Density Wave In A New Anisotropic Continuum Model For Traffic Flow

In this paper, we apply a new anisotropic continuum model proposed by Gupta and Katiyar (GK model, for short) [J. Phys. A: Math. Gen.38, 4069 (2005)] to study the density wave of traffic flow. The GK model guarantees the characteristic speeds are always less than or equal to the macroscopic flow speed and overcomes the wrong way travel problem which exists in many high-order continuum models. The stability condition of the GK model is obtained. Applying nonlinear analysis to the GK model, we can obtain the soliton, one type of local density wave, which is induced by the density fluctuation in traffic flow. The soliton wave, which is determined near the neutral stability line by the Korteweg-de Vries (KdV) equation, is discussed in great detail. The numerical results show that local cluster effects which are consistent with the diverse nonlinear phenomena observed in realistic traffic flow can be induced from the GK model.

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