Kai Nagel, Martin Skutella
Leon Sering (TU), Theresa Ziemke (TU)
01.01.2019 – 31.12.2021
This interdisciplinary project aims to make progress at the intersection of network flows, algorithmic game theory, and traffic simulation and control. The goal is to gain a better structural understanding and, based upon this, provide efficient algorithmic methods to handle real-world traffic scenarios, e.g., in the context of evacuation planning. To this end, in interdisciplinary collaboration between mathematicians and traffic engineers, advanced flow over time models for dynamic user equilibria will be developed and mathematically analyzed. Solutions resulting from novel flow over time methods will be empirically evaluated and integrated into the large-scale agent-based transport simulation tool MATSim.
Even though real-world traffic consists of non-splittable vehicles, continuous flows over time describe average traffic rates. Our first results show that, from a stochastic point of view, the discrete MATSim model can be interpreted as a realization of a random experiment where the average of the distribution is given by a dynamic user equilibrium in the flow over time model. To confirm the strong connection between the two models even further, we analyze the discretization error by decreasing the time step and vehicle size within MATSim and show experimentally that the average deviation in travel times and cumulative inflow rates decreases.
In addition to that, we extend the flow over time model by several real-world traffic features, such as spillback, kinematic waves and time-varying capacities and transit times and proof the existence of dynamic user equilibria in this generalized model.
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