During my time as a PhD student in Maastricht, we studied planning problems in Local Access Telecommunication Networks (LATN). Telecommunication networks are hierarchically structured. At lower levels of this structure typically less reliability is required since failures cause the disconnection of only a small part of the network. Therefore, operators are satisfied with a tree structure as local access network. Moreover, at these levels of the network the intelligence of the routing hardware is limited and typically all demand is routed from/to the root of the tree.

We studied the design and expansion of those tree networks by capacity expansion on the links and installation of so-called concentrators (multiplexers) with dedicated lines with the purpose to minimize cost. In Flippo et al., 2000 we present a dynamic programming algorithm to solve this design and expansion problem.

A related problem is the ATM (Asynchronous Transmission Mode) network installation problem studied in cooperation with KPN Research. Again, in the lower levels of the network, a tree is used as network structure. In this case the problem is to decide the capacity installation on the links as well as the installation of ATM cross connects in the nodes. Based on the experience with the LATN problem, in Van de Leensel et al., 1998 we propose a dynamic programming algorithm for this problem as well.

The problem of installating an ATM network did not only play a role in the access network, but also in the backbone network. The backbone (or core) is the highest level of a telecommunication network where the lower levels are interconnected. In cooperation with KPN Research this problem was studied as well. Besides a software tool that is presented in the PhD thesis of Robert van de Leensel, we wrote a paper about an important substructure in the integer programming formulation of this (and other) network design problem (see Van Hoesel et al., 2002). Moreover, in Van Hoesel et al., 2003 a computational comparison of this and similar network design problems is presented.

As technological developments go on, the optimization problems change. Since I am working at ZIB, a large portion of my time has been dedicated to to cost-efficient design of all-optical networks. In the last decade optics has become the transmission technology in the core of telecommunication networks. By the replacement of copper cables by optical fibers the capacity of the links was increased substantially. Moreover, optics allows the transmission of multiple optical signals without interference through one and the same fiber. This concept, called Wavelength Division Multiplexing (WDM) is responsable for another tremendous increase of the capaicty.

So far the switching technology still works with electronic signals which implies that the optical signals at links have to be converted to electronics before switching can be carried out. To avoid this delay, technology is pushing towards optical switching with so-called optical cross-connects (OXCs).

The design of optical networks where both WDM and OXCs are used has been the topic of to research projects with Telekom Austria, and DFN-Verein / T-Systems Nova. For both partners we study the application of mathematical optimization for the dimensioning of the physical topology, the routing of lightpaths, and the assignment of wavelengths. Also survivability aspects are taken into account. The results of these investigations are documented in Zymolka et al., 2002.

"It's all about reliability", that is probably the best way to describe our research for signaling networks. The signaling network is what the nerve system is for the human body: without it nothing works anymore. Every telephone connection needs signaling to establish the connection, to maintain the connection, and to close the connection. So, if the signaling network breaks down, telecom operators are in deep trouble. To avoid this all elements of these networks are designed with highest reliability in mind.

The central components in a signaling network are the signaling transfer points (STPs). To have reliable STPs, the between the different processors have to be balanced on a regular basis. To most efficient way to balance an STP can be found by mathematical optimization techniques. In Koster, 2000 and Eisenblätter et al., 2002 integer programming techniques are applied to solve this task. This work has been done in cooperation with E-Plus Mobilfunk. The results are implemented in a software tool by Atesio.

With the deployment of third generation wireless networks (the famous UMTS standard) new optimization challenges were popping up. In particular, the planning of the radio interface has large optimization potential. Within the MOMENTUM project (a european IST-project) we study topics like site selection and site configuration for the radio interface of UMTS networks. A mathematical model for this task is discussed in Eisenblätter et al., 2002.