Dynamic user equilibrium based on a hydrodynamic model

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Title: Dynamic user equilibrium based on a hydrodynamic model
Author(s): Friesz, TL
Han, K
Neto, PA
Meimand, A
Yao, T
Item Type: Journal Article
Abstract: In this paper we present a continuous-time network loading procedure based on the Lighthill–Whitham–Richards model proposed by Lighthill and Whitham, 1955, Richards, 1956. A system of differential algebraic equations (DAEs) is proposed for describing traffic flow propagation, travel delay and route choices. We employ a novel numerical apparatus to reformulate the scalar conservation law as a flow-based partial differential equation (PDE), which is then solved semi-analytically with the Lax–Hopf formula. This approach allows for an efficient computational scheme for large-scale networks. We embed this network loading procedure into the dynamic user equilibrium (DUE) model proposed by Friesz et al. (1993). The DUE model is solved as a differential variational inequality (DVI) using a fixed-point algorithm. Several numerical examples of DUE on networks of varying sizes are presented, including the Sioux Falls network with a significant number of paths and origin–destination pairs (OD). The DUE model presented in this article can be formulated as a variational inequality (VI) as reported in Friesz et al. (1993). We will present the Kuhn–Tucker (KT) conditions for that VI, which is a linear system for any given feasible solution, and use them to check whether a DUE solution has been attained. In order to solve for the KT multiplier we present a decomposition of the linear system that allows efficient computation of the dual variables. The numerical solutions of DUE obtained from fixed-point iterations will be tested against the KT conditions and validated as legitimate solutions.
Publication Date: 1-Jan-2013
Date of Acceptance: 1-Nov-2012
URI: http://hdl.handle.net/10044/1/63120
DOI: https://dx.doi.org/10.1016/j.trb.2012.10.001
ISSN: 0191-2615
Publisher: Elsevier
Start Page: 102
End Page: 126
Journal / Book Title: Transportation Research Part B: Methodological
Volume: 47
Copyright Statement: © 2012 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International 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
LWR model
Dynamic user equilibrium
Dynamic network loading
Lax-Hopf formula
VARIATIONAL INEQUALITY FORMULATION
CELL TRANSMISSION MODEL
NETWORK LOADING PROBLEM
TRAFFIC FLOW
KINEMATIC WAVES
BOUNDARY-CONDITIONS
ASSIGNMENT PROBLEM
CONSERVATION-LAWS
HIGHWAY
EQUATIONS
1507 Transportation And Freight Services
0102 Applied Mathematics
Logistics & Transportation
Publication Status: Published
Online Publication Date: 2012-11-19
Appears in Collections:Faculty of Engineering
Civil and Environmental Engineering



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