Computing User Equilibria for Schedule-Based Transit Networks with Hard Vehicle Capacities
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Date
2024-10-07
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en
Pages
17
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24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems, ATMOS 2024, pp. 1-17, OpenAccess Series in Informatics ; Volume 123
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.Description
Publisher Copyright: © Tobias Harks, Sven Jäger, Michael Markl, and Philine Schiewe.
Keywords
public transportation, side-constrained equilibrium, traffic assignment
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Citation
Harks, T, Jäger, S, Markl, M & Schiewe, P 2024, Computing User Equilibria for Schedule-Based Transit Networks with Hard Vehicle Capacities . in P C Bouman & S C Kontogiannis (eds), 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems, ATMOS 2024 ., 17, OpenAccess Series in Informatics, vol. 123, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, pp. 1-17, Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems, London, United Kingdom, 05/09/2024 . https://doi.org/10.4230/OASIcs.ATMOS.2024.17