Skip to main content
SpringerLink
Log in

A comparison of routing sets for robust network design

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

Designing a network able to route a set of non-simultaneous demand vectors is an important problem arising in telecommunications. In this paper, we compare the optimal capacity allocation costs for six routing sets: affine routing, volume routing and its two simplifications, the routing based on an unrestricted 2-cover of the uncertainty set, and the routing based on a cover delimited by a hyperplane.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Altin, A., Amaldi, E., Belotti, P., Pinar, M.Ç.: Provisioning virtual private networks under traffic uncertainty. Networks 49(1), 100–115 (2007)

    Google Scholar 

  2. Applegate, D., Cohen, E.: Making intra-domain routing robust to changing and uncertain traffic demands: understanding fundamental tradeoffs. In: Proceedings of the 2003 conference on Applications, technologies, architectures, and protocols for computer communications, SIGCOMM ’03, pp. 313–324. ACM, New York (2003)

  3. Ben-Ameur, W.: Between fully dynamic routing and robust stable routing. In: 6th International Workshop on Design and Reliable Communication Networks, 2007. DRCN 2007 (2007)

  4. Ben-Ameur, W., Kerivin, H.: New economical virtual private networks. Commun. ACM 46(6), 69–73 (2003)

    Article  Google Scholar 

  5. Ben-Ameur, W., Kerivin, H.: Routing of uncertain demands. Optim. Eng. 3, 283–313 (2005)

    Article  MathSciNet  Google Scholar 

  6. Ben-Ameur, W., Zotkiewicz, M.: Volume oriented routing. In: 14th International Telecommunications Network Strategy and Planning Symposium (NETWORKS), pp. 1–7 (2010)

  7. Ben-Ameur, W., Zotkiewicz, M.: Robust routing and optimal partitioning of a traffic demand polytope. Int. Trans. Oper. Res. 18(3), 307–333 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  8. Ben-Tal, A., Goryashko, A., Guslitzer, E., Nemirovski, A.: Adjustable robust solutions of uncertain linear programs. Math. Program. 99(2), 351–376 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  9. Ben-Tal, A., Nemirovski, A.: Robust solutions of uncertain linear programs. Oper. Res. Lett. 25(1), 1–13 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  10. Bertsimas, D., Caramanis, C.: Finite adaptability in multistage linear optimization. IEEE Trans. Automat. Contr. 55(12), 2751–2766 (2010)

    Article  MathSciNet  Google Scholar 

  11. Bertsimas, D., Sim, M.: The price of Robustness. Oper. Res. 52(1), 35–53 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  12. Chekuri, C., Oriolo, G., Scutellà, M.G., Shepherd, F.B.: Hardness of robust network design. Networks 50(1), 50–54 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  13. Duffield, N.G., Goyal, P., Greenberg, A., Mishra, P., Ramakrishnan, K.K., van der Merive, J.E.: A flexible model for resource management in virtual private networks. SIGCOMM Comput. Commun. Rev. 29(4), 95–108 (1999)

    Google Scholar 

  14. Fingerhut, J.A., Suri, S., Turner, J.S.: Designing least-cost nonblocking broadband networks. J. Algorithms 24(2), 287–309 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  15. Goyal, N., Olver, N., Shepherd, F.B.: Dynamic vs. oblivious routing in network design. In: Proceedings of the ESA 2009, pp. 277–288 (2009)

  16. Gupta, A., Kleinberg, J., Kumar, A., Rastogi, R., Yener, B.: Provisioning a virtual private network: a network design problem for multicommodity flow. In: STOC ’01: Proceedings of the thirty-third annual ACM symposium on Theory of computing, pp. 389–398 (2001)

  17. ILOG CPLEX Division, Gentilly, France. ILOG. ILOG CPLEX 12.4 Reference Manual (2007)

  18. Koster, A.M.C.A., Kutschka, M., Raack, C.: Robust network design: Formulations, valid inequalities, and computations. Technical Report 11–34, ZIB (2011)

  19. Minoux, M.: Robust network optimization under polyhedral demand uncertainty is np-hard. Discrete Appl. Math. 158(5), 597–603 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  20. Ordóñez, F., Zhao, J.: Robust capacity expansion of network flows. Networks 50(2), 136–145 (2007)

    Google Scholar 

  21. S. Orlowski, M. Pióro, A. Tomaszewski, R. Wessäly. SNDlib 1.0-Survivable Network Design Library. Networks 55(3):276–286 (2010). http://sndlib.zib.de

  22. Ouorou, A., Vial, J.-P.: A model for robust capacity planning for telecommunications networks under demand uncertainty. In: 6th International Workshop on Design and Reliable Communication Networks, 2007. DRCN 2007, pp. 1–4 (2007)

  23. Poss, M., Raack, C.: Affine recourse for the robust network design problem: between static and dynamic routing. Networks 61(2), 180–198 (2013)

    Google Scholar 

  24. Scutellà, M.G.: On improving optimal oblivious routing. Oper. Res. Lett. 37(3), 197–200 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  25. Scutellà, M. G.: Hardness of some optimal oblivious routing generalizations. Technical Report TR-10-05, Universitá di Pisa (2010)

  26. Soyster, A.L.: Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper. Res. 21, 1154–1157 (1973)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

The author is grateful to Christian Raack and to a referee for numerous comments that helped in improving the presentation of the paper.

Author information

Authors and Affiliations

  1. UMR CNRS 7253 Heudiasyc, Centre de Recherches de Royallieu, Université de Technologiede Compiègne, Compiègne, 60200, France

    Michael Poss

Authors
  1. Michael Poss
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael Poss.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Poss, M. A comparison of routing sets for robust network design. Optim Lett 8, 1619–1635 (2014). https://doi.org/10.1007/s11590-013-0679-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-013-0679-5

Keywords

Search

Navigation