Dynamic user equilibrium based on a hydrodynamic model

Terry L. Friesz, Ke Han, Pedro A. Neto, Amir Meimand and Tao Yao

Transportation Research Part B: Methodological, 2013, vol. 47, issue C, 102-126

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) and 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).

Keywords: LWR model; Dynamic user equilibrium; Dynamic network loading; Lax–Hopf formula (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (33)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S019126151200135X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:transb:v:47:y:2013:i:c:p:102-126

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.trb.2012.10.001

Access Statistics for this article

Transportation Research Part B: Methodological is currently edited by Fred Mannering

More articles in Transportation Research Part B: Methodological from Elsevier
Bibliographic data for series maintained by Catherine Liu ().