Cybernetics and Systems Analysis

, Volume 46, Issue 1, pp 105–114 | Cite as

Verification of hypercube communication structures via parametric Petri nets1

  • D. A. Zaitsev
  • T. R. Shmeleva

A model of a hypercube communication structure of arbitrary size with an arbitrary number of dimensions is constructed in the form of a parametric Petri net. A technique for calculating linear invariants of parametric Petri nets is developed that allows one to analyze information transmission processes in such a hypercube. The structure of complicated deadlocks caused by a path (loop) of blockings and the isolation of devices is investigated. In real-life networks, the described deadlocks lead to a considerable decrease in performance and can be induced by some ill-intentioned traffic.


communication structure hypercube router parametric Petri net linear invariant deadlock 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. M. Marsan, G. Chiola, and A. Fumagalli, “An accurate performance model of CSMA/CD Bus LAN,” Advances in Petri Nets, LNCS, 266, 146–161 (1987).Google Scholar
  2. 2.
    D. A. Zaitsev and I. D. Zaitsev, “Verification of Ethernet protocols via parametric composition of Petri net,” in: 12th IFAC/IFIP/IFORS/IEEE/IMS Symposium on Information Control Problems in Manufacturing (INCOM’2006), Saint-Etienne, France (2006), pp. 261–267.Google Scholar
  3. 3.
    D. A. Zaitsev, Functional Petri nets, Universite Paris-Dauphine, Cahier du Lamsade 224, Avril 2005,
  4. 4.
    T. R. Shmeleva, “Verification of switched Ethernet protocols using infinite Petri nets,” in: 3rd International Conference on Modern Information-Communication Technologies (COMINFO’2007), Levadia, Ukraine (2007), pp. 161–163.Google Scholar
  5. 5.
    D. A. Zaitsev and T. R. Shmeleva, “Hypercube communication structures analysis via parametric Petri nets,” in: Proc. 24th UK Performance Engineering Workshop (UKPEW 2008), Department of Computing, Imperial College London, UK (2008), pp. 358–371.Google Scholar
  6. 6.
    T. Murata, “Petri nets: Properties, analysis, and applications,” Proc. IEEE, 77, 541–580 (1989).CrossRefGoogle Scholar
  7. 7.
    G. Berthelot and R. Terrat, “Petri Nets Theory for the Correctness of Protocols,” IEEE Trans. Comm., 30, No. 12, 2497–2505 (1982).CrossRefMathSciNetGoogle Scholar
  8. 8.
    M. Diaz, “Modeling and analysis of communication and cooperation protocols using Petri net based model,” Computer Network, No. 6, 419–441 (1982).Google Scholar
  9. 9.
    B. Berthomieu, O.-P. Ribet, and F. Vernadat, “The tool TINA-construction of abstract state space for Petri nets and time Petri nets,” International Journal of Production Research, 42, No. 4 (2004),

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.Odessa National A. S. Popov Academy of TelecommunicationsOdessaUkraine

Personalised recommendations