Variational Formulation of Multi-class Traffic Flow Models: Theory and Applications
Since the 1970s, various multi-class traffic flow models have been proposed to address different empirical observations, behavioral postulations and practical needs. In this paper, the authors present a variational theory of multi-class traffic flow models. This theory extends the minimum principle, namely variational formulation, of the classical Lighthill-Whitham-Richards (LWR) model. The authors demonstrate that this theory actually bridges the traffic flow models with an optimal control problem associated with an auxiliary system of conservation laws. They develop the variational formulation of a multi-class model explicitly. Utilizing the variational character of the multi-class traffic flow models, they are able to devise a simple numerical scheme for solving them. Numerical experiments indicate the effectiveness of the proposed solution scheme.
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Supplemental Notes:
- This paper was sponsored by TRB committee AHB45 Traffic Flow Theory and Characteristics.
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Corporate Authors:
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Authors:
- Li, Jia
- Zhang, H Michael
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Conference:
- Transportation Research Board 92nd Annual Meeting
- Location: Washington DC, United States
- Date: 2013-1-13 to 2013-1-17
- Date: 2013
Language
- English
Media Info
- Media Type: Digital/other
- Features: Appendices; Figures; References;
- Pagination: 20p
- Monograph Title: TRB 92nd Annual Meeting Compendium of Papers
Subject/Index Terms
- TRT Terms: Highway traffic; Highway traffic control; Traffic flow; Traffic models; Variational inequalities
- Identifier Terms: Lighthill-Whitham-Richards traffic flow model
- Uncontrolled Terms: Multiclass traffic assignment
- Subject Areas: Highways; Operations and Traffic Management; I71: Traffic Theory; I73: Traffic Control;
Filing Info
- Accession Number: 01478021
- Record Type: Publication
- Report/Paper Numbers: 13-5148
- Files: TRIS, TRB, ATRI
- Created Date: Apr 15 2013 1:13PM