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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (4): 425-434.doi: https://doi.org/10.1007/s10483-009-0403-z

• Articles • 上一篇    下一篇

Kinetic description of bottleneck effects in traffic flow

张鹏1 吴冬艳1 黄仕进2 陶亦舟1   

    1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;
    2. Department of Civil Engineering, The University of Hong Kong Hong Kong SAR,  P. R. China)
  • 收稿日期:2008-10-14 修回日期:2009-02-13 出版日期:2009-04-16 发布日期:2009-04-16

Kinetic description of bottleneck effects in traffic flow

 Peng ZHANG1 Dong-Yan WU1 Shi-Jin HUANG2 Yi-Zhou TAO1   

    1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;
    2. Department of Civil Engineering, The University of Hong Kong Hong Kong SAR,  P. R. China)
  • Received:2008-10-14 Revised:2009-02-13 Online:2009-04-16 Published:2009-04-16

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摘要： 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 $\delta$-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.

关键词: LWR model;discontinuous flux;$\delta$-mapping algorithm;stop-and-go waves

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 $\delta$-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.

Key words: LWR model;discontinuous flux;$\delta$-mapping algorithm;stop-and-go waves

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