Phase-plane analysis of conserved higher-order traffic flow model

WU Chun-xiu; SONG Tao; ZHANG Peng; WONG S. C.

doi:10.3879/j.issn.1000-0887.2012.12.003

Volume 33 Issue 12

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WU Chun-xiu, SONG Tao, ZHANG Peng, WONG S. C.. Phase-plane analysis of conserved higher-order traffic flow model[J]. Applied Mathematics and Mechanics, 2012, 33(12): 1403-1410. doi: 10.3879/j.issn.1000-0887.2012.12.003

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Phase-plane analysis of conserved higher-order traffic flow model

doi: 10.3879/j.issn.1000-0887.2012.12.003

¹ Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;²Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, P. R. China;³Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, P. R. China

Funds: Project supported by the National Natural Science Foundation of China (No. 11072141), the Shanghai Program for Innovative Research Team in Universities, the Graduate Innovation Foundation of Shanghai University (No. SHUCX101078), and the University Research Committee, HKU SPACE Research Fund and Faculty of Engineering Top-up Grant of the University of Hong Kong (No. 201007176059)

Received Date: 2012-01-05
Rev Recd Date: 2012-04-30
Publish Date: 2012-12-15

Abstract

Abstract

The phase-plane analysis is used to study the traveling wave solution of a recently proposed higher-order traffic flow model under the Lagrange coordinate system. The analysis identifies the types and stabilities of the equilibrium solutions, and the overall distribution structure of the nearby solutions is drawn in the phase plane for the further analysis and comparison. The analytical and numerical results are in agreement, and may help to explain the simulated phenomena, such as the stop-and-go wave and oscillation near a bottleneck. The findings demonstrate the model ability to describe the complexity of congested traffic.
- traffic flow,
- Lagrange coordinates,
- phase-plane analysis,
- traffic congestion pattern

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References(20)

References

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