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.
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References
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)
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)
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)
Waxman, B.M.: Routing of multipoint connections. IEEE J. Sel. A. Commun. 6(9), 1617–1622 (2006)
Doar, M.: Multicast in the ATM environment. Ph.D. Thesis, Cambridge University, Computer Lab (1993)
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)
Albert, R., Barabasi A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)
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]
Bobbio, A., Terruggia, R., Ciancamerla, E., Minichino, M.: Evaluating Network Reliability Versus Topology by Means of BDD Algorithms. PSAM-9, Hong Kong (2008)
Milner, R.: Bigraphs, a Tutorial, at http://www.cl.cam.ac.uk/users/rm135 (2005)
Kim, J.H., Vu, V.: Sandwiching random graphs. Adv. Math. 188, 444–469 (2004)
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)
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)
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)
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)
Kurant, M., Thiran, P.: Layered complex networks. Phys. Rev. Lett. 96, 138701-1–138701-4 (2006)
Popkov, V.K.: Mathematical models of connectivity. Inst. Comp. Math. Math. Geophys. Novosibirsk (2006) (in Russian)
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)
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)
Rodionov, A.S., Choo, H., Nechunaeva, K.A.: Framework for biologically inspired graph optimization. In: Proceedings of ICUIMC 2011, Seoul, Paper 2.5 (2011)
Popkov, V.K.: Using s-hypernet theory for modeling systems with network structure. Probl. Inf. 4, 17–40 (2010) (in Russian)
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)
Satyanarayana, A., Chang, M.K.: Network reliability and the factoring theorem. Networks 13, 107–120 (1983)
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This work is supported by the grant of the Program of basic researches of the Presidium of Russian Academy of Science.
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Rodionov, A., Rodionova, O. (2015). Random Hypernets in Reliability Analysis of Multilayer Networks. In: Mastorakis, N., Bulucea, A., Tsekouras, G. (eds) Computational Problems in Science and Engineering. Lecture Notes in Electrical Engineering, vol 343. Springer, Cham. https://doi.org/10.1007/978-3-319-15765-8_17
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DOI: https://doi.org/10.1007/978-3-319-15765-8_17
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