Elastic demand dynamic network user equilibrium: Formulation, existence and computation

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Title: Elastic demand dynamic network user equilibrium: Formulation, existence and computation
Author(s): Han, K
Friesz, TL
Szeto, WY
Liu, H
Item Type: Journal Article
Abstract: This paper is concerned with dynamic user equilibrium with elastic travel demand (E-DUE) when the trip demand matrix is determined endogenously. We present an infinite-dimensional variational inequality (VI) formulation that is equivalent to the conditions defining a continuous-time E-DUE problem. An existence result for this VI is established by applying a fixed-point existence theorem (Browder, 1968) in an extended Hilbert space. We present three computational algorithms based on the aforementioned VI and its re-expression as a differential variational inequality (DVI): a projection method, a self-adaptive projection method, and a proximal point method. Rigorous convergence results are provided for these methods, which rely on increasingly relaxed notions of generalized monotonicity, namely mixed strongly-weakly monotonicity for the projection method; pseudomonotonicity for the self-adaptive projection method, and quasimonotonicity for the proximal point method. These three algorithms are tested and their solution quality, convergence, and computational efficiency are compared. Our convergence results, which transcend the transportation applications studied here, apply to a broad family of VIs and DVIs, and are the weakest reported to date.
Publication Date: 25-Sep-2015
Date of Acceptance: 7-Jul-2015
URI: http://hdl.handle.net/10044/1/62787
DOI: https://dx.doi.org/10.1016/j.trb.2015.07.008
ISSN: 0191-2615
Publisher: Elsevier
Start Page: 183
End Page: 209
Journal / Book Title: Transportation Research Part B - Methodological
Volume: 81
Copyright Statement: © 2015 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/
Keywords: Social Sciences
Science & Technology
Technology
Economics
Engineering, Civil
Operations Research & Management Science
Transportation
Transportation Science & Technology
Business & Economics
Engineering
Dynamic user equilibrium
Elastic demand
Variational inequality
Existence
Computation
Convergence
CELL TRANSMISSION MODEL
VARIATIONAL INEQUALITY FORMULATION
DIFFERENTIAL-EQUATION FORMULATION
VICKREYS BOTTLENECK MODEL
TRAFFIC ASSIGNMENT MODEL
PROXIMAL POINT METHOD
DEPARTURE TIME
SIMULTANEOUS ROUTE
KINEMATIC WAVES
CHOICE
math.OC
math.OC
90B06, 90B10, 90B20, 90C90
1507 Transportation And Freight Services
0102 Applied Mathematics
Logistics & Transportation
Publication Status: Published
Appears in Collections:Faculty of Engineering
Civil and Environmental Engineering



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