A Chance-Constrained Model and Cutting Planes for Fixed Broadband Wireless Networks

  • Grit Claßen
  • David Coudert
  • Arie M. C. A. Koster
  • Napoleão Nepomuceno
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6701)


In this paper, we propose a chance-constrained mathematical program for fixed broadband wireless networks under unreliable channel conditions. The model is reformulated as an integer linear program and valid inequalities are derived for the corresponding polytope. Computational results show that by an exact separation approach the optimality gap is closed by 42% on average.


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  1. 1.
    Achterberg, T., Raack, C.: The MCF-separator: detecting and exploiting multi-commodity flow structures in MIPs. Mathematical Programming Computation 2, 125–165 (2010)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Anderson, H.: Fixed Broadband Wireless System Design, 1st edn. John Wiley & Sons, Chichester (2003)CrossRefGoogle Scholar
  3. 3.
    Claßen, G., Coudert, D., Koster, A., Nepomuceno, N.: Bandwidth assignment for reliable fixed broadband wireless networks. In: IEEE WoWMoM 2011. IEEE, Lucca (2011)Google Scholar
  4. 4.
    Coudert, D., Nepomuceno, N., Rivano, H.: Power-efficient radio configuration in fixed broadband wireless networks. Computer Communications 33(8), 898–906 (2010)CrossRefGoogle Scholar
  5. 5.
    Fischetti, M., Lodi, A., Salvagnin, D.: Just MIP it! Ann. Info. Systems 10, 39–70 (2009)CrossRefGoogle Scholar
  6. 6.
    IBM – ILOG: CPLEX Optimization Studio 12.2, http://www.ilog.com/products/cplex
  7. 7.
    Koster, A.M.C.A., Kutschka, M., Raack, C.: Cutset inequalities for robust network design. In: Pahl, J., Reiners, T., Voß, S. (eds.) INOC 2011, 128–133. LNCS, vol. 6701, Springer, Heidelberg (2011)Google Scholar
  8. 8.
    Larsson, T., Yuan, D.: An augmented lagrangian algorithm for large scale multicommodity routing. Computational Optimization and Applications 27(2), 187–215 (2004)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Lehpamer, H.: Microwave transmission networks: planning, design, and deployment. McGraw-Hill, New York (2010)Google Scholar
  10. 10.
    Raack, C., Koster, A.M.C.A., Orlowski, S., Wessäly, R.: On cut-based inequalities for capacitated network design polyhedra. Networks 57, 141–156 (2011)MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Grit Claßen
    • 1
  • David Coudert
    • 2
  • Arie M. C. A. Koster
    • 1
  • Napoleão Nepomuceno
    • 3
  1. 1.Lehrstuhl II für MathematikRWTH Aachen UniversityAachenGermany
  2. 2.Project-team MascotteI3S (CNRS/UNS) INRIA Université de Nice SophiaSophia AntipolisFrance
  3. 3.Institut for Matematik og DatalogiSyddansk UniversitetOdenseDenmark

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