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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 6: Poster
SOE 6.15: Poster
Montag, 16. März 2020, 17:00–20:00, P2/4OG
Optimal transport flow networks with a linear congestion model — •Matthias Dahlmanns1,2, Franz Kaiser1,2, and Dirk Witthaut1,2 — 1Forschungszentrum Jülich, Institute for Energy and Climate Research (IEK-STE), 52428 Jülich, Germany — 2Institute for Theoretical Physics, University of Cologne, 50937 Köln, Germany
In our daily life, we rely on the proper functioning of various types of supply networks, such as power grids, water supply networks or transportation networks. But what determines the optimal structure of such networks, i.e. how should they be designed? And what happens to them in case of link failures or damages?
A variety of analytical results are available for optimal structures and the response to damages for shortest path flow networks on the one hand and potential flow networks, such as electrical power grids, on the other hand.
In a transportation network, however, travelers try to minimise their travel time, but congestion effects occur on highly frequented links due to limited capacity.
In this contribution, we introduce an approach to study the congestion by a travel time that depends linearly on the local flow which leads to a combination of the two well studied flow types. We then focus on the impact of link failures in this interpolating model and analyse the transition between both flow types in detail. Our results can be applied to understand the influence of congestion on the design of optimal traffic flow networks.