Verification of hypercube communication structures via parametric Petri nets1
- 34 Downloads
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.
Keywordscommunication structure hypercube router parametric Petri net linear invariant deadlock
Unable to display preview. Download preview PDF.
- 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.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.D. A. Zaitsev, Functional Petri nets, Universite Paris-Dauphine, Cahier du Lamsade 224, Avril 2005, www.lamsade.dauphine.fr/cahiers.html.
- 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.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
- 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.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), http://www.laas.fr/tina.