TY - GEN A1 - Zymolka, Adrian A1 - Koster, Arie M.C.A. A1 - Wessäly, Roland T1 - Transparent optical network design with sparse wavelength conversion N2 - We consider the design of transparent optical networks from a practical perspective. Network operators aim at satisfying the communication demands at minimum cost. Such an optimization involves three interdependent planning issues: the dimensioning of the physical topology, the routing of lightpaths, and the wavelength assignment. Further topics include the reliability of the configuration and sparse wavelength conversion for efficient use of the capacities. In this paper, we investigate this extensive optical network design task. Using a flexible device-based model, we present an integer programming formulation that supports greenfield planning as well as expansion planning on top of an existing network. As solution method, we propose a suitable decomposition approach that separates the wavelength assignment from the dimensioning and routing. Our method in particular provides a lower bound on the total cost which allows to rate the solution quality. Computational experiments on realistic networks approve the solution approach to be appropriate. T3 - ZIB-Report - 02-34 KW - optical network design KW - wavelength conversion KW - integer programming Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7017 ER - TY - GEN A1 - Hülsermann, Ralf A1 - Jäger, Monika A1 - Krumke, Sven A1 - Poensgen, Diana A1 - Rambau, Jörg A1 - Tuchscherer, Andreas T1 - Dynamic Routing Algorithms in Transparent Optical Networks An Experimental Study Based on Real Data N2 - Today's telecommunication networks are configured statically. Whenever a connection is established, the customer has permanent access to it. However, it is observed that usually the connection is not used continuously. At this point, dynamic provisioning could increase the utilization of network resources. WDM based Optical Transport Networks (OTNs) will shortly allow for fast dynamic network reconfiguration. This enables optical broadband leased line services on demand. Since service requests competing for network resources may lead to service blocking, it is vital to use appropriate strategies for routing and wavelength assignment in transparent optical networks. We simulate the service blocking probabilities of various dynamic algorithms for this problem using a well-founded traffic model for two realistic networks. One of the algorithms using shortest path routings performs best on all instances. Surprisingly, the tie-breaking rule between equally short paths in different wavelengths decides between success or failure. T3 - ZIB-Report - 02-35 KW - Dynamic Network Configuration KW - Routing and Wavelength Allocation KW - Transparent Optical Networks KW - Blocking Probability KW - Simulation Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7025 ER - TY - GEN A1 - Bley, Andreas A1 - Koch, Thorsten T1 - Integer programming approaches to access and backbone IP-network planning N2 - 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. T3 - ZIB-Report - 02-41 KW - Network design KW - Traffic enineering KW - Internet routing KW - Mixed-integer programming Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7081 ER - TY - GEN A1 - Eisenblätter, Andreas A1 - Fügenschuh, Armin A1 - Koch, Thorsten A1 - Koster, Arie M.C.A. A1 - Martin, Alexander A1 - Pfender, Tobias A1 - Wegel, Oliver A1 - Wessäly, Roland T1 - Modelling Feasible Network Configurations for UMTS N2 - A model for the optimisation of the location and configuration of base stations in a UMTS network is described. The focus is primarily on modelling the configuration problem sufficiently accurate using mixed-integer variables and (essentially) linear constraints. These constraints reflect the limited downlink code capacity in each cell, the interference limitations for successful up- and downlink transmissions, the need for sufficiently strong (cell) pilot signals, and the potential gain for mobiles from being in soft(er) hand-over. It is also explained how to use the model as a basis for rating network configurations. T3 - ZIB-Report - 02-16 KW - UMTS KW - radio interface KW - network planning KW - configuration KW - perfect power control KW - mathematical model KW - mixed integer programming KW - MOMENTUM KW - IST-20 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6837 ER - TY - GEN A1 - Krumke, Sven A1 - Poensgen, Diana T1 - Online Call Admission in Optical Networks with Larger Wavelength Demands N2 - In the problem of \emph{Online Call Admission in Optical Networks}, briefly called \textsc{oca}, we are given a graph $G=(V,E)$ together with a set of wavelengths~$W$ and a finite sequence $\sigma=r_1,r_2,\dots$ of calls which arrive in an online fashion. Each call~$r_j$ specifies a pair of nodes to be connected and an integral demand indicating the number of required lightpaths. A lightpath is a path in~$G$ together with a wavelength~$\lambda \in W$. Upon arrival of a call, an online algorithm must decide immediately and irrevocably whether to accept or to reject the call without any knowledge of calls which appear later in the sequence. If the call is accepted, the algorithm must provide the requested number of lightpaths to connect the specified nodes. The essential restriction is the wavelength conflict constraint: each wavelength is available only once per edge, which implies that two lightpaths sharing an edge must have different wavelengths. Each accepted call contributes a benefit equal to its demand to the overall profit. The objective in \textsc{oca} is to maximize the overall profit. Competitive algorithms for \textsc{oca} have been known for the special case where every call requests just a single lightpath. In this paper we present the first competitive online algorithms for the general case of larger demands. T3 - ZIB-Report - 02-22 KW - Call Admission KW - Routing and Wavelength Allocation KW - Optical Networks KW - Competitive Analysis KW - Colorability Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6890 ER - TY - THES A1 - Krumke, Sven T1 - Online Optimization: Competitive Analysis and Beyond N2 - Traditional optimization techniques assume, in general, knowledge of all data of a problem instance. There are many cases in practice, however, where decisions have to be made before complete information about the data is available. In fact, it may be necessary to produce a part of the problem solution as soon as a new piece of information becomes known. This is called an \emph{online situation}, and an algorithm is termed \emph{online}, if it makes a decision (computes a partial solution) whenever a new piece of data requests an action. \emph{Competitive analysis} has become a standard yardstick to measure the quality of online algorithms. One compares the solution produced by an online algorithm to that of an optimal (clairvoyant) offline algorithm. An