Abstract
In this article we study the problem of designing a nation-wide communication network. Such networks usually consist of an access layer, a backbone layer, and maybe several intermediate layers. The nodes of each layer must be connected to those of the next layer in a tree-like fashion. The backbone layer must satisfy survivability and IP-routing constraints.
Given the node locations, the demands between them, the possible connections and hardware configurations, and various other technical and administrational constraints, the goal is to decide, which node is assigned to which network level, how the nodes are connected, what hardware must be installed, and how traffic is routed in the backbone.
Mixed integer linear programming models and solution methods are presented for both the access and the backbone network design problem. The focus is on the design of IP-over-SDH networks, but the access network design model and large parts of the backbone network design models are general and also applicable for other types of communication networks. Results obtained with these methods in the planning of the German research network are presented.
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References
D. Alevras, M. Grötschel, and R. Wessäly, Capacity and survivability models for telecommunications networks, Tech. Report SC 97-24, Konrad-Zuse-Zentrum für Informationstechnik, Berlin, 1997.
K. Aardal, M. Labbé, J. Leung, and M. Queyranne, On the two-level uncapacitated facility location problem, INFORMS Journal on Computing 8 (1996), 289–301.
W. Ben-Ameur and E. Gourdin, Internet routing and related topology issues, SIAM Journal on Discrete Mathematics 17 (2003), 18–49.
W. Ben-Ameur, E. Gourdin, and B. Liau, Internet routing and topology problems, Proceedings of DRCN2000 (Munich), 2000.
D. Bienstock, S. Chopra, O. Günlük, and C-Y. Tsai, Minimum cost capacity installation for multicommodity network flows, Mathematical Programming 81 (1998), 177–199.
S. Borne, E. Gourdin, B. Liau, and A. Mahjoub, Design of survivable IP-over-optical networks, Proceedings of the First International Network Optimization Conference (INOC 2003), Paris, 2003, pp. 114–118.
A. Bley, M. Grötschel, and R. Wessäly, Design of broadband virtual private networks: Model and heuristics for the B-WiN, Robust Communication Networks: Interconnection and Survivability (N. Dean, D. F. Hsu, and R. Ravi, eds.), DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 53, AMS, 1998, pp. 1–16.
A. Bley and T. Koch, Optimierung des G-WiN, DFN-Mitteilungen 54 (2000), 13–15.
A. Bley, T. Koch, and R. Wessäly, Large-scale hierarchical networks: How to compute an optimal architecture?, Proceedings of Networks 2004 (Vienna), VDE Verlag, 2004, pp. 429–434.
A. Bley, A Lagrangian approach for integrated network design and routing in IP networks, Proceedings of the First International Network Optimization Conference (INOC 2003), Paris, 2003, pp. 107–113.
A. Bley, On the approximability of the minimum congestion unsplittable shortest path routing problem, Proceedings of 11th Conference on Integer Programming and Combinatorial Optimization (IPCO 2005), Berlin, 2005, pp. 97–110.
A. Bley, Inapproximability results for the inverse shortest paths problem with integer lengths and unique shortest paths, Networks 50 (2007), 29–36.
A. Bley, Routing and capacity optimization for IP networks, Ph.D. thesis, Technische Universität Berlin, 2007.
E. A. Boyd, Polyhedral results for the precedence-constrained knapsack problem, Discrete Applied Mathematics 41 (1993), 185–201.
L. Buriol, M. Resende, C. Ribeiro, and M. Thorup, A hybrid genetic algorithm for the weight setting problem in OSPF/IS-IS routing, Networks 46 (2005), 36–56.
L. Buriol, M. Resende, and M. Thorup, Survivable IP network design with OSPF routing, Optimization Online (2004).
E. Balas and E. Zemel, Facets of the knapsack polytope from minimal covers, SIAM Journal on Applied Mathematics 34 (1978), 119–148.
ILOG CPLEX Division, 889 Alder Avenue, Suite 200, Incline Village, NV 89451, USA, ILOG CPLEX 7.5 reference manual, 2001, Information available at http://www.cplex.com
J. Crowcroft and Z. Wang, Analysis of shortest-path routing algorithms in a dynamic network environment, ACM SIGCOM Computer Communication Review 22 (1992), 63–71.
M. Ericsson, M. G. C. Resende, and P. M. Pardalos, A genetic algorithm for the weight setting problem in OSPF routing, Tech. report, AT&T Labs Research, 2001.
A. Feldmann, A. Greenberg, C. Lund, N. Reingold, and J. Rexford, NetScope: Traffic engineering for IP networks, IEEE Network 14 (2000), 11–19.
C. E. Ferreira, A. Martin, C. C. de Souza, R. Weismantel, and L. A. Wolsey, Formulations and valid inequalities of the node capacitated graph partitioning problem, Mathematical Programming 74 (1996), 247–266.
B. Fortz and M. Thorup, Internet traffic engineering by optimizing OSPF weights, Proceedings of IEEE INFOCOM 2000, 2000.
B. Fortz and M. Thorup, Increasing internet capacity using local search, Computational Optimization and Applications 29 (2004), 13–48.
M. Grötschel, C. L. Monma, and M. Stoer, Design of survivable networks, Handbooks in Operations Research and Management Science, vol. Network Models, ch. 10, pp. 617–672, North-Holland, 1995.
E. Gourdin, Optimizing internet networks, OR/MS Today (2001), 46–49.
L. Hall, Experience with a cutting plane algorithm for the capacitated spanning tree problem, INFORMS Journal on Computing 8 (1996), 219–234.
K. Holmberg and D. Yuan, Optimization of Internet protocol network design and routing, Networks 43 (2004), 39–53.
T. Koch and A. Martin, Solving Steiner tree problems in graphs to optimality, Networks 32 (1998), 207–232.
H. Kerivin and A. Mahjoub, Design of survivable networks: A survey, Networks 46 (2005), 1–21.
F. Y. S. Lin and J. L. Wang, Minimax open shortest path first routing algorithms in networks suporting the SMDS service, Tech. report, Bell Communications Research, 1993.
A. Martin, Integer programs with block structure, Habilitations-Schrift, Technische Universität Berlin, 1998.
S. Melkote and M. S. Daskin, Capacitated facility location/network design problems, European Journal of Operations Research 129 (2001), 481–495.
P. Mirchandani and R. Francis (eds.), Discrete location theory, Wiley, New York, 1990.
G. L. Nemhauser and P. H. Vance, Lifted cover facets of the 0-1 knapsack polytope with GUB constraints, Operations Research Letters 16 (1994), 255–263.
K. Park, K. Lee, S. Park, and H. Lee, Telecommunication node clustering with node compatibility and network survivability requirements, Management Science 46 (2000), 263–374.
M. Prytz, On optimization in design of telecommunications networks with multicast and unicast traffic, Ph.D. thesis, Royal Institute of Technology, Stockholm, Sweden, 2002.
D. Staehle, S. Köhler, and U. Kohlhaas, Towards an optimization of the routing parameters for IP networks, Tech. report, Department of Computer Science, University of Würzburg, 2000.
R. Wunderling, Paralleler und objektorientierter simplex, Tech. Report TR 96-09, Konrad-Zuse-Zentrum für Informationstechnik, Berlin, 1996, Information available at http://www.zib.de/Optimization/Software/Soplex
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Bley, A., Koch, T. (2008). Integer Programming Approaches to Access and Backbone IP Network Planning. In: Bock, H.G., Kostina, E., Phu, H.X., Rannacher, R. (eds) Modeling, Simulation and Optimization of Complex Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79409-7_7
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DOI: https://doi.org/10.1007/978-3-540-79409-7_7
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