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Mathematics for Metropolitan Infrastructure

Our society relies on the availability of efficient infrastructure for transportation, communication, energy supply, health care, and education, to mention some examples. Infrastructure design has a long-term impact, it is expensive and design decisions are often almost irreversible. They should therefore be taken with great care, using the best possible methods and ensuring optimal usability.

In the metropolitan area of Berlin, infrastructure evolution includes the construction of the BBI airport, the railway system including the main railway station, the U55 subway line, and the (canceled) maglev line to Hamburg, the projected extension of the A100 highway and the bicycle lane system, the licensing of the bus, light rail, water supply, electricity, and waste disposal systems, the allocation of hospital and school capacities as well as costs for street reconstruction. In all these areas and many more there is large potential for mathematical methods to better support decisions about the design, the organization, and the regulation and cost recovery of such metropolitan infrastructure.

Projects

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MI1
Project heads Prof. Dr. Martin Skutella
Staff Julie Meißner
Duration: - Status: running Located at: Technische Universität Berlin (TU Berlin)

Description

Uncertainty in the input data is an omnipresent issue in most real world planning processes. Metropolitan infrastructure -its design, operation and maintenance- induces complex planning processes where data uncertainty lies, e. g. in processing durations, transit times, cost, market prices, customer demands, capacity, bandwidth, energy consumption, et cetera. Since decisions on the infrastructure are typically very cost-intensive and of long-term impact, there is an urgent need of best possible mathematical support in this decision making process.

The quality of solutions for optimization problems (e. g. in infrastructure networks) with uncertain input data crucially depends on the amount of uncertainty. More information, or even knowing the exact data, allows for significantly improved solutions. It is impossible to fully abolish/avoid uncertainty. Nevertheless, it is sometimes possible to obtain exact data, but it may involve certain exploration cost in time, money, energy, bandwidth, etc.

In telecommunication networks planning, for example, information on the existing infrastructure (copper lines, optical fiber etc.) or the transmission range might not be easily available. The challenging major task of this project is to develop a structural understanding and algorithmic methods on how to balance the cost for data exploration with the actual benefit for the quality of solution to the optimization problem under consideration.

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MI2
Project heads Dr. Kersten Schmidt
Staff Robert Gruhlke
Dr. Anastasia Thöns
Duration: 01.06.2014 - 31.05.2017 Status: running Located at: Technische Universität Berlin (TU Berlin)

Description

The reduction of the excited noise of transportation, especially in gas turbines of airplanes and ships or mufflers of cars, is currently of major public and industrial interest. We aim to describe the effective absorption properties of sound absorbing resonator structures and perforated walls. As the governing equations and structures possess several scales, we study the problems asymptotically. In this project we derive and study approximative boundary and transmission conditions, that take into account the physical phenomena on the small scales inside the holes of the perforated absorber and the boundary layers in their neighbourhood.

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MI3
Project heads Prof. Dr. Ralf Borndörfer
Dr. Marika Karbstein
Staff Heide Hoppmann
Duration: 01.06.2014 - 31.05.2017 Status: running Located at: Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB)

Description

The strategic planning process in public transport is usually divided into consecutive planning steps - network design, line planning, and timetabling. In line planning, one has to find a set of lines defined by their paths and frequencies in a public transportation network such that a given travel demand can be routed. The task of timetabling is to schedule the trips of each line, i.e., by determining periodic arrival and departure times at their stations. The goal of each planning step is to provide a transportation system that is both attractive for passengers and can be operated economically. Integrating passenger behaviour is a major challenge in infrastructure design optimization.

The aim of this project is the adequate treatment of passenger routing in optimization models for public transport. We want to extend our existing theoretic and algorithmic base in line planning and timetabling by (advanced) passenger routing methods in order to construct efficiently solvable integrated models.

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MI4
Project heads Prof. Dr. Ralf Borndörfer
Staff Jonad Pulaj
Duration: 01.06.2014 - 31.05.2017 Status: running Located at: Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB)

Description

Over the last years, telecommunications have assumed a central role in our everyday life and the volume of exchanged traffic has astonishingly increased, causing a growth of networks in size and complexity. Major telecommunications companies forecast that such traffic increase will continue, reaching the volume of more than 1000 exabyte/ year by the end of 2015 (T. Theimer, ECOC 2009, Vienna). In order to tackle such growth, an important recent trend is the integration of fixed and wireless access networks, leading to so-called fiber-wireless (Fi-Wi) networks. In a Fi-Wi network, optical fibers support long-distance access with high capacity, whereas wireless links are adopted to cover the last connection segment to bring the service directly to the final users. The essential aim of this integration is to get the best of both worlds: the high capacity offered by optical fiber networks and the mobility and ubiquity offered by wireless networks. Such integration also grants a critical cost advantage, since deploying wireless transceivers is in general simpler and less expensive than deploying optical fibers. Last but not least, the integration offers a convenient way of providing a backup in case of failing connections. In Project ROUAN, we aim at developing mathematical programming models for the integrated and robust design of fixed and wireless components of a Fi-Wi network. As a general theoretical objective, we aim at enlarging the knowledge about Robust Optimization by investigating the topic of how to construct uncertainty sets using available historical data.

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MI5
Project heads Prof. Dr. Max Klimm
Staff Antje Bjelde
Jan Hackfeld
Duration: 01.06.2014 - 31.05.2017 Status: running Located at: Technische Universität Berlin (TU Berlin)

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