online algorithm is called $c$-competitive if on every input the solution it produces has cost'' at most $c$~times that of the optimal offline algorithm. This situation can be imagined as a game between an online player and a malicious adversary. Although competitive analysis is a worst-case analysis and henceforth pessimistic, it often allows important insights into the problem structure. One can obtain an idea about what kind of strategies are promising for real-world systems and why. On the other hand there are also cases where the offline adversary is simply too powerful and allows only trivial competitiveness results. This phenomenon is called hitting the triviality barrier''. We investigate several online problems by means of competitive analysis. We also introduce new concepts to overcome the weaknesses of the standard approach and to go beyond the triviality barrier. T3 - ZIB-Report - 02-25 KW - competitive analysis KW - online optimization KW - online algorithm KW - approximation algorithm Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6925 ER - TY - THES A1 - Koch, Thorsten T1 - Rapid Mathematical Programming N2 - The thesis deals with the implementation and application of out-of-the-box tools in linear and mixed integer programming. It documents the lessons learned and conclusions drawn from five years of implementing, maintaining, extending, and using several computer codes to solve real-life industrial problems. By means of several examples it is demonstrated how to apply algebraic modeling languages to rapidly devise mathematical models of real-world problems. It is shown that today's MIP solvers are capable of solving the resulting mixed integer programs, leading to an approach that delivers results very quickly. Even though, problems are tackled that not long ago required the implementation of specialized branch-and-cut algorithms. In the first part of the thesis the modeling language Zimpl is introduced. Chapter 2 contains a complete description of the language. In the subsequent chapter details of the implementation are described. Both theoretical and practical considerations are discussed. Aspects of software engineering, error prevention, and detection are addressed. In the second part several real-world projects are examined that employed the methodology and the tools developed in the first part. Chapter 4 presents three projects from the telecommunication industry dealing with facility location problems. Chapter 5 characterizes questions that arise in UMTS planning. Problems, models, and solutions are discussed. Special emphasis is put on the dependency of the precision of the input data and the results. Possible reasons for unexpected and undesirable solutions are explained. Finally, the Steiner tree packing problem in graphs, a well-known hard combinatorial problem, is revisited. A formerly known, but not yet used model is applied to combine switchbox wire routing and via minimization. All instances known from the literature are solved by this approach, as are some newly generated bigger problem instances. T3 - ZIB-Report - 04-58 KW - Modelling Languages KW - Mixed Integer Programming KW - Steiner Tree Packing in Graphs KW - Location Planning in Telecommunications KW - UMTS Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8346 ER - TY - GEN A1 - Bley, Andreas T1 - Inapproximability Results for the Inverse Shortest Paths Problem with Integer Length and Unique Shortest Paths N2 - We study the complexity of two Inverse Shortest Paths (ISP) problems with integer arc lengths and the requirement for uniquely determined shortest paths. Given a collection of paths in a directed graph, the task is to find positive integer arc lengths such that the given paths are uniquely determined shortest paths between their respective terminals. The first problem seeks for arc lengths that minimize the length of the longest of the prescribed paths. In the second problem, the length of the longest arc is to be minimized. We show that it is $np-hard$ to approximate the minimal longest path length within a factor less than $8/7$ or the minimal longest arc length within a factor less than $9/8$. This answers the (previously) open question whether these problems are $np-hard$ or not. We also present a simple algorithm that achieves an $\mathcal{O}(|V|)$-approximation guarantee for both variants. Both ISP problems arise in the planning of telecommunication networks with shortest path routing protocols. Our results imply that it is $\mathcal{NP}$-hard to decide whether a given path set can be realized with a real shortest path routing protocol such as OSPF, IS-IS, or RIP. T3 - ZIB-Report - 05-04 KW - Inverse Shortest Paths KW - Computational Complexity KW - Approximation KW - Shortest Path Routing Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8388 ER - TY - GEN A1 - Koster, Arie M.C.A. T1 - Wavelength Assignment in Multi-Fiber WDM Networks by Generalized Edge Coloring N2 - In this paper, we study wavelength assignment problems in multi-fiber WDM networks. We focus on the special case that all lightpaths have at most two links. This in particular holds in case the network topology is a star. As the links incident to a specific node in a meshed topology form a star subnetwork, results for stars are also of interest for general meshed topologies. We show that wavelength assignment with at most two links per lightpath can be modeled as a generalized edge coloring problem. By this relation, we show that for a network with an even number of fibers at all links and at most two links per lightpath, all lightpaths can be assigned a wavelength without conversion. Moreover, we derive a lower bound on the number of lightpaths to be converted for networks with arbitrary numbers of fibers at the links. A comparison with linear programming lower bounds reveals that the bounds coincide for problems with at most two links per lightpath. For meshed topologies, the cumulative lower bound over all star subnetworks equals the best known solution value for all realistic wavelength assignment instances available, by this proving optimality. T3 - ZIB-Report - 05-13 KW - wavelength assignment KW - optical networks KW - graph theory KW - combinatorial optimization KW - integer programming Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8478 ER - TY - GEN A1 - Koster, Arie M.C.A. A1 - Zymolka, Adrian T1 - Provably Good Solutions for Wavelength Assignment in Optical Networks N2 - In this paper, we study the minimum converter wavelength assignment problem in optical networks. To benchmark the quality of solutions obtained by heuristics, we derive an integer programming formula tion by generalizing the formulation of Mehrotra and Trick (1996) for the vertex coloring problem. To handle the exponential number of variables, we propose a column generation approach. Computational experiments show that the value of the linear relaxation states a good