On the equivalence between continuum and car-following models of traffic flow

Recently different formulations of the first-order Lighthill-Whitham-Richards (LWR) model have been identified in different coordinates and state variables. However, relationships between higher-order continuum and car-following traffic flow models are still not well understood. In this study, the authors first categorize traffic flow models according to their coordinates, state variables, and orders in the three-dimensional representation of traffic flow and propose a unified approach to convert higher-order car-following models into continuum models and vice versa. The conversion method consists of two steps: equivalent transformations between the secondary Eulerian (E-S) formulations and the primary Lagrangian (L-P) formulations, and approximations of L-P derivatives with anisotropic (upwind) finite differences. The authors use the method to derive continuum models from general second- and third-order car-following models and derive car-following models from second-order continuum models. Furthermore, the authors demonstrate that corresponding higher-order continuum and car-following models have the same fundamental diagrams, and that the string stability conditions for vehicle-continuous car-following models are the same as the linear stability conditions for the corresponding continuum models. A numerical example verifies the analytical results. In a sense, the authors establish a weak equivalence between continuum and car-following models, subject to errors introduced by the finite difference approximation. Such an equivalence relation can help to discover anisotropic solutions of higher-order models with non-concave fundamental diagrams.

• Record URL:
  • https://doi.org/10.1016/j.trb.2016.08.007
• Record URL:
  • http://www.sciencedirect.com/science/article/pii/S0191261516305926
• Availability:
  • Find a library where document is available. Order URL: http://worldcat.org/issn/01912615
• Supplemental Notes:
  • Abstract reprinted with permission of Elsevier.
• Authors:
  • Jin, Wenlong
  • 0000-0002-5413-8377
• Publication Date: 2016-11

Language

• English

Media Info

• Media Type: Web
• Features: Figures; References; Tables;
• Pagination: pp 543-559
• Serial:
  • Transportation Research Part B: Methodological
  • Volume: 93, Part A
  • Publisher: Elsevier
  • ISSN: 0191-2615
  • Serial URL: http://www.sciencedirect.com/science/journal/01912615

Subject/Index Terms

• TRT Terms: Car following; Continuum (Mathematics); Coordinates; Diagrams; Lagrangian functions; Mathematical models; Traffic flow; Traffic models
• Identifier Terms: Lighthill-Whitham-Richards traffic flow model
• Uncontrolled Terms: Fundamental diagram
• Subject Areas: Highways; Planning and Forecasting;

Filing Info

• Accession Number: 01615106
• Record Type: Publication
• Files: TRIS
• Created Date: Oct 26 2016 2:44PM