Verification of the hexagonal communication grid by infinite Petri nets

Authors

  • T.R. Shmeleva

DOI:

https://doi.org/10.30837/rt.2018.3.194.07

Keywords:

computing grids, hexagonal communication structure, infinite Petri net, direct parametric specification, linear invariant, verification of protocols

Abstract

A formal direct parametric description of the hexagonal grid model with side k is constructed according to the specified grid composition rules. A system of linear equations is constructed for finding invariants of positions on the basis of a direct description of the model. A method for calculating linear invariants of infinite Petri nets with a regular structure for an open hexagonal grid is used, and a solution of a system of linear equations in parametric form is obtained. It is proved that the hexagonal grid model, represented in the form of infinite Petri net, is a p-invariant Petri net for an arbitrary natural number k and has the boundedness and conservativeness properties. Communication grids, representing the implementation of the studied model, can be constructed using devices with limited capacity without overflow.

References

Телекоммуникационные системы и сети : учеб. пособие : в 3 т. / Г. П. Катунин, В. Н. Попантонопуло, В. П. Шувалов, Г. В. Мамчев. – 2-е изд., испр. и доп. – Москва : Горячая линия – Телеком, 2004 ; 2005.

Sayandev Mukherjee. Analytical Modeling of Heterogeneous:Cellular Networks Geometry, Coverage, and Capacity. – Cambridge University Press, 2014. – 180 p.

Kolchin A.V., Letichevsky A.A., Potienko S.V., Peschanenko V.S.. Overview of modern systems and verification methods of formal models // Problems of Programming. 2012. – No. 4. – Р. 75-88.

Shmeleva T.R., Zaitsev D.A., Zaitsev I.D. Analysis of Square Communication Grids via Infinite Petri Nets // Transactions of Odessa National Academy of Telecommunication. – 2009. – no. 1. – Р. 27–35.

Zaitsev D.A., Zaitsev I.D., Shmeleva T.R. Infinite Petri Nets: Part 1, Modeling Square Grid Structures // Complex Systems. – 2017. – 26(2). – Р. 157-195.

Murata T. Petri Nets: Properties, Analysis and Applications // Proceedings of the IEEE. – 1989. – 77(4). – p. 541–580.

Berthelot G., Terrat R. Petri Nets Theory for the Correctness of Protocols // IEEE Trans. on Communications, no. 12, 1982, vol. 30, p. 2497-2505.

Zaitsev D.A. Verification of Computing Grids with Special Edge Conditions by Infinite Petri Nets // Automatic Control and Computer Sciences. – 2013. – Vol. 47, N 7. – Р. 403-412.

Шмелёва Т.Р. Параметрическая спецификация открытой шестиугольной

решетки // 71 НТ конферен-ция ОНАС, декабрь 6-8, 2016. – Одесса, 2016. – С. 65-68.

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Published

2018-09-26

How to Cite

Shmeleva, T. (2018). Verification of the hexagonal communication grid by infinite Petri nets. Radiotekhnika, 3(194), 38–45. https://doi.org/10.30837/rt.2018.3.194.07

Issue

No. 194 (2018): Radiotekhnika

Section

Articles

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