lower bound and can often prove optimality of the best solution generated heuristically. T3 - ZIB-Report - 04-40 KW - wavelength assignment KW - integer programming KW - column generation Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8155 ER - TY - GEN A1 - Koster, Arie M.C.A. A1 - Zymolka, Adrian T1 - Linear Programming Lower Bounds for Minimum Converter Wavelength Assignment in Optical Networks N2 - In this paper, we study the conflict-free assignment of wavelengths to lightpaths in an optical network with the opportunity to place wavelength converters. To benchmark heuristics for the problem, we develop integer programming formulations and study their properties. Moreover, we study the computational performance of the column generation algorithm for solving the linear relaxation of the most promising formulation. In many cases, a non-zero lower bound on the number of required converters is generated this way. For several instances, we in fact prove optimality since the lower bound equals the best known solution value. T3 - ZIB-Report - 04-41 KW - optical networks KW - wavelength assignment KW - integer programming Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8160 ER - TY - GEN A1 - Bley, Andreas A1 - Pattloch, Marcus T1 - Modellierung und Optimierung der X-WiN Plattform N2 - In diesem Artikel werden die Optimierungsmodelle und -verfahren beschrieben, die bei der Planung des Kernnetzes und der Zugangsinfrastruktur des X-WiN verwendet wurden. T3 - ZIB-Report - 05-21 Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8551 ER - TY - GEN A1 - Bley, Andreas T1 - A Lagrangian Approach for Integrated Network Design and Routing in IP Networks N2 - 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. T3 - ZIB-Report - 03-29 KW - Network Planning KW - Routing KW - IP Routing KW - Lagrangian relaxation Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7515 ER - TY - GEN A1 - Eisenblätter, Andreas A1 - Koster, Arie M.C.A. A1 - Wallbaum, Randolf A1 - Wessäly, Roland T1 - Load Balancing in Signaling Transfer Points N2 - Signaling is crucial to the operation of modern telecommunication networks. A breakdown in the signaling infrastructure typically causes customer service failures, incurs revenue losses, and hampers the company image. Therefore, the signaling network has to be highest reliability and survivability. This in particular holds for the routers in such a network, called \textit{signaling transfer points\/} (STPs). The robustness of an STP can be improved by equally distributing the load over the internal processing units. Several constraints have to be taken into account. The load of the links connected to a processing unit changes over time introducing an imbalance of the load. In this paper, we show how integer linear programming can be applied to reduce the imbalance within an STP, while keeping the number of changes small. Two alternative models are presented. Computational experiments validate the integer programming approach in practice. The GSM network operator E-Plus saves substantial amounts of time and money by employing the proposed approach. T3 - ZIB-Report - 02-50 KW - Signaling network KW - STP KW - load-balancing KW - integer programming KW - computations Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7179 ER - TY - GEN A1 - Koster, Arie M.C.A. A1 - Zymolka, Adrian A1 - Jäger, Monika A1 - Hülsermann, Ralf A1 - Gerlach, Christoph T1 - Demand-wise Shared Protection for Meshed Optical Networks N2 - In this paper, a new shared protection mechanism for meshed optical networks is presented. Significant network design cost reductions can be achieved in comparison to the well-known 1+1 protection scheme. Demand-wise Shared Protection (DSP) bases on the diversification of demand routings and exploits the network connectivity to restrict the number of backup lightpaths needed to provide the desired level of prorection. Computational experiments approve the benefits of the concept DSP for cost efficient optical network designs. T3 - ZIB-Report - 03-24 KW - optical network design KW - shared protection KW - meshed optical networks KW - diversification Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7461 ER - TY - GEN A1 - Geerdes, Hans-Florian A1 - Karl, Holger T1 - The Potential of Relaying in Cellular Networks N2 - Relaying is a protocol extension for cellular wireless computer networks; in order to utilize radio resources more efficiently, several hops are allowed within one cell. This paper investigates the principle potential of relaying by casting transmission scheduling as a mathematical optimization problem, namely, a linear program. We analyze the throughput gains showing that, irrespective of the concrete scheduling algorithm, performance gains of up to 30\% on average for concrete example networks are achievable. T3 - ZIB-Report - 03-42 KW - Wireless ad hoc networks KW - Resource Allocation KW - Integer Programming KW - Routing KW - Scheduling KW - Operation Research KW - Network Performance Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7641 ER - TY - GEN A1 - Geerdes, Hans-Florian T1 - Assessing Capacity Improvements by Relaying in Cellular Networks N2 - Relaying -- allowing multiple wireless hops -- is a protocol extension for cellular networks conceived to improve data throughput. Its benefits have only been quantified for small example networks. For assessing its general potential, we define a complex resource allocation\slash{}scheduling problem. Several mathematical models are presented for this problem; while a time-expanded MIP approach turns out intractable, a sophisticated column generation scheme leads to good computational results. We thereby show that for selected cases relaying can increase data throughput by 30\% on the average. T3 - ZIB-Report - 03-43 KW - Wireless ad hoc networks KW - Resource Allocation KW - Integer Programming KW - Routing KW - Scheduling KW - Operation Research KW - Network Performance Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7651 ER - TY - GEN A1 - Koster, Arie M.C.A. A1 - Zymolka, Adrian T1 - Minimum Converter Wavelength Assignment in All-Optical Networks N2 - Finding conflict-free wavelength assignments with a minimum number of required conversions for a routing of the lightpaths is one of the important tasks within the design of all-optical networks. We consider this problem in multi-fiber networks with different types of WDM systems. We give a detailed description of the problem and derive its theoretical complexity. For practical application, we propose several sequential algorithms to compute appropriate wavelength assignments. We also perform computational experiments to evaluate their performance. For the iterative algorithms, we identify characteristic patterns of progression. Two of these algorithms qualify for application in practice. T3 - ZIB-Report - 03-45 KW - minimum converter wavelength assignment KW - optical networks