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  • 2000-2004  (7)
  • English  (7)
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  • 1
    Publication Date: 2014-11-11
    Description: We consider the problem of designing a network that employs a non-bifurcated shortest path routing protocol. The network's nodes and the set of potential links are given together with a set of forecasted end-to-end traffic demands. All relevant hardware components installable at links or nodes are considered. The goal is to simultaneously choose the network's topology, to decide which hardware components to install on which links and nodes, and to find appropriate routing weights such that the overall network cost is minimized. In this paper, we present a mathematical optimization model for this problem and an algorithmic solution approach based on a Lagrangian relaxation. Computational results achieved with this approach for several real-world network planning problems are reported.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 2
    Publication Date: 2020-08-05
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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  • 3
    Publication Date: 2020-02-11
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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  • 4
    Publication Date: 2020-08-05
    Language: English
    Type: article , doc-type:article
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  • 5
    Publication Date: 2020-02-11
    Description: In this article, we present a mathematical model and an algorithm to support one of the central strategic planning decisions of network operators: How to organize a large number of locations into a hierarchical network? We propose a solution approach that is based on mixed-integer programming and Lagrangian relaxation techniques. As major advantage, our approach provides not only solutions but also worst-case quality guarantees. Real-world scenarios with more than 750 locations have been solved within 30 minutes to less than 1\% off optimality.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 6
    Publication Date: 2014-02-26
    Description: This paper addresses the problem of designing a minimum cost network whose capacities are sufficiently large to allow a feasible routing of a given set of multicast commodities. A multicast commodity consists of a set of two or mo re terminals that need to be connected by a so called broadcast tree, which consumes on all of its edges a capacity as large as the demand value associated with that commodity. We model the network design problem with multicast commodities as the problem of packing capacitated Steiner trees in a graph. In the first part of the paper we present three mixed-integer programming formulations for this problem. The first natural formulation uses only one integer capacity variable for each edge and and one binary tree variable for each commodity-edge pair. Applying well-known techniques from the Steiner tree problem, we then develop a stronger directed and a multicommodity flow based mixed-integer programming formulation. In the second part of the paper we study the associated polyhedra and derive valid and even facet defining inequalities for the natural formulation. Finally, we describe separation algorithms for these inequalities and present computational results that demonstrate the strength of our extended formulations.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 7
    Publication Date: 2020-02-11
    Description: 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 has to satisfy certain survivability and 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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