Abstract
Due to the increasing importance of effective communication in today’s business, designing net- works efficiently has started to attract more attention. In this chapter, we consider the Robust Network Loading Problem (Rob-NLP), which includes private network design as a special case, an important problem in telecommunications sector. We study the problem from the view point of a com- munications service provider who wants to lease private communication lines to its customers in the most cost-efficient manner. Rather than assuming that the point-to-point communication demands are given in advance, we introduce a polyhedral demand model, which inherits the strengths of two known polyhedral demand definitions. We first develop two compact mixed integer programming for- mulations of the problem. Then we provide some experimental results for several well-known network design instances to discuss the economic and performance implications of incorporating robustness into our design efforts.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Altın A, Amaldi A, Belotti P, Pınar MÇ (2007) Provisioning virtual private networks under traffic uncertainty. Networks 49(1):100–115
Altın A, Belotti P, Pınar MÇ (2010) OSPF routing with optimal oblivious performance ratio under polyhedral demand uncertainty. Optimiz Eng, 11(3), pp 395–422
Altın A, Yaman H, Pınar MÇ (to appear) The robust network loading problem under hose demand uncertainty: formulation, polyhedral analysis, and computations. INFORMS J Comput
Atamtürk A (2006) Strong reformulations of robust mixed 0–1 programming. Math Program 108:235–250
Atamtürk A, Rajan D (2002) On splittable and unsplittable capacitated network design arc-set polyhedra. Math Program 92:315–333
Atamtürk A, Zhang M (2007) Two-stage robust network flow and design under demand uncertainty, Oper Res 55:662–673
Avella P, Mattia S, Sassano A (2007) Metric inequalities and the network loading problem. Discrete Optimiz 4:103–114
Ben-Ameur W, Kerivin H (2005) Routing of uncertain demands. Optimiz Eng 3:283–313
Ben-Tal A, Goryashko A, Guslitzer E, Nemirovski A (2004) Adjustable robust solutions of uncertain linear programs. Mathem Program Ser A 99:351–376
Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math Oper Res 23(4):769–805
Ben-Tal A, Nemirovski A (1999) Robust solutions of uncertain linear programs. Oper Res Lett 25:1–13
Ben-Tal A, Nemirovski A (2008) Selected topics in robust convex optimization. Math Program 112(1):125–158
Bertsimas D, Sim M (2003) Robust discrete optimization and network flows. Math Program Ser B 98:49–71
Bertsimas D, Sim M (2004) The price of robustness. Oper Res 52:35–53
Berger D, Gendron B, Potvin J, Raghavan S, Soriano P (2000) Tabu search for a network loading problem with multiple facilities. J Heurist 6:253–267
Bienstock D, Chopra S, Günlük O, Tsai C-Y (1998) Minimum cost capacity installation for multi-commodity network flows. Math Program 81:177–199
Bienstock D, Günlük O (1996) Capacitated network design – polyhedral structure and computation. INFORMS J Comput 8:243–259
Duffield N, Goyal P, Greenberg A, Mishra P, Ramakrishnan K, van der Merive JE (1999) A flexible model for resource management in virtual private networks. In: Proceedings of ACM SIGCOMM, pp 95–108, Massachusetts, USA.
Erlebach T, Rúegg M (2004) Optimal bandwidth reservation in hose-model vpns with multi-path routing. Proc IEEE Infocom, 4:2275–2282
Fingerhut JA, Suri S, Turner JS (1997) Designing least-cost nonblocking broadband networks. J Algorithm, 24(2):287–309
Günlük O (1999) A Branch-and-Cut algorithm for capacitated network design problems. Math Program 86:17–39
Günlük O, Brochmuller B, Wolsey L (2004) Designing private line networks – polyhedral analysis and computation. Trans Oper Res 16:7–24. Math Program Ser. A (2002) 92:335–358
Gupta A, Kleinberg J, Kumar A, Rastogi R, Yener B (2001) Provisioning a virtual private network: a network design problem for multicommodity flow. In: Proceedings of ACM symposium on theory of computing (STOC), Crete, Greece, pp 389–398
Gupta A, Kumar A, Roughgarden T (2003) Simpler and better approximation algorithms for network design. In: Proceedings of the ACM symposium on theory of computing (STOC), pp 365–372, San Diego, CA.
Italiano G, Rastogi R, Yener B (2002) Restoration algorithms for virtual private networks in the hose model. In: IEEE INFOCOM, pp 131–139.
A. Jüttner, Szabó I, Szentesi Á (2003) On bandwidth efficiency of the hose resource management in virtual private networks. In: IEEE INFOCOM, 1:386–395.
Karaşan O, Pınar MÇ, Yaman H (2006) Robust DWDM routing and provisioning under polyhedral demand uncertainty. Technical report, Bilkent University
Kumar A, Rastogi R, Silberschatz A, Yener B (2001) Algorithms for provisioning virtual private networks in the hose model. In: SIGCOMM’01, August 27–31, 2001, San Diego, CA, USA
Magnanti TL, Mirchandani P (1993) Shortest paths single origin-destination network design, and associated polyhedra. Networks 23:103–121
Magnanti TL, Mirchandani P, Vachani R (1993) The convex hull of two core capacitated network design problems. Math Program 60:233–250
Magnanti TL, Mirchandani P, Vachani R (1995) Modeling and solving the two-facility capacitated network loading problem. Oper Res 43(1):142–157
Mirchandani P (2000) Projections of the capacitated network loading problem. Eur J Oper Res 122:534–560
Mudchanatongsuk S, Ordoñez F, Liu J (2008) Robust solutions for network design under transportation cost and demand uncertainty. J Oper Res Soc 59(5):652–662
Ordoñez F, Zhao J (2007) Robust capacity expansion of network flows. Networks 50(2):136–145
Rardin RL, Wolsey LA (1993) Valid inequalities and projecting the multicommodity extended formulation for uncapacitated fixed charge network flow problems. Eur J Oper Res 71:95–109
Sim M (2009) Distributionally robust optimization: a marriage of robust optimization and stochastic optimization. In: Third nordic optimization symposium, Stockholm, Sweden.
Soyster AL (1973) Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper Res 21:1154–1157
Swamy C, Kumar A (2002) Primal-dual algorithms for connected facility location problems. In: Proceedings of the international workshop on approximation algorithms for combinatorial optimization (APPROX), Lecture Notes in Computer Science series, 2462:256–270
Yaman H, Karaşan OE, Pınar MÇ (2007) Restricted robust uniform matroid maximization under interval uncertainty. Math Program 110(2):431–441
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Altın, A., Yaman, H., Pınar, M.Ç. (2011). A Hybrid Polyhedral Uncertainty Model for the Robust Network Loading Problem. In: Gülpınar, N., Harrison, P., Rüstem, B. (eds) Performance Models and Risk Management in Communications Systems. Springer Optimization and Its Applications, vol 46. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0534-5_7
Download citation
DOI: https://doi.org/10.1007/978-1-4419-0534-5_7
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-0533-8
Online ISBN: 978-1-4419-0534-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)