05/06/2024: ALOP-Colloquium

Lecture: Mathematics in Traffic Modeling: Nash Flows over Time (Prof. Dr. Laura Vargas Koch, University Bonn)

As part of the colloquium of the Research Training Group Algorithmic Optimization will take place on

Monday, May 06, 2024 16:00 c.t. Lecture hall 9

the following lecture will take place:

Mathematics in Traffic Modeling: Nash Flows over Time
Prof. Dr. Laura Vargas Koch, University of Bonn

In traffic planning, traffic simulations are widely used. However, effective practical traffic simulations require good mathematical models as a foundation, and one such model is Nash flows over time.
Traffic is not a centrally controlled system. Instead, each participant in traffic decides individually which route is best for them. When all participants do this, so-called equilibrium states emerge. In our research, we focus on these equilibria and their properties.
Unlike static, classical models, the unique aspect of Nash flows over time is that temporal changes can be depicted. This means that a flow, which models traffic, moves through the network over time, and the situation in the network can dynamically change.
In this presentation, we will learn about the model of Nash flows over time, understand its close connection to the traffic simulation software MATSim and see what properties of the equilibria have already been understood, and what questions are still open.