Verification of computing grids with special edge conditions by infinite Petri nets
- 30 Downloads
A technique of the computing grids verification using invariants of infinite Petri nets was presented. Models of square grid structures in the form of parametric Petri nets for such edge conditions as connection of edges and truncated devices were constructed. Infinite systems of linear algebraic equations were composed on parametric Petri nets for calculating p-invariants; their parametric solutions were obtained. P-invariant Petri nets are structurally conservative and bounded that together with liveness are the properties of ideal systems. Liveness investigation based on siphons and traps can be implemented using p-invariants of modified nets.
Keywordscomputing grid infinite Petri net invariant boundedness safeness liveness
Unable to display preview. Download preview PDF.
- 1.Grid Computing: Towards a Global Interconnected Infrastructure, Preve, N.P., Ed., Springer, 2011.Google Scholar
- 4.Achasova, S.M. and Bandman, O.L., Correctness of Concurrent Computational Processes, N.: Nauka, 1990 [in Russian].Google Scholar
- 6.Diaz, M., Modelling and analysis of communication and cooperation protocols using Petri net based model, Computer Networks, 1982, no. 6, pp. 419–441.Google Scholar
- 7.Li, Z.W. and Zhou, M.C., Deadlock Resolution in Automated Manufacturing Systems, Springer, 2010.Google Scholar
- 8.Zaitsev, D.A. and Zaitsev, I.D., Verification of Ethernet protocols via parametric composition of Petri net, INCOM’2006: 12th IFAC/IFIP/IFORS/IEEE/IMS Symposium Information Control Problems in Manufacturing, May 17–19 2006, Saint-Etienne, France, pp. 261–267.Google Scholar
- 9.Shmeleva, T.R., Verification of switched Ethernet protocols via infinite Petri nets, Proc. of DUIKT: Special Issue, Kyiv, 2007, pp. 96–102 [in Russian].Google Scholar
- 10.Shmeleva, T.R., Zaitsev, D.A., and Zaitsev, I.D., Analysis of square communication grids via infinite Petri nets, Transactions of Odessa National Academy of Telecommunication, 2009, no. 1, pp. 27–35.Google Scholar
- 12.Shmeleva. T.R., Proving consistency of Petri net grid models, Book of Abstracts of the International Scientific Conference on Computer Algebra and Information Technology, August 20–26, 2012, Odessa, Ukraine, pp. 83–86.Google Scholar
- 13.Zaitsev, D.A., Li, Z.W., Litvin, D.A., and Hou, Y.F., Calculating Petri net siphons via composition of clans, Proceedings of International Humanitarian University: Series ITPM, 2012, vol. 4, pp. 32–44 [in Ukr.].Google Scholar