Skip to main content
Open Access Publications from the University of California

UC Irvine

UC Irvine Previously Published Works bannerUC Irvine

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, 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.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View