KW - generalized coloring KW - complexity KW - heuristics Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7673 ER - TY - GEN A1 - Bley, Andreas T1 - On the Hardness of Finding Small Shortest Path Routing Conflicts N2 - Nowadays most data networks use shortest path protocols such as OSPF or IS-IS to route traffic. Given administrative routing lengths for the links of a network, all data packets are sent along shortest paths with respect to these lengths from their source to their destination. One of the most fundamental problems in planning shortest path networks is to decide whether a given set of routing paths forms a valid routing and, if this is not the case, to find a small subset of the given paths that cannot be shortest paths simultaneously for any routing lengths. In this paper we show that it is NP-hard to approximate the size of the smallest shortest path conflict by a factor less than 7/6. T3 - ZIB-Report - 09-15 KW - shortest path routing KW - computational complexity Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11276 SN - 1438-0064 ER - TY - GEN A1 - Bley, Andreas T1 - An Integer Programming Algorithm for Routing Optimization in IP Networks N2 - Most data networks nowadays use shortest path protocols to route the traffic. Given administrative routing lengths for the links of the network, all data packets are sent along shortest paths with respect to these lengths from their source to their destination. In this paper, we present an integer programming algorithm for the minimum congestion unsplittable shortest path routing problem, which arises in the operational planning of such networks. Given a capacitated directed graph and a set of communication demands, the goal is to find routing lengths that define a unique shortest path for each demand and minimize the maximum congestion over all links in the resulting routing. We illustrate the general decomposition approach our algorithm is based on, present the integer and linear programming models used to solve the master and the client problem, and discuss the most important implementational aspects. Finally, we report computational results for various benchmark problems, which demonstrate the efficiency of our algorithm. T3 - ZIB-Report - 08-30 KW - Shortest Path Routing KW - Integer Programming Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10814 SN - 1438-0064 ER - TY - GEN A1 - Raack, Christian A1 - Koster, Arie M.C.A. A1 - Wessäly, Roland T1 - On the strength of cut-based inequalities for capacitated network design polyhedra N2 - In this paper we study capacitated network design problems, differentiating directed, bidirected and undirected link capacity models. We complement existing polyhedral results for the three variants by new classes of facet-defining valid inequalities and unified lifting results. For this, we study the restriction of the problems to a cut of the network. First, we show that facets of the resulting cutset polyhedra translate into facets of the original network design polyhedra if the two subgraphs defined by the network cut are (strongly) connected. Second, we provide an analysis of the facial structure of cutset polyhedra, elaborating the differences caused by the three different types of capacity constraints. We present flow-cutset inequalities for all three models and show under which conditions these are facet-defining. We also state a new class of facets for the bidirected and undirected case and it is shown how to handle multiple capacity modules by Mixed Integer Rounding (MIR). T3 - ZIB-Report - 07-08 KW - cutset-polyhedra KW - flow-cutset inequalities KW - network design KW - mixed integer programming Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9512 ER - TY - GEN A1 - Raack, Christian A1 - Koster, Arie M.C.A. A1 - Orlowski, Sebastian A1 - Wessäly, Roland T1 - Capacitated network design using general flow-cutset inequalities N2 - This paper deals with directed, bidirected, and undirected capacitated network design problems. Using mixed integer rounding (MIR), we generalize flow-cutset inequalities to these three link types and to an arbitrary modular link capacity structure, and propose a generic separation algorithm. In an extensive computational study on 54 instances from the Survivable Network Design Library (SNDlib), we show that the performance of cplex can significantly be enhanced by this class of cutting planes. The computations reveal the particular importance of the subclass of cutset-inequalities. T3 - ZIB-Report - 07-14 KW - general flow-cutset inequalities KW - capacitated network design KW - mixed integer rounding KW - SNDlib Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9576 ER - TY - GEN A1 - Orlowski, Sebastian A1 - Pioro, Michal A1 - Tomaszewski, Artur A1 - Wessäly, Roland T1 - SNDlib 1.0--Survivable Network Design Library N2 - We provide information on the Survivable Network Design Library (SNDlib), a data library for fixed telecommunication network design that can be accessed at http://sndlib.zib.de. In version 1.0, the library contains data related to 22 networks which, combined with a set of selected planning parameters, leads to 830 network planning problem instances. In this paper, we provide a mathematical model for each planning problem considered in the library and describe the data concepts of the SNDlib. Furthermore, we provide statistical information and details about the origin of the data sets. T3 - ZIB-Report - 07-15 KW - telecommunication network design KW - data library KW - optimization Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9582 ER - TY - GEN A1 - Bley, Andreas T1 - Approximability of Unsplittable Shortest Path Routing Problems N2 - In this paper, we discuss the relation of unsplittable shortest path routing (USPR) to other routing schemes and study the approximability of three USPR network planning problems. Given a digraph $D=(V,A)$ and a set $K$ of directed commodities, an USPR is a set of flow paths $\Phi_{(s,t)}$, $(s,t)\in K$, such that there exists a metric $\lambda=(\lambda_a)\in \mathbb{Z}^A_+$ with respect to which each $\Phi_{(s,t)}$ is the unique shortest $(s,t)$-path. In the \textsc{Min-Con-USPR} problem, we seek for an USPR that minimizes the maximum congestion over all arcs. We show that this problem is hard to approximate within a factor of $\mathcal{O}(|V|^{1-\epsilon})$, but easily approximable within min$(|A|,|K|)$ in general and within $\mathcal{O}(1)$ if the underlying graph is an undirected cycle or a bidirected ring. We also construct examples where the minimum congestion that can be obtained by USPR is a factor of $\Omega(|V|^2)$ larger than that achievable by unsplittable flow routing or by shortest multi-path routing, and a factor of $\Omega(|V|)$ larger than by unsplittable source-invariant routing. In the CAP-USPR problem, we seek for a minimum cost installation of integer arc capacities that admit an USPR of the given