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Kinetic description of bottleneck effects in traffic flow

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Abstract

This paper deals with the effects of traffic bottlenecks using an extended Lighthill-Whitham-Richards (LWR) model. The solution structure is analytically indicated by the study of the Riemann problem characterized by a discontinuous flux. This leads to a typical solution describing a queue upstream of the bottleneck and its width and height, and informs the design of a δ-mapping algorithm. More significantly, it is found that the kinetic model is able to reproduce stop-and-go waves for a triangular fundamental diagram. Some simulation examples, which are in agreement with the analytical solutions, are given to support these conclusions.

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, P. R. China

    Peng Zhang  (张鹏), Dong-yan Wu  (吴冬艳) & Yi-zhou Tao  (陶亦舟)

  2. Department of Civil Engineering, The University of Hong Kong, Hong Kong SAR, P. R. China

    S. C. Wong  (黄仕进)

Authors
  1. Peng Zhang  (张鹏)
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  2. Dong-yan Wu  (吴冬艳)
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  3. S. C. Wong  (黄仕进)
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  4. Yi-zhou Tao  (陶亦舟)
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Corresponding author

Correspondence to Peng Zhang  (张鹏).

Additional information

(Communicated by Shi-qiang DAI)

Project supported by the National Natural Science Foundation of China (Nos. 70629001 and 10771134), the National Basic Research Program of China (973 Program) (No. 2006CB705500), the Research Grants Council of the Hong Kong Special Administrative Region of China (No. HKU7183/08E), and the Research Committee of The University of Hong Kong (No. 10207394)

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Zhang, P., Wu, Dy., Wong, S.C. et al. Kinetic description of bottleneck effects in traffic flow. Appl. Math. Mech.-Engl. Ed. 30, 425–434 (2009). https://doi.org/10.1007/s10483-009-0403-z

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  • DOI: https://doi.org/10.1007/s10483-009-0403-z

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