STABILIZATION ANALYSIS AND MODIFIED KdV EQUATION OF LATTICE MODELS WITH CONSIDERATION OF RELATIVE CURRENT

In this paper, the lattice model which depends not only on the difference of the optimal current and the local current but also on the relative current is presented and analyzed in detail. We derive the stability condition of the extended model by considering a small perturbation around the homogeneous flow solution with finding that the improvement in the stability of the traffic flow is obtained by taking into account the relative current, which is also confirmed by direct simulations. Moreover, from the nonlinear analysis to the extended models, the relative current dependence of the propagating kink solutions for traffic jam is obtained by deriving the modified KdV equation near the critical point by using the reductive perturbation method.

[1]  Dirk Helbing,et al.  GENERALIZED FORCE MODEL OF TRAFFIC DYNAMICS , 1998 .

[2]  G. F. Newell.  Nonlinear Effects in the Dynamics of Car Following , 1961 .

[3]  S. Dai,et al.  Stabilization effect of traffic flow in an extended car-following model based on an intelligent transportation system application. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Shiqiang Dai,et al.  KdV and kink–antikink solitons in car-following models , 2005 .

[5]  Takashi Nagatani,et al.  Delay effect on phase transitions in traffic dynamics , 1998 .

[6]  Nakayama,et al.  Dynamical model of traffic congestion and numerical simulation. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  Takashi Nagatani,et al.  Modified KdV equation for jamming transition in the continuum models of traffic , 1998 .

[8]  Dirk Helbing,et al.  Coherent moving states in highway traffic , 1998, Nature.

[9]  Takashi Nagatani,et al.  Phase transition in a difference equation model of traffic flow , 1998 .

[10]  Kerner,et al.  Experimental properties of complexity in traffic flow. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  Kerner,et al.  Cluster effect in initially homogeneous traffic flow. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  T. Nagatani.  Stabilization and enhancement of traffic flow by the next-nearest-neighbor interaction. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  Kurtze,et al.  Traffic jams, granular flow, and soliton selection. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  S. Dai,et al.  Stabilization analysis and modified Korteweg-de Vries equation in a cooperative driving system. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  B. Kerner,et al.  EXPERIMENTAL PROPERTIES OF PHASE TRANSITIONS IN TRAFFIC FLOW , 1997 .

[16]  Komatsu,et al.  Kink soliton characterizing traffic congestion. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.