Document Open Access Logo

Spillback Changes the Long-Term Behavior of Dynamic Equilibria in Fluid Queuing Networks

Authors Theresa Ziemke , Leon Sering , Kai Nagel

PDF
Thumbnail PDF

File

OASIcs.ATMOS.2023.11.pdf
  • Filesize: 0.99 MB
  • 14 pages

Document Identifiers

Author Details

Theresa Ziemke
  • Combinatorial Optimization and Graph Algorithms, Technische Universität Berlin, Germany
  • Transport Systems Planning and Transport Telematics, Technische Universität Berlin, Germany
Leon Sering
  • Institute for Operations Research, ETH Zürich, Switzerland
Kai Nagel
  • Transport Systems Planning and Transport Telematics, Technische Universität Berlin, Germany

Funding

  • Ziemke, Theresa: Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - The Berlin Mathematics Research Center MATH+ (EXC-2046/1, project ID: 390685689).

Acknowledgements

We thank Max Zimmer for technical work on the Nash flow over time computation tool.

Cite As Get BibTex

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) https://doi.org/10.4230/OASIcs.ATMOS.2023.11

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.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Agent / discrete models
  • Mathematics of computing → Network flows
  • Applied computing → Transportation
Keywords
  • flows over time
  • transport simulation
  • Nash flow
  • dynamic equilibrium
  • long-term behavior
  • steady state
  • oscillation
  • spillback
  • MATSim

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. M. Balmer, N. Cetin, K. Nagel, and B. Raney. Towards truly agent-based traffic and mobility simulations. In Proceedings of the Third International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS), pages 60-67, 2004. Google Scholar
  2. D. Braess. Über ein Paradoxon aus der Verkehrsplanung. Unternehmensforschung, 12:258-268, 1968. Google Scholar
  3. R. Cominetti, J. Correa, and N. Olver. Long-term behavior of dynamic equilibria in fluid queuing networks. Operations Research, published online, 2021. Google Scholar
  4. A. Horni, K. Nagel, and K. Axhausen, editors. Multi-agent transport simulation MATSim. Ubiquity Press, London, UK, 2016. Google Scholar
  5. J. Israel and L. Sering. The impact of spillback on the price of anarchy for flows over time. In International Symposium on Algorithmic Game Theory (SAGT), pages 114-129, Augsburg, Germany, 2020. Springer, Springer. Google Scholar
  6. R. Koch and M. Skutella. Nash equilibria and the price of anarchy for flows over time. Theory of Computing Systems, 49(1):71-97, 2011. Google Scholar
  7. N. Olver, L. Sering, and L. Vargas Koch. Continuity, uniqueness and long-term behavior of Nash flows over time. IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS), pages 851-860, 2021. Google Scholar
  8. N. Olver, L. Sering, and L. Vargas Koch. Convergence of approximate and packet routing equilibria to Nash flows over time. IEEE 64nd Annual Symposium on Foundations of Computer Science (FOCS), 2023. Google Scholar
  9. M. Rieser and K. Nagel. Network breakdown "at the edge of chaos" in multi-agent traffic simulations. European Journal of Physics, 63(3):321-327, 2008. Google Scholar
  10. R.W. Rosenthal. The network equilibrium problem in integers. Networks, 3(1):53-59, 1973. Google Scholar
  11. L. Sering. Nash flows over time. PhD thesis, Technische Universität Berlin (Germany), 2020. Google Scholar
  12. L. Sering, L. Vargas Koch, and T. Ziemke. Convergence of a Packet Routing Model to Flows Over Time. Mathematics of Operations Research, 2022. Google Scholar
  13. L. Sering and L. Vargas Koch. Nash flows over time with spillback. In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 935-945, San Diego, California, USA, 2019. SIAM. Google Scholar
  14. Y. Sheffi. Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods. Prentice-Hall, Englewood Cliffs, NJ, USA, 1985. Google Scholar
  15. T. Thunig and K. Nagel. Braess’s paradox in an agent-based transport model. Procedia Computer Science, 83:946-951, 2016. Google Scholar
  16. J.G. Wardrop. Some theoretical aspects of road traffic research. Proceedings of the Institute of Civil Engineers, 1(3):325-378, 1952. Google Scholar
  17. T. Ziemke, L. Sering, L. Vargas Koch, M. Zimmer, K. Nagel, and M. Skutella. Flows over time as continuous limit of packet-based network simulations. Transportation Research Procedia, 52:123-130, 2021. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact