Effect of explicit lane changing in traffic lattice hydrodynamic model with interruption

In this paper, the explicit lane changing effect for two-lane traffic system with interruption is studied based on lattice hydrodynamic model. Through linear stability analysis, the neutral stability criterion for the two-lane traffic system is derived, and the density–sensitivity space is divided into the stable and unstable regions by the neutral stability curve. By applying nonlinear reductive perturbation method, the Burgers equation and modified Korteweg–de Vries (mKdV) equation are obtained to depict the density waves in the stable and unstable regions, respectively. Numerical simulations confirm the theoretical results showing that the traffic characteristics in the stable and unstable regions can be described respectively by the triangular shock waves of the Burgers equation and the kink–antikink solution of the mKdV equation. Also it is proved that lane changing can average the traffic situation of each lane for two-lane traffic system and enhance the stability of traffic flow, but traffic interruption of the current lattice can deteriorate the stable level of traffic flow and easily result in traffic congestion.

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

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

[3]  Arvind Kumar Gupta,et al.  A NEW MULTI-CLASS CONTINUUM MODEL FOR TRAFFIC FLOW , 2007 .

[4]  Bin Jia,et al.  The stabilization effect of the density difference in the modified lattice hydrodynamic model of traffic flow , 2012 .

[5]  Isha Dhiman,et al.  Phase diagram of a continuum traffic flow model with a static bottleneck , 2015 .

[6]  Min Zhang,et al.  Modeling and simulation for microscopic traffic flow based on multiple headway, velocity and acceleration difference , 2011 .

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

[8]  Sukanta Das,et al.  Cellular automata based traffic model that allows the cars to move with a small velocity during congestion , 2011 .

[9]  Thomas Pitz,et al.  A simple stochastic cellular automaton for synchronized traffic flow , 2014 .

[10]  Arvind Kumar Gupta,et al.  Nonlinear analysis of traffic jams in an anisotropic continuum model , 2010 .

[11]  Dihua Sun,et al.  Lattice hydrodynamic traffic flow model with explicit drivers’ physical delay , 2013 .

[12]  Wei-Zhen Lu,et al.  Impact of the traffic interruption probability of optimal current on traffic congestion in lattice model , 2015 .

[13]  Michael Schreckenberg,et al.  A cellular automaton model for freeway traffic , 1992 .

[14]  Guanghan Peng,et al.  A new lattice model of two-lane traffic flow with the consideration of optimal current difference , 2013, Commun. Nonlinear Sci. Numer. Simul..

[15]  Hongxia Ge,et al.  The theoretical analysis of the anticipation lattice models for traffic flow , 2014 .

[16]  Poonam Redhu,et al.  Phase transition in a two-dimensional triangular flow with consideration of optimal current difference effect , 2014 .

[17]  T. Nagatani,et al.  Density waves in traffic flow. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[19]  Xiao-Mei Zhao,et al.  Flow difference effect in the two-lane lattice hydrodynamic model , 2012 .

[20]  Fuqiang Liu,et al.  STABILIZATION ANALYSIS AND MODIFIED KdV EQUATION OF LATTICE MODELS WITH CONSIDERATION OF RELATIVE CURRENT , 2008 .

[21]  Arvind Kumar Gupta,et al.  Delayed-feedback control in a Lattice hydrodynamic model , 2015, Commun. Nonlinear Sci. Numer. Simul..

[22]  D. Helbing,et al.  Gas-Kinetic-Based Traffic Model Explaining Observed Hysteretic Phase Transition , 1998, cond-mat/9810277.

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

[24]  Guanghan Peng,et al.  A new lattice model of traffic flow with the consideration of individual difference of anticipation driving behavior , 2013, Commun. Nonlinear Sci. Numer. Simul..

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

[26]  A. Gupta,et al.  Analyses of a continuum traffic flow model for a nonlane-based system , 2014 .

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

[28]  A. Gupta,et al.  Analyses of Lattice Traffic Flow Model on a Gradient Highway , 2014 .

[29]  Arvind Kumar Gupta,et al.  Analysis of a modified two-lane lattice model by considering the density difference effect , 2014, Commun. Nonlinear Sci. Numer. Simul..

[30]  Arvind Kumar Gupta,et al.  Analysis of the wave properties of a new two-lane continuum model with the coupling effect , 2012 .

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

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

[33]  Sapna Sharma,et al.  Lattice hydrodynamic modeling of two-lane traffic flow with timid and aggressive driving behavior , 2015 .

[34]  Yu Cui,et al.  The control method for the lattice hydrodynamic model , 2015, Commun. Nonlinear Sci. Numer. Simul..

[35]  Zhao Min,et al.  Density waves in a lattice hydrodynamic traffic flow model with the anticipation effect , 2012 .

[36]  Serge P. Hoogendoorn,et al.  Generic gas-kinetic traffic systems modeling with applications to vehicular traffic flow , 2001 .

[37]  V. K. Katiyar,et al.  A new anisotropic continuum model for traffic flow , 2006 .

[38]  Dihua Sun,et al.  Nonlinear analysis of lattice model with consideration of optimal current difference , 2011 .

[39]  Sapna Sharma.  Effect of driver’s anticipation in a new two-lane lattice model with the consideration of optimal current difference , 2015 .

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

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

[42]  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 .

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

[44]  R. Jiang,et al.  A new continuum model for traffic flow and numerical tests , 2002 .

[45]  A. Gupta,et al.  Jamming transitions and the effect of interruption probability in a lattice traffic flow model with passing , 2015 .