Guarantees of convergence to a dynamic user equilibrium for a single arc network
File(s)
Accepted version
Author(s)
Burger, Guillaume
Paccagnan, Dario
Gentile, Basilio
Lygeros, John
Type
Conference Paper
Abstract
While steady state traffic equilibrium problems have been successfully studied, the analysis complicates when the dynamics of the vehicles is taken into account. The literature on the topic presents a variety of models, but usually the algorithms suggested do not possess convergence guarantees. We propose a simple game where all the vehicles travel along the same arc and choose the starting time of their trip. Based on the first Wardrop principle, we formulate the traffic user equilibrium as a variational inequality. Since monotonicity of the corresponding operator guarantees convergence of gradient-based algorithms, we provide theoretical guarantees for short time horizons, and analyze it numerically for longer ones. We conclude with simulations showing that convergence can be achieved also in more general setups, for example with multiple origins or destinations.
Date Issued
2017-10-18
Date Acceptance
2017-10-01
Citation
IFAC PAPERSONLINE, 2017, 50 (1), pp.9674-9679
ISSN
2405-8963
Publisher
ELSEVIER
Start Page
9674
End Page
9679
Journal / Book Title
IFAC PAPERSONLINE
Volume
50
Issue
1
Copyright Statement
© 2017 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000423965100109&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Source
20th World Congress of the International-Federation-of-Automatic-Control (IFAC)
Subjects
Dynamic user equilibrium
Convergence guarantees
Traffic road network
Cell transmission model
Monotonicity
EXISTENCE
Publication Status
Published
Start Date
2017-07-09
Finish Date
2017-07-14
Coverage Spatial
Toulouse, FRANCE
Date Publish Online
2017-10-18