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Documents authored by Nagel, Kai

Document
DOI: 10.4230/OASIcs.ATMOS.2023.11
Spillback Changes the Long-Term Behavior of Dynamic Equilibria in Fluid Queuing Networks

Authors: Theresa Ziemke, Leon Sering, and Kai Nagel

Published in: OASIcs, Volume 115, 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)

Abstract
We study the long-term behavior of dynamic traffic equilibria and find that it heavily depends on whether spillback is captured in the traffic model or not. We give an example where no steady state is reached. Although the example consists of a single-commodity instance with constant inflow rate, the Nash flow over time consists of infinitely many phases. This is in contrast to what has been proven for Nash flows over time without spillback [Cominetti et al., 2021; N. Olver et al., 2021]. Additionally, we show that similar phase oscillations as in the Nash flow over time with spillback can be observed in the co-evolutionary transport simulation MATSim. This reaffirms the robustness of the findings as the simulation does (in contrast to Nash flows over time) not lead to exact user equilibra and, moreover, models discrete time steps and vehicles.
Cite as

Theresa Ziemke, Leon Sering, and Kai Nagel. Spillback Changes the Long-Term Behavior of Dynamic Equilibria in Fluid Queuing Networks. In 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023). Open Access Series in Informatics (OASIcs), Volume 115, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ziemke_et_al:OASIcs.ATMOS.2023.11,
  author =	{Ziemke, Theresa and Sering, Leon and Nagel, Kai},
  title =	{{Spillback Changes the Long-Term Behavior of Dynamic Equilibria in Fluid Queuing Networks}},
  booktitle =	{23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)},
  pages =	{11:1--11:14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-302-7},
  ISSN =	{2190-6807},
  year =	{2023},
  volume =	{115},
  editor =	{Frigioni, Daniele and Schiewe, Philine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2023.11},
  URN =		{urn:nbn:de:0030-drops-187722},
  doi =		{10.4230/OASIcs.ATMOS.2023.11},
  annote =	{Keywords: flows over time, transport simulation, Nash flow, dynamic equilibrium, long-term behavior, steady state, oscillation, spillback, MATSim}
}
Document
DOI: 10.4230/DagRep.5.10.19
Dynamic Traffic Models in Transportation Science (Dagstuhl Seminar 15412)

Authors: José R. Correa, Tobias Harks, Kai Nagel, Britta Peis, and Martin Skutella

Published in: Dagstuhl Reports, Volume 5, Issue 10 (2016)

Abstract
Traffic assignment models are crucial for traffic planners to be able to predict traffic distributions, especially, in light of possible changes of the infrastructure, e.g., road constructions, traffic light controls, etc. The starting point of the seminar was the observation that there is a trend in the transportation community (science as well as industry) to base such predictions on complex computer-based simulations that are capable of resolving many elements of a real transportation system. On the other hand, within the past few years, the theory of dynamic traffic assignments in terms of equilibrium existence and equilibrium computation has not matured to the point matching the model complexity inherent in simulations. In view of the above, this interdisciplinary seminar brought together leading scientists in the areas traffic simulations, algorithmic game theory and dynamic traffic assignment as well as people from industry with strong scientific background who identified possible ways to bridge the described gap.
Cite as

José R. Correa, Tobias Harks, Kai Nagel, Britta Peis, and Martin Skutella. Dynamic Traffic Models in Transportation Science (Dagstuhl Seminar 15412). In Dagstuhl Reports, Volume 5, Issue 10, pp. 19-34, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@Article{correa_et_al:DagRep.5.10.19,
  author =	{Correa, Jos\'{e} R. and Harks, Tobias and Nagel, Kai and Peis, Britta and Skutella, Martin},
  title =	{{Dynamic Traffic Models in Transportation Science (Dagstuhl Seminar 15412)}},
  pages =	{19--34},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2016},
  volume =	{5},
  number =	{10},
  editor =	{Correa, Jos\'{e} R. and Harks, Tobias and Nagel, Kai and Peis, Britta and Skutella, Martin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.5.10.19},
  URN =		{urn:nbn:de:0030-drops-56938},
  doi =		{10.4230/DagRep.5.10.19},
  annote =	{Keywords: Dynamic traffic equilibria, Complexity of equilibrium computation, Simulation, Dynamic network flow theory, Network optimization}
}
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