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

Wen-Long Jin

Transportation Research Part B: Methodological, 2016, vol. 93, issue PA, 543-559

Abstract: 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, we 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. We 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, we 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, we 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 us to pick out anisotropic solutions of higher-order models with non-concave fundamental diagrams.

Keywords: Three-dimensional representation; Eulerian and Lagrangian coordinates; Continuum models; Car-following models; Fundamental diagram; Stability (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (9)

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DOI: 10.1016/j.trb.2016.08.007

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