commodities. We prove that this problem is $\mathcal{NP}$-hard to approximate within $2-\epsilon$ (even in the undirected case), and we devise approximation algorithms for various special cases. The fixed charge network design problem \textsc{Cap-USPR}, where the task is to find a minimum cost subgraph of $D$ whose fixed arc capacities admit an USPR of the commodities, is shown to be $\mathcal{NPO}$-complete. All three problems are of great practical interest in the planning of telecommunication networks that are based on shortest path routing protocols. Our results indicate that they are harder than the corresponding unsplittable flow or shortest multi-path routing problems. T3 - ZIB-Report - 06-02 KW - Shortest path routing KW - unsplittable flow KW - computational complexity KW - approximation Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8968 ER - TY - GEN A1 - Orlowski, Sebastian A1 - Koster, Arie M.C.A. A1 - Raack, Christian A1 - Wessäly, Roland T1 - Two-layer Network Design by Branch-and-Cut featuring MIP-based Heuristics N2 - This paper deals with MIP-based primal heuristics to be used within a branch-and-cut approach for solving multi-layer telecommunication network design problems. Based on a mixed-integer programming formulation for two network layers, we present three heuristics for solving important subproblems, two of which solve a sub-MIP. On multi-layer planning instances with many parallel logical links, we show the effectiveness of our heuristics in finding good solutions early in the branch-and-cut search tree. T3 - ZIB-Report - 06-47 KW - multi-layer network design KW - integer programming KW - branch-and-cut KW - heuristics Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9412 ER - TY - GEN A1 - Hülsermann, Ralf A1 - Jäger, Monika A1 - Koster, Arie M.C.A. A1 - Orlowski, Sebastian A1 - Wessäly, Roland A1 - Zymolka, Adrian T1 - Availability and Cost Based Evaluation of Demand-wise Shared Protection N2 - In this paper, we investigate the connection availabilities for the new protection scheme Demand-wise Shared Protection (DSP) and describe an appropriate approach for their computation. The exemplary case study on two realistic network scenarios shows that in most cases the availabilities for DSP are comparable with that for 1+1 path protection and better than in case of shared path protection. T3 - ZIB-Report - 06-15 KW - demand-wise shared protection KW - network availability KW - network optimization Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9080 ER - TY - GEN A1 - Gruber, Claus G. A1 - Koster, Arie M.C.A. A1 - Orlowski, Sebastian A1 - Wessäly, Roland A1 - Zymolka, Adrian T1 - A new model and a computational study for Demand-wise Shared Protection N2 - This report combines the contributions to INOC 2005 (Wessälly et al., 2005) and DRCN 2005 (Gruber et al., 2005). A new integer linear programming model for the end-to-end survivability concept deman d-wise shared protection (DSP) is presented. DSP is based on the idea that backup capacity is dedicated to a particular demand, but shared within a demand. It combines advantages of dedicated and shared protection: It is more cost-efficient than dedicated protection and operationally easier than shared protection. In a previous model for DSP, the number of working and backup paths to be configured for a particular demand has been an input parameter; in the more general model for DSP investigated in this paper, this value is part of the decisions to take. To use the new DSP model algorithmically, we suggest a branch-and-cut approach which employs a column generation procedure to deal with the exponential number of routing variables. A computational study to compare the new resilience mechanism DSP with dedicated and shared path protection is performed. The results for five realistic network planning scenarios reveal that the best solutions for DSP are on average 15\% percent better than the corresponding 1+1 dedicated path protection solutions, and only 15\% percent worse than shared path protection. T3 - ZIB-Report - 05-55 KW - demand-wise shared protection KW - resilience KW - network design KW - integer linear programming Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8880 ER - TY - THES A1 - Bley, Andreas T1 - Routing and Capacity Optimization for IP Networks N2 - This thesis is concerned with dimensioning and routing optimization problems for communication networks that employ a shortest path routing protocol such as OSPF, IS-IS, or RIP. These protocols are widely used in the Internet. With these routing protocols, all end-to-end data streams are routed along shortest paths with respect to a metric of link lengths. The network administrator can configure the routing only by modifying this metric. In this thesis we consider the unsplittable shortest path routing variant, where each communication demand must be sent unsplit through the network. This requires that all shortest paths are uniquely determined. The major difficulties in planning such networks are that the routing can be controlled only indirectly via the routing metric and that all routing paths depend on the same routing metric. This leads to rather complicated and subtle interdependencies among the paths that comprise a valid routing. In contrast to most other routing schemes, the paths for different communication demands cannot be configured independent of each other. Part I of the thesis is dedicated to the relation between path sets and routing metrics and to the combinatorial properties of those path sets that comprise a valid unsplittable shortest path routing. Besides reviewing known approaches to find a compatible metric for a given path set (or to prove that none exists) and discussing some properties of valid path sets, we show that the problem of finding a compatible metric with integer lengths as small as possible and the problem of finding a smallest possible conflict in the given path set are both NP-hard to approximate within a constant factor. In Part II of the thesis we discuss the relation between unsplittable shortest path routing and several other routing schemes and we analyze the computational complexity of three basic unsplittable shortest path routing problems. We show that the lowest congestion that can be obtained with unsplittable shortest path routing may significantly exceed that achievable with other routing paradigms and we prove several non-approximability results for unsplittable shortest path routing problems that are stronger than those for the corresponding unsplittable flow problems. In addition, we derive various polynomial time approximation algorithms for general and special cases of these problems. In Part III of the thesis we finally develop an integer linear programming approach to solve these and more realistic unsplittable shortest path routing problems to optimality. We present alternative formulations for these problems, discuss their strength and computational complexity, and show how to derive strong valid inequalities. Eventually, we describe our implementation of this solution approach and report on the numerical results obtained for real-world problems that came up in the planning the German National Research and Education Networks G-WiN and X-WiN and for several benchmark instances. N2 - Die Arbeit befasst sich mit der Kapazitäts- und Routenplanung für Kommunikationsnetze, die ein kürzeste-Wege Routingprotokoll verwenden. Diese Art von Protokollen ist im Internet weit verbreitet. Bei diesen Routingverfahren wird für jede Verbindung im Netz ein Längenwert festgelegt, diese Längen formen die sogenannte Routingmetrik. Die Routingwege der Kommunikationsbedarfe sind dann die jeweiligen kürzesten Wege bezüglich dieser Metrik. Bei der in der Arbeit untersuchten Variante dieser Routingprotokolle wird zusätzlich verlangt, dass es je Kommunikationsbedarf genau einen eindeutigen kürzesten Weg gibt. Die Schwierigkeit bei der Planung solcher Netze besteht darin, dass sich die Routingwege einerseits nur indirekt über die Routingmetrik beeinflussen lassen, andererseits aber alle Routingwege von der gleichen Metrik abhängen. Dadurch können die Wege verschiedener Kommunikationsanforderungen nicht wie bei anderen Routingverfahren unabhängig voneinander gewählt werden. Im erstem Teil der Arbeit werden der Zusammenhang zwischen gegebenen Wegesystemen und kompatiblen Routingmetriken sowie die Beziehungen der Wege eines zulässigen eindeutige-kürzeste-Wege-Routings untereinander untersucht. Dabei wird unter Anderem gezeigt, dass es NP-schwer ist, eine kompatible Metrik mit kleinstmöglichen Routinglängen zu einem gegebenen Wegesystem zu finden. Es wird auch bewiesen, dass das Finden eines kleinstmöglichen Konfliktes in einem gegebenen Wegesystem, zu dem keine kompatible Metrik existiert, NP-schwer ist. Im zweiten Teil der Arbeit wird die Approximierbarkeit von drei grundlegenden Netz- und Routenplanungsproblemen mit eindeutige-kürzeste-Wege-Routing untersucht. Für diese Probleme werden stärkere Nichtapproximierbarkeitsresultate als für die entsprechenden Einwege-Routing Probleme bewiesen und es werden verschiedene polynomiale Approximationsverfahren für allgemeine und Spezialfälle entworfen. Ausserdem wird die Beziehung zwischen eindeutige-kürzeste-Wege-Routing und anderen Routingverfahren diskutiert. Im dritten und letzten Teil der Arbeit wird ein (gemischt-) ganzzahliger Lösungsansatz für Planungsprobleme mit eindeutige-kürzeste-Wege-Routing vorgestellt. Für die im zweiten Teil diskutierten grundlegenden Netz- und Routenplanungsprobleme werden verschiedene (gemischt-) ganzzahlige lineare Modelle vorgestellt und es wird deren Lösbarkeit und die Stärke ihrer LP Relaxierungen untersucht. Es wird auch gezeigt, wie sich starke gültig Ungleichungen aus den in diesen Modellen enthalten Substrukturen ableiten lassen. Schlielich werden am Ende der Arbeit die Software-Implementierung dieses Lösungsverfahrens für eine praxisrelevante Verallgemeinerung der Planungsprobleme sowie die damit erzielten numerischen Ergebnisse vorgestellt und diskutiert. KW - kombinatorische Optimierung KW - gemischt-ganzzahlige Programmierung KW - kürzeste-Wege Routing KW - Approximationsalgorithmen KW - combinatorial optimization KW - mixed-integer programming KW - shortest path routing KW - approximation algorithms Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:83-opus-15530 SN - 978-3-86727-281-0 ER - TY - GEN A1 - Grötschel, Martin T1 - Frequency Assignment in Mobile Phone Systems N2 - Wireless communication networks employ radio frequencies to establish communication links. The available radio spectrum is very limited. To meet today's radio communication demand, this resource has to be administered and reused carefully in order to control mutual interference. The reuse can be organized via separation in space, time, or frequency, for example. The problem, therefore, arises to distribute frequencies to links in a ``reasonable manner''. This is the basic form of the frequency assignment problem. What ``reasonable'' means, how to quantify this measure of quality, which technical side constraints to consider cannot be answered in general. The exact specification of this task and its mathematical model depend heavily on the particular application considered. In this paper we discuss this issue with respect to the GSM standard for mobile communication. T3 - ZIB-Report - 00-58 KW - frequency assignment KW - telecommunication KW - mobile phone KW - integer programming KW - coloring Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6265 ER - TY - GEN A1 - Koster, Arie M.C.A. A1 - Orlowski, Sebastian A1 - Raack, Christian A1 - Bayer, Georg A1 - Engel, Thomas T1 - Single-layer Cuts for Multi-layer Network Design Problems N2 - We study a planning problem arising in SDH/WDM multi-layer telecommunication network design. The goal is to find a minimum cost installation of link and node hardware of both network layers such that traffic demands can be realized via grooming and a survivable routing. We present a mixed-integer programming formulation that takes many practical side constraints into account, including node hardware, several bitrates, and survivability against single physical node or link failures. This model is solved using a branch-and-cut approach with problem-specific preprocessing and cutting planes based on either of the two layers. On several realistic two-layer planning scenarios, we show that these cutting planes are still useful in the multi-layer context, helping to increase the dual bound and to reduce the optimality gaps. T3 - ZIB-Report - 07-21 KW - telecommunication network KW - multi-layer network design KW - mixed-integer programming KW - cutting planes Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9641 SN - 1438-0064 ER - TY - THES A1 - Zymolka, Adrian T1 - Design of Survivable Optical Networks by Mathematical Optimization N2 - Abstract The cost-efficient design of survivable optical telecommunication networks is the topic of this thesis. In cooperation with network operators, we have developed suitable concepts and mathematical optimization methods to solve this comprehensive planning task in practice. Optical technology is more and more employed in modern telecommunication networks. Digital information is thereby transmitted as short light pulses through glass fibers. Moreover, the optical medium allows for simultaneous transmissions on a single fiber by use of different wavelengths. Recent optical switches enable a direct forwarding of optical channels in the network nodes without the previously required signal retransformation to electronics. Their integration creates ongoing optical connections,which are called lightpaths. We study the problem of finding cost-efficient configurations of optical networks which meet specified communication requirements. A configuration