The optimal value of circular reserve for symmetrical hierarchical networks

Abstract

We consider the Symmetrical Hierarchical Network and analyse its survivability under uncertainty conditions. A formula calculates the optimum value of circular reserve of the symmetrical hierarchical network. We take into account the possibility of optimising the flow distribution after the fault. We suppose that the remaining capacity will be known. The guaranteed evaluation of the functional capability of the symmetrical hierarchical network assumes finding the worst distribution of the destruction. References Ahmadi M. B., The Survivability of Symmetrical Hierarchical Networks with Radial Reserve, Journal Application and Applied Mathematics: An International Journal (AAM), 3(2008) 30--41. Ahmadi M. B., Malashenko Yu. E., Novikova N. M., Research on survivability of a hierarchical network, J. Vestnik Moscow state university serial 15, computational mathematics and cybernetics 3(2001) 18--23 (in Russian). Ahmadi M. B., A comparison of effectiveness of circular and radial reserve in survivability of symmetrical hierarchical networks, J. WSEAS transaction on computer, Issue 6, 3(2004) 1764--1766. Chang B.-J., Hwang R.-H., Modeling and analyzing the performance of adaptive hierarchical networks, Information Sciences 176 (2006) 522--549. Chen Ch, Chen J., Nearly Optimal One-to-Many Parallel Routing in Star Networks, IEEE Transactions on Parallel and Distributed Systems, Issue 12, 8(1997) 1196--1202. Chen D., Garg S., Trivedi K. S., Network Survivability Performance Evaluation: A Quantitative Approach with Applications in Wireless Adhoc Networks, Proceedings of the 5th ACM international workshop on Modeling analysis and simulation of wireless and mobile systems, (2002) 61--68. Garg M., Smith J. C., Models and algorithms for the design of survivable multicommodity flownetworks with general failure scenarios, Omega 36 (2008) 1057--1071. Grubesic T. H., Murray A. T. Spatial-historical landscapes of telecommunication network survivability, Telecommunication policy, (2005) 801--820. Heegaard P. E., Trivedi K. S., Network survivability modeling, Computer Networks 53 (2009) 1215--1234. Kalamani K, Palaniswami S, and Nagarajan N, Network Survivability for a Regular WDM Optical Network from Double- Link Failures Using Greedy Algorithm, International Journal of Recent Trends in Engineering, 1 (2009) 478--482. Kan D. D., Narula-Tam A., Modiano E., Lightpath Routing and Capacity Assignment for Survivable IP-over-WDM Networks, 7th International Workshop on the Design of Reliable Communication Networks Washington, DC, USA (2009) 37--44. Lee K., Modiano E., Cross-layer Survivability in WDM based Networks, Proc. IEEE INFOCOM'09, Rio de Janeiro, Brazil, April (2009). Malashenko Yu. E., Novikova N. M., The Analysis of Multi user Network Systems under Uncertainty, J. of Computer and Systems Sciences International, 38(1999) 589--601. Morehead R. , Noore A., Novel hybrid mitigation strategy for improving the resiliency of hierarchical networks subjected to attacks, Physica A 378 (2007) 603--612. Phillips D., Garcia-Dias A., Fundamentals of network analysis, (Englewood Cliffs, N. J. : Prentice-Hall,1981). Shi J., Foneska J. P., Traffic Based Survivability Analysis of Telecommunications Networks,Proc. IEEE Globe-com 95, 2(1995) 936--940. Sterbenz J. P. G. , Hutchison D., Cetinskaya E. K., Jabbar A., Rohrer J. P., Schller M., Smith P., Resilience and survivability in communication networks: Strategies, principles, and survey of disciplines, Computer Networks 54 (2010) 1245--1265. Wu T., Kolar D. J., Cardwell R. H., Survivable networks architectures for broad-band fiber optic networks: Model and performance comparison, Journal of Lightwave Technology, (1998)1698--1709.