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Computing User Equilibria for Schedule-Based Transit Networks with Hard Vehicle Capacities

Authors Tobias Harks , Sven Jäger , Michael Markl , Philine Schiewe

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Author Details

Tobias Harks
  • University of Passau, Germany
Sven Jäger
  • RPTU Kaiserslautern-Landau, Germany
Michael Markl
  • University of Passau, Germany
Philine Schiewe
  • Aalto University, Finland

Funding

This research was funded by the German Federal Ministry of Education and Research (BMBF). FK 05M22UKB, 05M22WPA.

Acknowledgements

We thank the anonymous reviewers for their constructive feedback.

Cite AsGet BibTex

Tobias Harks, Sven Jäger, Michael Markl, and Philine Schiewe. Computing User Equilibria for Schedule-Based Transit Networks with Hard Vehicle Capacities. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/OASIcs.ATMOS.2024.17

Abstract

Modelling passenger assignments in public transport networks is a fundamental task for city planners, especially when deliberating network infrastructure decisions. A key aspect of a realistic model for passenger assignments is to integrate selfish routing behaviour of passengers on the one hand, and the limited vehicle capacities on the other hand. We formulate a side-constrained user equilibrium model in a schedule-based time-expanded transit network, where passengers are modelled via a continuum of non-atomic agents that want to travel with a fixed start time from a user-specific origin to a destination. An agent’s route may comprise several rides along given lines, each using vehicles with hard loading capacities. We give a characterization of (side-constrained) user equilibria via a quasi-variational inequality and prove their existence by generalizing a well-known existence result of Bernstein and Smith (Transp. Sci., 1994). We further derive a polynomial time algorithm for single-commodity instances and an exact finite time algorithm for the multi-commodity case. Based on our quasi-variational characterization, we finally devise a fast heuristic computing user equilibria, which is tested on real-world instances based on data gained from the Hamburg S-Bahn system and the Swiss long-distance train network. It turns out that w.r.t. the total travel time, the computed user-equilibria are quite efficient compared to a system optimum, which neglects equilibrium constraints and only minimizes total travel time.

Subject Classification

ACM Subject Classification
  • Theory of computation → Network games
  • Applied computing → Transportation
  • Theory of computation → Exact and approximate computation of equilibria
Keywords
  • traffic assignment
  • side-constrained equilibrium
  • public transportation

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References

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