comprises the determination of all lightpaths to establish as well as the detailed allocation of all required devices and systems. We use a flexible modeling framework for a realistic representation of the networks and their composition. For different network architectures, we formulate integer linear programs which model the design task in detail. Moreover, network survivability is an important issue due to the immense bandwidths offered by optical technology. Operators therefore request for designs which perpetuate protected connections and guarantee for a defined minimum throughput in case of malfunctions. In order to achieve an effective realization of scalable protection, we present a novel survivability concept tailored to optical networks and integrate several variants into the models. Our solution approach is based on a suitable model decomposition into two subtasks which separates two individually hard subproblems and enables this way to compute cost-efficient designs with approved quality guarantee. The first subtask consists of routing the connections with corresponding dimensioning of capacities and constitutes a common core task in the area of network planning. Sophisticated methods for such problems have already been developed and are deployed by appropriate integration. The second subtask is characteristic for optical networks and seeks for a conflict-free assignment of available wavelengths to the lightpaths using a minimum number of involved wavelength converters. For this coloring-like task, we derive particular models and study methods to estimate the number of unavoidable conversions. As constructive approach, we develop heuristics and an exact branch-and-price algorithm. Finally, we carry out an extensive computational study on realistic data, provided by our industrial partners. As twofold purpose, we demonstrate the potential of our approach for computing good solutions with quality guarantee, and we exemplify its flexibility for application to network design and analysis. KW - network design KW - optical networks KW - integer programming KW - mathematical optimization Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10408 ER - TY - GEN A1 - Idzikowski, Filip A1 - Orlowski, Sebastian A1 - Raack, Christian A1 - Woesner, Hagen A1 - Wolisz, Adam T1 - Dynamic routing at different layers in IP-over-WDM networks -- Maximizing energy savings N2 - We estimate potential energy savings in IP-over-WDM networks achieved by switching off router line cards in low-demand hours. We compare three approaches to react on dynamics in the IP traffic over time, FUFL, DUFL and DUDL. They provide different levels of freedom in adjusting the routing of lightpaths in the WDM layer and the routing of demands in the IP layer. Using MILP models based on three realistic network topologies as well as realistic demands, power, and cost values, we show that already a simple monitoring of the lightpath utilization in order to deactivate empty line cards (FUFL) brings substantial benefits. The most significant savings, however, are achieved by rerouting traffic in the IP layer (DUFL), which allows emptying and deactivating lightpaths together with the corresponding line cards. A sophisticated reoptimization of the virtual topologies and the routing in the optical domain for every demand scenario (DUDL) yields nearly no additional profits in the considered networks. These results are independent of the ratio between the demand and capacity granularities, the time scale and the network topology, and show little dependency on the demand structure. T3 - ZIB-Report - 10-07 KW - network design KW - energy efficiency KW - power consumption KW - multi-layer KW - multi-hour KW - multi-period Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11692 SN - 1438-0064 ER - TY - GEN A1 - Poss, Michael A1 - Raack, Christian T1 - Affine recourse for the robust network design problem: between static and dynamic routing N2 - Affinely-Adjustable Robust Counterparts provide tractable alternatives to (two-stage) robust programs with arbitrary recourse. We apply them to robust network design with polyhedral demand uncertainty, introducing the affine routing principle. We compare the affine routing to the well-studied static and dynamic routing schemes for robust network design. All three schemes are embedded into the general framework of two-stage network design with recourse. It is shown that affine routing can be seen as a generalization of the widely used static routing still being tractable and providing cheaper solutions. We investigate properties on the demand polytope under which affine routings reduce to static routings and also develop conditions on the uncertainty set leading to dynamic routings being affine. We show however that affine routings suffer from the drawback that (even totally) dominated demand vectors are not necessarily supported by affine solutions. Uncertainty sets have to be designed accordingly. Finally, we present computational results on networks from SNDlib. We conclude that for these instances the optimal solutions based on affine routings tend to be as cheap as optimal network designs for dynamic routings. In this respect the affine routing principle can be used to approximate the cost for two-stage solutions with free recourse which are hard to compute. T3 - ZIB-Report - 11-03 KW - robust optimization KW - network design KW - recourse KW - affine adjustable robust counterparts KW - affine routing Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12122 ER - TY - THES A1 - Schweiger, Jonas T1 - Application of Multistage Stochastic Programming in Strategic Telecommunication Network Planning N2 - Telecommunication is fundamental for the information society. In both, the private and the professional sector, mobile communication is nowadays taken for granted. Starting primarily as a service for speech communication, data service and mobile Internet access are now driving the evolution of network infrastructure. In the year 2009, 19 million users generated over 33 million GB of traffic using mobile data services. The 3rd generation networks (3G or UMTS) in Germany comprises over 39,000 base stations with some 120,000 cells. From 1998 to 2008, the four network operators in Germany invested over 33 billion Euros in their infrastructure. A careful allocation of the resources is thus crucial for the profitability for a network operator: a network should be dimensioned to match customers demand. As this demand evolves over time, the infrastructure has to evolve accordingly. The demand evolution is hard to predict and thus constitutes a strong source of uncertainty. Strategic network planning has to take this uncertainty into account, and the planned network evolution should adapt to changing market conditions. The application of superior planning methods under the consideration of uncertainty can improve the profitability of the network