A new lattice model for single-lane traffic flow with the consideration of driver’s memory during a period of time

In order to investigate the effect of driver’s memory during a period of time upon traffic dynamics, an extended lattice hydrodynamic model for traffic flow is proposed and studied analytically and numerically in this paper. The linear stability analysis reveals that the time length of driver’s memory has an important effect on stability of traffic flow. The factor will lead to the occurrence of traffic congestion. Three typical nonlinear wave equations including Burgers, Korteweg-de Vries and modified Korteweg-de Vries equation are derived to describe the evolution of density wave for traffic flow in three different regions, which are stable, meta-stable and unstable region, respectively. The simulations are given to illustrate and clarify the analytical results. The results indicate that the time length of driver’s memory has a negative effect upon stability of traffic flow.

[1]  G. Peng,et al.  A new lattice model of traffic flow with the consideration of the driver's forecast effects , 2011 .

[2]  W. Zhang,et al.  Using Fourier differential quadrature method to analyze transverse nonlinear vibrations of an axially accelerating viscoelastic beam , 2014 .

[3]  T. Nagatani.  The physics of traffic jams , 2002 .

[4]  Bao-gui Cao.  A new car-following model considering driver’s sensory memory , 2015 .

[5]  G. Peng,et al.  Non-lane-based lattice hydrodynamic model of traffic flow considering the lateral effects of the lan , 2011 .

[6]  Takashi Nagatani,et al.  Jamming transition of high-dimensional traffic dynamics , 1999 .

[7]  A. Schadschneider,et al.  Statistical physics of vehicular traffic and some related systems , 2000, cond-mat/0007053.

[8]  Andreas Schadschneider,et al.  Traffic flow: a statistical physics point of view , 2002 .

[9]  R. Jiang,et al.  Full velocity difference model for a car-following theory. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  G. Peng,et al.  Optimal velocity difference model for a car-following theory , 2011 .

[11]  Tie-Qiao Tang,et al.  A new car-following model accounting for varying road condition , 2012 .

[12]  Hongxia Ge,et al.  The “backward looking” effect in the lattice hydrodynamic model , 2008 .

[13]  A. Gupta,et al.  Effect of multi-phase optimal velocity function on jamming transition in a lattice hydrodynamic model with passing , 2015 .

[14]  Hai-Jun Huang,et al.  AN EXTENDED OV MODEL WITH CONSIDERATION OF DRIVER'S MEMORY , 2009 .

[15]  Boris S. Kerner,et al.  Empirical test of a microscopic three-phase traffic theory , 2007 .

[16]  Dirk Helbing,et al.  Memory effects in microscopic traffic models and wide scattering in flow-density data. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

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

[20]  Takashi Nagatani,et al.  Thermodynamic theory for the jamming transition in traffic flow , 1998 .

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

[22]  Jin-Liang Cao,et al.  Nonlinear analysis of the optimal velocity difference model with reaction-time delay , 2014 .

[23]  G. Peng,et al.  A new lattice model of traffic flow with the anticipation effect of potential lane changing , 2012 .

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

[25]  T. Nagatani.  Jamming transition in a two-dimensional traffic flow model. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  Robert Herman,et al.  Traffic Dynamics: Analysis of Stability in Car Following , 1959 .

[27]  Jie Zhou,et al.  Lattice hydrodynamic model for traffic flow on curved road , 2016 .

[28]  Takashi Nagatani,et al.  Jamming transition in traffic flow on triangular lattice , 1999 .

[29]  Ziyou Gao,et al.  Stabilization effect of multiple density difference in the lattice hydrodynamic model , 2013 .

[30]  Zhongke Shi,et al.  An extended traffic flow model on a gradient highway with the consideration of the relative velocity , 2014, Nonlinear Dynamics.

[31]  Guanghan Peng,et al.  A new lattice model of the traffic flow with the consideration of the driver anticipation effect in a two-lane system , 2013 .

[32]  Jie Zhou,et al.  Lattice hydrodynamic model for two-lane traffic flow on curved road , 2016 .

[33]  Silviu-Iulian Niculescu,et al.  Stability of Traffic Flow Behavior with Distributed Delays Modeling the Memory Effects of the Drivers , 2007, SIAM J. Appl. Math..

[34]  H. M. Zhang.  Driver memory, traffic viscosity and a viscous vehicular traffic flow model , 2003 .

[35]  Ziyou Gao,et al.  Phase transitions in the two-lane density difference lattice hydrodynamic model of traffic flow , 2014 .

[36]  G. Peng,et al.  A new lattice model of traffic flow with the consideration of the traffic interruption probability , 2012 .

[37]  A. Gupta,et al.  Analyses of the driver’s anticipation effect in a new lattice hydrodynamic traffic flow model with passing , 2014 .

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

[39]  A. Gupta,et al.  Analyses of driver’s anticipation effect in sensing relative flux in a new lattice model for two-lane traffic system , 2013 .

[40]  Tong Li,et al.  Density waves in a traffic flow model with reaction-time delay , 2010 .

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

[42]  D. Helbing.  Traffic and related self-driven many-particle systems , 2000, cond-mat/0012229.

[43]  Geng Zhang,et al.  Analysis of two-lane lattice hydrodynamic model with consideration of drivers’ characteristics , 2015 .

[44]  Wei-Zhen Lu,et al.  A new lattice model with the consideration of the traffic interruption probability for two-lane traffic flow , 2015 .

[45]  Fangyan Nie,et al.  A driver’s memory lattice model of traffic flow and its numerical simulation , 2012 .