Decomposition of Petri Nets,” IEEE Trans. Systems, Man, and Cybernetics, vol. SMC-15, No. 2, pp.272–281, 1985
K.H. Lee, J. Favrel, and P. Baptiste, “Generalized Petri Net Reduction Method,” IEEE Trans. Systems, Man, and Cybernetics, vol. SMC-17, No. 2, pp.297–303, 1987
Y.E. Lien, “Termination Properties of Generalized Petri Nets,” SIAM. J. Comput., vol. 5, No. 2, pp. 251–265, June 1976
T. Murata, “Petri Nets: Properties, Analysis and Applications,” Proceedings of the IEEE, vol. 77, N∘ 4, April 1989
Y. Narahari and N. Viswanadham, “A Petri Net Approach to the Modelling and Analysis of Flexible Manufacturing Systems,” Annals of Operations Research, vol. 3, pp. 449–472, 1985
M. Silva, “Petri Nets and Flexible Manufacturing,” in Advances in Petri Nets 1989, G. Rozenberg (ed.), Lecture Notes of Computer Science, Springer Verlag, 1989
I. Suzuki and T. Murata, “A Method for Stepwise Refinement and Abstraction of Petri Nets,” J. of Computer and System Sciences, Vol. 27, pp.51–76, 1983
R. Valette, “Analysis of Petri Nets by Stepwise Refinements,” J. of Computer and System Sciences, Vol. 18, pp.35–46, 1979
M.C. Zhou, F. Dicesare, and A.A. Desrochers, “A Top-down Modular Approach to Synthesis of Petri Net Models for Manufacturing Systems,” Proc. of IEEE Robotics and Automation Conf., pp. 534–539, Scottsdale, AZ, May, 1989
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Savi, V.M., Xie, X. (1992). Liveness and boundedness analysis for Petri nets with event graph modules. In: Jensen, K. (eds) Application and Theory of Petri Nets 1992. ICATPN 1992. Lecture Notes in Computer Science, vol 616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55676-1_19
Download citation
DOI: https://doi.org/10.1007/3-540-55676-1_19
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55676-3
Online ISBN: 978-3-540-47270-4
eBook Packages: Springer Book Archive