Traffic flow on road networks modeled by nonlocal balance laws (2019-2022)

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In recent years, nonlocal balance laws (NBL) have drawn more attention in macroscopic traffic flow modeling of single roads. However, at road networks intersections have also to be modeled in a way that vehicle drivers close to the considered intersection choose their velocity appropriately and make routing decisions based on traffic density of the roads next to the intersection and/or based on real time navigational apps. (Non-)mandatory lane changes on multi-lane roads and different classes of vehicles have to be modeled as well. All the previous modeling approaches rely in their mathematical analysis on effects which can be described by systems of NBLs. So far, none of the existing models of traffic networks incorporate nonlocal effects in general.

Thus, in this project sequel, the existing mathematical framework based on NBLs will be extended properly and justified rigorously in order to obtain more reliable traffic flow models on networks which can predict real world traffic. Moreover, from this theory, numerically efficient algorithms based on so-called characteristical methods will be implemented to obtain simulations of large traffic networks via HPC (parallel computing).

The design of traffic controllers like traffic lights, speed limits, navigational apps, etc. will greatly benefit from this theoretical research and in the end result in optimized traffic flow. Last but not least, nonlocal balance laws have a far more reaching applicability and some of the described results on networks can easily been implemented to corresponding models of crowd dynamics, pedestrian flow and chemical ripening process chains.

Runtime: 2019-2022, Funding: Travel Funding by BaCaTeC to establish a collaboration between FAU and Institute of Transportation Studies, University Berkeley, USA.

Alexandre Bayen (ITS, Berkeley), Alexander Keimer (ITS, Berkeley), Günter Leugering (Dep. Mathematics, FAU) and Lukas Pflug (CSC@FAU)