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Random Hypernets in Reliability Analysis of Multilayer Networks

  • Alexey RodionovEmail author
  • Olga Rodionova
Chapter
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 343)

Abstract

The general approach to constructing structural models of non-stable multi-level networks is proposed. This approach is based on hypernets—relatively new mathematical object, which is successively used for modeling different multi-level networks in the Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Russia, for last 30 years. Hypernets allow standard description of neighboring levels interconnection in a mathematically correct way. Using this mathematical object allows easy modifications of data with model changing and/or development and efficiently organize data search for different computational or optimization algorithms. Optimization of mapping of secondary (logical) network onto structure of unreliable primary (physical) network is considered as example.

Keywords

Multilevel networks Modeling Hypernets Reliability analysis 

Notes

Acknowledgements

This work is supported by the grant of the Program of basic researches of the Presidium of Russian Academy of Science.

References

  1. 1.
    Jain, M., Chand, S.: On connectivity of ad hoc network using fuzzy logic. In: Proceedings of the 2014 International Conference on Applied Mathematics and Computational Methods in Engineering II (AMCME ’14) and the 2014 International Conference on Economics and Business Administration II (EBA ’14), pp. 159–165 (2014)Google Scholar
  2. 2.
    Seytnazarov, S., Kim, Y.-T.: QoS-aware MPDU aggregation of IEEE 802.11n WLANs for VoIP services. In: Proceedings of the 2014 International Conference on Electronics and Communication Systems II (ECS ’14) and the 2014 International Conference on Education and Educational Technologies II (EET ’14), pp. 64–71 (2014)Google Scholar
  3. 3.
    Mosharraf, N., Khayyambashi, M.R.: Improving performance and reliability of adaptive fault tolerance structure in distributed real time systems. Comput. Simul. Mod. Sci. 3, 133–143 (2010)Google Scholar
  4. 4.
    Waxman, B.M.: Routing of multipoint connections. IEEE J. Sel. A. Commun. 6(9), 1617–1622 (2006)CrossRefGoogle Scholar
  5. 5.
    Doar, M.: Multicast in the ATM environment. Ph.D. Thesis, Cambridge University, Computer Lab (1993)Google Scholar
  6. 6.
    Kumar, R., Raghavan, P., Rajagopalan, S., Sivakumar, D., Tomkins, A., Upfal, E.: Stochastic models for the Web graph. In: Proceedings 41st Annual Symposium on Foundations of Computer Science, pp. 57–65 (2000)Google Scholar
  7. 7.
    Albert, R., Barabasi A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)zbMATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Yano, A., Wadayama, T.: Probabilistic analysis of the network reliability problem on a random graph ensemble. http://arxiv.org/pdf/1105.5903.pdf (2011) [arXiv:1105.5903v3]
  9. 9.
    Bobbio, A., Terruggia, R., Ciancamerla, E., Minichino, M.: Evaluating Network Reliability Versus Topology by Means of BDD Algorithms. PSAM-9, Hong Kong (2008)Google Scholar
  10. 10.
    Milner, R.: Bigraphs, a Tutorial, at http://www.cl.cam.ac.uk/users/rm135 (2005)
  11. 11.
    Kim, J.H., Vu, V.: Sandwiching random graphs. Adv. Math. 188, 444–469 (2004)zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Dijkstra, F., Andree, B., Koymans, K., van der Hama, J., Grosso, P., de Laat, C.: A multi-layer network model based on ITU-T G.805. Comput. Netw. 52, 1927–1937 (2008)Google Scholar
  13. 13.
    He, F., Xin, C.: Cross-layer path computation for dynamic traffic grooming in mesh WDM optical networks. Technical Report #NSUCS-2004-009, Norfolk State University (2004)Google Scholar
  14. 14.
    Koster, A.M.C.A., Orlowski, S., Raack, C., Baier, G., Engel, T., Belotti, P.: Branch-and-cut techniques for solving realistic two-layer network design problems. In: Graphs and Algorithms in Communication Networks, pp. 95–118. Springer, Heidelberg (2009)Google Scholar
  15. 15.
    Chigan, C., Atkinson, G., Nagarajan, R.: On the modeling issue of joint cross-layer network protection/restoration. In: Proceedings of Advanced Simulation Technologies Conference (ASTC ’04), pp. 57–62 (2004)Google Scholar
  16. 16.
    Kurant, M., Thiran, P.: Layered complex networks. Phys. Rev. Lett. 96, 138701-1–138701-4 (2006)Google Scholar
  17. 17.
    Popkov, V.K.: Mathematical models of connectivity. Inst. Comp. Math. Math. Geophys. Novosibirsk (2006) (in Russian)Google Scholar
  18. 18.
    Popkov, V.K., Sokolova, O.D.: Application of hyperneet theory for the networks optimazation problems. In: 17th IMACS World Congress, July 2005, Paper T4-I-42-011 (2005)Google Scholar
  19. 19.
    Rodionov, A.S., Sokolova, O., Yurgenson, A., Choo, H.: On Optimal placement of the monitoring devices on channels of communication network. In: ICCSA 2009, Part II. Lecture Notes in Computer Science, vol. 5593, pp. 465–478 (2009)CrossRefGoogle Scholar
  20. 20.
    Rodionov, A.S., Choo, H., Nechunaeva, K.A.: Framework for biologically inspired graph optimization. In: Proceedings of ICUIMC 2011, Seoul, Paper 2.5 (2011)Google Scholar
  21. 21.
    Popkov, V.K.: Using s-hypernet theory for modeling systems with network structure. Probl. Inf. 4, 17–40 (2010) (in Russian)Google Scholar
  22. 22.
    Rodionova, O.K., Rodionov, A.S., Choo, H.: Network probabilistic connectivity: Exact calculation with use of chains. In: ICCSA-2004. Springer Lecture Notes in Computer Science, vol. 3046, pp. 315–324 (2004)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Satyanarayana, A., Chang, M.K.: Network reliability and the factoring theorem. Networks 13, 107–120 (1983)zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of Computational Mathematics and Mathematical Geophysics SB RASNovosibirskRussia
  2. 2.Higher College of Informatics of the Novosibirsk State UniversityNovosibirskRussia

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