and creates a competitive advantage. Multistage stochastic programming is a suitable framework to model strategic telecommunication network planning. We present mathematical models and effective optimization procedures for strategic cellular network design. The demand evolution is modeled as a continuous stochastic process which is approximated by a discrete scenario tree. A tree-stage approach is used for the construction of non-uniform scenario trees that serve as input of the stochastic program. The model is calibrated by historical traffic observations. A realistic system model of UMTS radio cells is used that determines coverage areas and cell capacities and takes signal propagation and interferences into account. The network design problem is formulated as a multistage stochastic mixed integer linear program, which is solved using state-of-the-art commercial MIP solvers. Problem specific presolving is proposed to reduce the problem size. Computational results on realistic data is presented. Optimization for the expected profit and the conditional value at risk are performed and compared. Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12206 ER - TY - GEN A1 - Eisenblätter, Andreas A1 - Schweiger, Jonas T1 - Multistage Stochastic Programming in Strategic Telecommunication Network Planning N2 - Mobile communication is nowadays taken for granted. Having started primarily as a service for speech communication, data service and mobile Internet access are now driving the evolution of network infrastructure. Operators are facing the challenge to match the demand by continuously expanding and upgrading the network infrastructure. However, the evolution of the customer's demand is uncertain. We introduce a novel (long-term) network planning approach based on multistage stochastic programming, where demand evolution is considered as a stochastic process and the network is extended as to maximize the expected profit. The approach proves capable of designing large-scale realistic UMTS networks with a time-horizon of several years. Our mathematical optimization model, the solution approach, and computational results are presented in this paper. T3 - ZIB-Report - 11-06 KW - UMTS KW - Network Evolution KW - Multistage KW - Stochastic Programming Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12232 ER - TY - GEN A1 - Betker, Andreas A1 - Kosiankowski, Dirk A1 - Lange, Christoph A1 - Pfeuffer, Frank A1 - Raack, Christian A1 - Werner, Axel T1 - Energy efficiency in extensive multilayer core and regional networks with protection N2 - Energy-efficient operation of large telecommunication networks is an important issue today and in the near future. Given that the energy consumption rises with the ever increasing demand for capacity and network speed, there is a growing interest in strategies for a sustainable network management. It is a well-known fact that traffic demands vary significantly over time, most notably in day/night- and in weekly cycles. This provides the main potential for energy-saving strategies. We study the question of how much power is necessary to operate a network with state-of-the-art hardware during peak or low-traffic times. The study respects realistic side constraints, such as protection requirements and routing schemes, and takes the special structure of an extensive nation-wide optical network, including backbone and regional sections, into account. We formulate mixed integer programming models for the corresponding optimization problems using predictions for traffic matrices, as well as state-of-the-art hardware and power models. We address questions as the following: How much energy is spent in the core and in metro regions of the network and how big are the savings in low-demand scenarios if we always assume the system power-minimum in these situations? What is the influence of different hardware on the overall energy consumption? How much do different routing schemes or protection scenarios restrict potential energy savings? T3 - ZIB-Report - 12-45 KW - telecommunications KW - network design KW - routing KW - energy efficiency Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17154 SN - 1438-0064 ER - TY - GEN A1 - Menne, Ulrich A1 - Raack, Christian A1 - Wessäly, Roland A1 - Kharitonov, Daniel T1 - Optimal Degree of Optical Circuit Switching in IP-over-WDM Networks N2 - In this paper, we study the influence of technology, traffic properties and price trends on optimized design of a reference IP-over-WDM network with rich underlying fiber topology. In each network node, we investigate the optimal degree of traffic switching in an optical (lambda) domain versus an electrical (packet) domain, also known as measure of \emph{node transparency}. This measure is studied in connection to changes in traffic volume, demand affinity, optical circuit speeds and equipment cost. By applying variable design constraints, we assess the relative roles of the two distinct equipment groups, IP routers and optical cross-connects, with respect to resulting changes in cost-sensitive network architectures. T3 - ZIB-Report - 11-50 KW - IP-over-WDM KW - Circuit Switching KW - Opacity Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14843 SN - 1438-0064 ER - TY - GEN A1 - Koster, Arie M.C.A. A1 - Kutschka, Manuel A1 - Raack, Christian T1 - Robust Network Design: Formulations, Valid Inequalities, and Computations N2 - Traffic in communication networks fluctuates heavily over time. Thus, to avoid capacity bottlenecks, operators highly overestimate the traffic volume during network planning. In this paper we consider telecommunication network design under traffic uncertainty, adapting the robust optimization approach of Bertsimas and Sim [2004]. We present three different mathematical formulations for this problem, provide valid inequalities, study the computational implications, and evaluate the realized robustness. To enhance the performance of the mixed-integer programming solver we derive robust cutset inequalities generalizing their deterministic counterparts. Instead of a single cutset inequality for every network cut, we derive multiple valid inequalities by exploiting the extra variables available in the robust formulations. We show that these inequalities define facets under certain conditions and that they completely describe a projection of the robust cutset polyhedron if the cutset consists of a single edge. For realistic networks and live traffic measurements we compare the formulations and report on the speed up by the valid inequalities. We study the "price of robustness" and evaluate the approach by analyzing the real network load. The results show that the robust optimization approach has the potential to support network planners better than present methods. T3 - ZIB-Report - 11-34 KW - robust network design KW - cutset inequalities Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-13890 SN - 1438-0064 ER -