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Das vom BMBF geförderte Projekt FTTX-PLAN entwickelt mathematische Modelle und Optimierungsverfahren, um automatisiert kostenoptimierte FTTx-Netze berechnen zu können. Wir zeigen anhand einer Praxisstudie in Zusammenarbeit mit der Regensburger R-KOM, wie ein Planer von diesen Verfahren profitieren kann, um die Auswirkungen bestimmter Entscheidungen auf die Netzstruktur und -kosten zu untersuchen. Wir illustrieren dies am Beispiel eines FTTB/FTTH-Vergleichs, der Variation von Kundenanbindungsraten und der gezielten Ausnutzung existierender Leerrohre, um Tiefbau zu vermeiden.

In this paper we assess to which extent trenching costs of an FTTx network are unavoidable, even if technical side constraints are neglected. For that purpose we present an extended Steiner tree model. Using a variety of realistic problem instances we demonstrate that the total trenching cost can only be reduced by about 5 percent in realistic scenarios. This work has been funded by BMBF (German Federal Ministry of Education and Research) within the program "KMU-innovativ".

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.

This survey concerns optimization problems arising in the design of survivable communication networks. It turns out that such problems can be modeled in a natural way as non-compact linear programming formulations based on multicommodity flow network models. These non-compact formulations involve an exponential number of path flow variables, and therefore require column generation to be solved to optimality. We consider several path-based survivability mechanisms and present results, both known and new, on the complexity of the corresponding column generation problems (called the pricing problems). We discuss results for the case of the single link (or node) failures scenarios, and extend the considerations to multiple link failures. Further, we classify the design problems corresponding to different survivability mechanisms according to the structure of their pricing problem. Finally, we show that almost all encountered pricing problems are hard to solve for scenarios admitting multiple failures.

Telecommunication transport networks consist of a stack of technologically different subnetworks, so-called layers, which are strongly interdependent. For example, one layer may correspond to an Internet (IP) backbone network whose links are realized by lightpath connections in an underlying optical fiber layer. To ensure that the network can fulfill its task of routing all communication requests, the inter-layer dependencies have to be taken into account already in the planning phase of the network. This is particularly important with survivability constraints, where connections in one layer have to be protected against cable cuts or equipment failures in another layer. The traditional sequential planning approach where one layer is optimized after the other cannot properly take care of the inter-layer dependencies; this can only be achieved with an integrated planning of several network layers at the same time. This thesis provides mathematical models and algorithmic techniques for the integrated optimization of two network layers with survivability constraints. We describe a multi-layer network design problem which occurs in various technologies, and model it mathematically using mixed-integer programming (MIP) formulations. The presented models cover many important practical side constraints from different technological contexts. In contrast to previous models from the literature, they can be used to design large two-layer networks with survivability requirements. We discuss modeling alternatives for various aspects of a multi-layer network and compare different routing formulations under multi-layer survivability constraints. We solve our models using a branch-and-cut-and-price approach with various problemspecific enhancements. This includes a presolving technique based on linear programming to reduce the problem size, combinatorial and sub-MIP-based primal heuristics to compute feasible network configurations, cutting planes which take the multi-layer survivability constraints into account to improve the lower bound on the optimal network cost, and column generation to generate flow variables dynamically during the algorithm. We develop techniques to speed up computations in a Benders decomposition approach and compare this approach to the standard formulation with a single MIP. We use the developed techniques to design large survivable two-layer networks by means of linear and integer programming methods. On realistic test instances with up to 67 network nodes and survivability constraints, we investigate the algorithmic impact of our techniques and show how to use them to compute good network configurations with quality guarantees. Most of the smaller test instances with up to 17 nodes can be solved to near-optimality. Moreover, we can compute feasible solutions and dual bounds even for large networks with survivability constraints, which has not been possible before.

We investigate the impact of link and path restoration on the cost of telecommunication networks. The surprising result is the following: the cost of an optimal network configuration is almost independent of the restoration concept if (i) the installation of network elements (ADMs, DXCs, or routers) and interface cards, (ii) link capacities, and (iii) working and restoration routings are simultaneously optimized. We present a mixed-integer programming model which integrates all these decisions. Using a branch-and-cut algorithm (with column generation to deal with all potential routing paths), we solve structurally different real-world problem instances and show that the cost of optimal solutions is almost independent of the used restoration concept. In addition, we optimize spare capacities for given shortest working paths which are predetermined with respect to different link metrics. In comparison to simultaneous optimization of working and restoration routings, it turns out that this approach does not allow to obtain predictably good results.

We present an integer linear programming model for the design of multi-layer telecommunication networks. The formulation integrates hardware, capacity, routing, and grooming decisions in \emph{any} n umber of network layers. Practical hardware restrictions and cost can accurately be taken into account for technologies based on connection-oriented routing protocols.

We investigate the impact of hop-limited routing paths on the total cost of a telecommunication network. For different survivability settings (dedicated protection, link and path restoration), the optimal network cost without restrictions on the admissible path set is compared to the results obtained with two strategies to impose hop limits on routing paths. In a thorough computational study on optimal solutions for nine real-world based problem instances, we show that hop limits should be avoided if the technology allows it and network cost is a major planning issue. In this case, column generation should be employed to deal with all routing paths. If hop-limits are required, these should be defined for each demand individually and as large as possible.

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.

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.