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New Perspectives on Continuum Traffic Flow Models

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Abstract

This paper discusses the mathematical properties of two classes of continuum models that extend the basic kinematic wave model of Lighthill and Whitham, and Richards (LWR)—lower-order and higher-order continuum models. While the differences among the discussed models are pointed out and contrasted, the emphasis is on their commonality. In the latter we found that 1) both classes of models, including the basic kinematic wave model, can violate the anisotropic property of traffic flow, 2) both types of models produce waves non-existent in the LWR model, and 3) both lower and higher order models can be reduced to a kinematic wave model with an effective fundamental diagram. It can therefore be said that the two classes of models are much more closely related than their appearances had led people to believe. The paper concludes with a discussion on the treatment of inhomogeneities and a proposal of a proper procedure for experimentally validating any continuum traffic flow models.

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  1. University of California at Davis, Davis, CA, 95616

    H.M. Zhang

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Zhang, H. New Perspectives on Continuum Traffic Flow Models. Networks and Spatial Economics 1, 9–33 (2001). https://doi.org/10.1023/A:1011539112438

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