Journal of Communications and Networks

The Korean Institute of Commucations and Information Sciences (한국통신학회)
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A Scheduling and Synchronization Technique for RAPIEnet Switches Using Edge-Coloring of Conflict Multigraphs

  • Received : 2012.07.03
  • Accepted : 2013.02.04
  • Published : 2013.06.30
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Abstract

In this paper, we present a technique for obtaining conflict-free schedules for real-time automation protocol for industrial Ethernet (RAPIEnet) switches. Mathematical model of the switch is obtained using graph theory. Initially network traffic entry and exit parts in a single RAPIEnet switch are identified, so that a bipartite conflict graph can be constructed. The obtained conflict graph is transformed to three kinds of matrices to be used as inputs for our simulation model, and selection of any of the matrix forms is application-specific. A greedy edge-coloring algorithm is used to schedule the network traffic and to solve the minimum coloring problem. After scheduling, empty slots are identified for forwarding the non real-time traffic of asynchronous devices. Finally, an algorithm for synchronizing the schedules of adjacent switches is proposed using edge-contraction and minors. All simulations were carried out using Matlab.

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References

  1. "IEC 61158-3-21: 2010, Industrial communication networks - Fieldbus specifications - Part 3-21: Data-link layer service definition Type 21 elements."
  2. "IEC 61158-4-21: 2010, Industrial communication networks - Fieldbus specifications - Part 4-21: Data-link layer protocol specification - Type 21 elements."
  3. "IEC 61158-5-21: 2010, Industrial communication networks - Fieldbus specifications - Part 5-21: Application layer service definition - Type 21 elements."
  4. "IEC 61158-6-21: 2010, Industrial communication networks - Fieldbus specifications - Part 6-21: Application layer protocol specification - Type 21 elements."
  5. "IEC 61784-2: 2010, Industrial communication networks - Profiles - Part 2: Additional fieldbus profiles for real-time networks based on ISO/IEC 8802-3."
  6. "IEC 62439-7, Industrial communication networks - High availability automation networks - Part 7: Ring-based Redundancy Protocol (RRP)."
  7. F. Dopatka and R.Wismller, "Design of a realtime industrial-Ethernet network including hot-pluggable asynchronous devices," in Proc. IEEE ISIE, 2007, pp. 1826-1831.
  8. F. Dopatka and R. Wismller, "A top-down Approach for realtime industrial-Ethernet networks using edge-coloring of conflict-multigraphs," in Proc. SPEEDAM, Taormina, Italy, May 2006, pp. 883-890.
  9. GE fanuc intelligent platforms. (2009). Switched Ethernet latency analysis [Online]. Available: http://www.gefanuc.com
  10. J. Gross and Yellen, Graph Theory and Its Applications. Washington, DC: CRC Press, 1999.
  11. G. Chartrand and O. R. Oellermann, Applied and Algorithmic Graph Theory. New York: McGraw-Hill, 1993.
  12. V. K. Balakrishan, Schaums Outline of Graph Theory. New York: McGraw-Hill, 1997.
  13. G. Chartrand and L. Lesniak, Graphs and Digraphs. 4th Ed., Washington, DC: CRC Press, 2005.
  14. M. Russell, Graph Theory. New York: John Wiley, 2001.
  15. R. J. Wilson, Introduction to Graph Theory. 4th ed., Prentice Hall, 1996.
  16. IEEE 802.3 LAN/MAN CSMA/CD Access Method, IEEE Standard, 802.3, 2002.
  17. U. Nowak, "Graphentheoretische modellierung eines automatisierungstechnischen echtzeitnetzwerks und algorithmenentwurf zum kommunikations- scheduling," Diploma Thesis, Dept. of Math., Univ. Siegen, Germany, 2006.
  18. D. Marx. (2003). Graph coloring problems and their applications in scheduling [Online]. Available: http://citeseer.ist.psu.edu/672702.html
  19. I. Holyer, "The NP-completeness of edge-coloring," SIAMJ. Comput., vol. 10, no. 4, pp. 718-720, 1981. https://doi.org/10.1137/0210055
  20. N. Alon, "A simple algorithm for edge-coloring bipartite multigraphs," Inf. Process. Lett. vol. 85, no. 6, pp. 301-302, 2003. https://doi.org/10.1016/S0020-0190(02)00446-5
  21. R. Jain and J. Werth, "Analysis of approximate algorithms for edgecoloring bipartite graphs," Inf. Process. Lett., vol.54(3), pp. 163-168, 1995. https://doi.org/10.1016/0020-0190(95)00013-3
  22. T. H. Cormen, C. E. Leiserson, and R. L. Rivest, Introduction to Algorithms. 2nd ed., MIT Press and McGraw-Hill, 2001.
  23. S. Iglin, "GrTheory-Graph Theory Toolbox," Mathworks Inc. Matlab.