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Computing dynamic user equilibrium on large-scale networks without knowing global parameters

Computing dynamic user equilibrium on large-scale networks without knowing global parameters
Computing dynamic user equilibrium on large-scale networks without knowing global parameters
Dynamic user equilibrium (DUE) is a Nash-like solution concept describing an equilibrium in dynamic traffic systems over a fixed planning period. DUE is a challenging class of equilibrium problems, connecting network loading models and notions of system equilibrium in one concise mathematical framework. Recently, Friesz and Han introduced an integrated framework for DUE computation on large-scale networks, featuring a basic fixed-point algorithm for the effective computation of DUE. In the same work, they present an open-source MATLAB toolbox which allows researchers to test and validate new numerical solvers. This paper builds on this seminal contribution, and extends it in several important ways. At a conceptual level, we provide new strongly convergent algorithms designed to compute a DUE directly in the infinite-dimensional space of path flows. An important feature of our algorithms is that they give provable convergence guarantees without knowledge of global parameters. In fact, the algorithms we propose are adaptive, in the sense that they do not need a priori knowledge of global parameters of the delay operator, and which are provable convergent even for delay operators which are non-monotone. We implement our numerical schemes on standard test instances, and compare them with the numerical solution strategy employed by Friesz and Han.
Dynamic Traffic Assignment, Fixed Point Iteration, Strong Convergence
1566-113X
735-768
Thong, Duong Viet
fd3a43aa-7d60-453e-a7e7-2f2fcd9d3823
Gibali, Aviv
3e4f6225-8c98-42de-821a-cba3a069ea50
Staudigl, Mathias
29741423-e83a-47c6-907e-0edbb2a7c9b7
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Thong, Duong Viet
fd3a43aa-7d60-453e-a7e7-2f2fcd9d3823
Gibali, Aviv
3e4f6225-8c98-42de-821a-cba3a069ea50
Staudigl, Mathias
29741423-e83a-47c6-907e-0edbb2a7c9b7
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf

Thong, Duong Viet, Gibali, Aviv, Staudigl, Mathias and Vuong, Phan Tu (2021) Computing dynamic user equilibrium on large-scale networks without knowing global parameters. Networks and Spatial Economics, 21 (3), 735-768. (doi:10.1007/s11067-021-09548-3).

Record type: Article

Abstract

Dynamic user equilibrium (DUE) is a Nash-like solution concept describing an equilibrium in dynamic traffic systems over a fixed planning period. DUE is a challenging class of equilibrium problems, connecting network loading models and notions of system equilibrium in one concise mathematical framework. Recently, Friesz and Han introduced an integrated framework for DUE computation on large-scale networks, featuring a basic fixed-point algorithm for the effective computation of DUE. In the same work, they present an open-source MATLAB toolbox which allows researchers to test and validate new numerical solvers. This paper builds on this seminal contribution, and extends it in several important ways. At a conceptual level, we provide new strongly convergent algorithms designed to compute a DUE directly in the infinite-dimensional space of path flows. An important feature of our algorithms is that they give provable convergence guarantees without knowledge of global parameters. In fact, the algorithms we propose are adaptive, in the sense that they do not need a priori knowledge of global parameters of the delay operator, and which are provable convergent even for delay operators which are non-monotone. We implement our numerical schemes on standard test instances, and compare them with the numerical solution strategy employed by Friesz and Han.

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Accepted/In Press date: 11 June 2021
e-pub ahead of print date: 14 July 2021
Published date: September 2021
Additional Information: Funding Information: D. V. Thong is supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) project 101.01-2019.320. M. Staudigl acknowledges financial support from the European Cooperation in Science & Technology, COST Action CA16288, and the Gaspard Monge Program (PGMO) for optimization and operations research, project number P-2020-0005. Publisher Copyright: © 2021, The Author(s).
Keywords: Dynamic Traffic Assignment, Fixed Point Iteration, Strong Convergence

Identifiers

Local EPrints ID: 450345
URI: http://eprints.soton.ac.uk/id/eprint/450345
ISSN: 1566-113X
PURE UUID: efa489c7-82ac-4b5e-9b55-6cda98f3011c
ORCID for Phan Tu Vuong: ORCID iD orcid.org/0000-0002-1474-994X

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Date deposited: 23 Jul 2021 18:13
Last modified: 29 Nov 2022 02:57

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Contributors

Author: Duong Viet Thong
Author: Aviv Gibali
Author: Mathias Staudigl
Author: Phan Tu Vuong ORCID iD

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