Density waves in traffic flow model with relative
velocity |
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Authors: | L Yu Z-K Shi |
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Institution: | (1) College of Automation, Northwestern Polytechnical University, 710072, Xi' an, P.R. China |
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Abstract: | The car-following model of traffic flow is extended to
take into account the relative velocity. The stability condition
of this model is obtained by using linear stability theory. It is
shown that the stability of uniform traffic flow is improved by
considering the relative velocity. From nonlinear analysis, it is
shown that three different density waves, that is, the triangular
shock wave, soliton wave and kink-antikink wave, appear in the
stable, metastable and unstable regions of traffic flow
respectively. The three different density waves are described by
the nonlinear wave equations: the Burgers equation, Korteweg-de
Vries (KdV) equation and modified Korteweg-de Vries (mKdV)
equation, respectively. |
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Keywords: | 89 40 -a Transportation 64 60 Cn Order-disorder transformations statistical mechanics of model systems 02 60 Cb Numerical simulation solution of equations 05 70 Fh Phase transitions: general studies |
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