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Telecommunications Modeling, Policy, and Technology pp 81–99Cite as

Error Bounds for Hierarchical Routing

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Part of the book series: Operations Research/Computer Science Interfaces ((ORCS,volume 44))

Abstract

We present a general model of hierarchical routing, with multiple levels of hierarchy, which introduces the concept of a cluster estimator to approximate the distance from a border node of a cluster to any node in the cluster. We characterize the hierarchical path length c HE and prove that the average error is minimized using the overall best routing cluster estimator. We present the first worst case upper bound on the error c HE – c* in hierarchical routing that is valid for any cluster estimator, and show the bound is sharp for two-level networks.

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References

  1. R.K. Ahuja, T.L. Magnanti, and J.B. Orlin, Network Flows, Prentice-Hall, New Jersey, 1993.

    Google Scholar 

  2. J. Ash and G. Choudhury, “PNNI Routing Congestion Control,” IEEE Communications Magazine, vol. 42, pp. 154-160, 2004.

    Article  Google Scholar 

  3. A.E. Baratz and J.M. Jaffe, “Establishing Virtual Circuits in Large Computer Networks.” Computer Networks and ISDN Systems, 12 (1986) 27-37.

    Article  Google Scholar 

  4. J. Behrens and J.J. Garcia-Luna-Aceves, “Hierarchical Routing Using Link Vectors,” Proc. IEEE InfoCom ’98, pp. 702-710, 1998.

    Google Scholar 

  5. B.-J. Chang and R.-H. Hwang, “Performance Analysis for Hierarchical Multirate Loss Networks,” IEEE/ACM Transactions on Networking, vol. 12, pp. 187-199, 2004.

    Article  Google Scholar 

  6. J. Hagouel, “Issues in Routing for Large and Dynamic Networks,” Ph.D. Thesis, Columbia University, May 1983.

    Google Scholar 

  7. L. Kleinrock and F. Kamoun, “Hierarchical Routing for Large Networks: Performance Evaluation and Optimization,” Computer Networks, vol. 1, pp. 155-174, 1977.

    MathSciNet  Google Scholar 

  8. L. Kleinrock and F. Kamoun, “Optimal Clustering Structures for Hierarchical Topological Design of Large Computer Networks,” Networks, vol. 10, pp. 221-248, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  9. W.S. Lai, E. Rosenberg, L. Amiri, M. Ball, Y. Levy, H. Shulman, H. Tong, and M. Ungar, “Analysis and Design of AT&T’s Global PNNI Network,” Proc. IEEE Pacific Rim Conference on Communications, Computers, and Signal Processing(PacRim 2005), August, 2005, pp. 129-132.

    Google Scholar 

  10. W.S. Lai, L. Amiri, M. Ball, E. Rosenberg, and H. Tong, “The Scalable Growth of AT&T’s Global PNNI Network,” Proc. 2006 Symposium on Performance Evaluation of Computer and Telecommunication Systems(SPECTS 2006), Calgary, Alberta, Canada, July 31 - August 2, 2006, pp. 363-370.

    Google Scholar 

  11. X. Masip-Bruin, S. Sánchez-López, J. Solé-Pareta, J. Domingo-Pascual, and E. Marin- Tordera, “Hierarchical Routing with QoS Constraints in Optical Transport Networks,” Lecture Notes in Computer Science, Springer-Verlag, Heidelberg, vol. 3042, pp. 662-674, 2004.

    Google Scholar 

  12. J.T. Moy, OSPF: Anatomy of an Internet Routing Protocol, Addison-Wesley, Reading, MA, 1998.

    Google Scholar 

  13. A. Orda and A. Sprintson, “Precomputation Schemes for QoS Routing,” IEEE/ACM Transactions on Networking, vol. 11, pp. 578-591, 2003.

    Article  Google Scholar 

  14. Private Network-Network Interface Specification Version 1.1, The ATM Forum Technical Committee, af-pnni-0055.002, April, 2002.

    Google Scholar 

  15. E. Rosenberg, “The Expected Length of a Random Line Segment in a Rectangle,” Operations Research Letters, vol. 32, pp. 99-102, 2004.

    MATH  Google Scholar 

  16. E. Rosenberg, “Hierarchical PNNI Addressing by Recursive Partitioning,” Proc. IEEE Pacific Rim Conference on Communications, Computers, and Signal Processing(PacRim 2005), August, 2005, pp. 133-136.

    Google Scholar 

  17. E. Rosenberg, “Hierarchical Topological Network Design,” IEEE/ACM Transactions on Networkingvol. 13, pp. 1402-1409, 2005.

    Article  Google Scholar 

  18. J.W. Stewart, BGP4: Inter-Domain Routing in the Internet, Addison-Wesley, Reading, MA, 1999.

    Google Scholar 

  19. P. Van Mieghem, “Estimation of an Optimal PNNI Topology,” in Proc. IEEE ATM’97 Workshop, Lisbon, Portugal, May 26-28, 1997.

    Google Scholar 

  20. W.T. Tsai, C.V. Ramamoorthy,W.K. Tsai, and O. Nishiguchi, “An Adaptive Hierarchical Routing Protocol,” IEEE Trans. on Computers, vol. 38, pp. 1059-1075, 1989.

    Google Scholar 

  21. A. Vasilakos, M.P. Saltouros, A. F. Atlassis, and W. Pedrycz, “Optimizing QoS Routing in Hierarchical ATM Networks Using Computation Intelligence Techniques,” IEEE Transactions on Systems, Man, and Cybernetics - Part C, vol. 33, pp. 297-312, 2003.

    Article  Google Scholar 

  22. E.W. Zegura, K.L. Calvert, and M.J. Donahoo, “A Quantitative Comparison of Graph- Based Models for Internet Topology,” IEEE/ACM Transactions on Networkingvol. 5, pp. 770-783, 1997.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. AT &T Labs, Middle Town, NJ 07748, USA

    Eric Rosenberg

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  1. Eric Rosenberg
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Editor information

Editors and Affiliations

  1. University of Maryland, College Park, MD, USA

    S. Raghavan  & Bruce Golden  & 

  2. American University, Washington, DC, USA

    Edward Wasil

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Rosenberg, E. (2008). Error Bounds for Hierarchical Routing. In: Raghavan, S., Golden, B., Wasil, E. (eds) Telecommunications Modeling, Policy, and Technology. Operations Research/Computer Science Interfaces, vol 44. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-77780-1_5

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  • DOI: https://doi.org/10.1007/978-0-387-77780-1_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-387-77779-5

  • Online ISBN: 978-0-387-77780-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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