Stability analysis of dynamic collaboration model with control signals on two lanes

Abstract In this paper, the influence of control signals on the stability of two-lane traffic flow is mainly studied by applying control theory with lane changing behaviors. We present the two-lane dynamic collaboration model with lateral friction and the expressions of feedback control signals. What is more, utilizing the delayed feedback control theory to the two-lane dynamic collaboration model with control signals, we investigate the stability of traffic flow theoretically and the stability conditions for both lanes are derived with finding that the forward and lateral feedback signals can improve the stability of traffic flow while the backward feedback signals cannot achieve it. Besides, direct simulations are conducted to verify the results of theoretical analysis, which shows that the feedback signals have a significant effect on the running state of two vehicle groups, and the results are same with the theoretical analysis.

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

[2]  A. Schadschneider.  The Nagel-Schreckenberg model revisited , 1999, cond-mat/9902170.

[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]  Wen-Xing Zhu,et al.  Analysis of energy dissipation in traffic flow with a variable slope , 2013 .

[5]  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.

[6]  Guanghan Peng,et al.  A new car-following model with the consideration of anticipation optimal velocity , 2013 .

[7]  J. R. Wootton,et al.  Intelligent transportation systems: A global perspective , 1995 .

[8]  J. M. D. Castillo,et al.  On the functional form of the speed-density relationship—I: General theory , 1995 .

[9]  Akihiro Nakayama,et al.  Dynamical model of a cooperative driving system for freeway traffic. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Sun Dihua,et al.  Multiple car-following model of traffic flow and numerical simulation , 2009 .

[11]  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.

[12]  J Kertész,et al.  Nondeterministic Nagel-Schreckenberg traffic model with open boundary conditions. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[15]  L. A. Pipes.  An Operational Analysis of Traffic Dynamics , 1953 .

[16]  Hongxia Ge,et al.  Two velocity difference model for a car following theory , 2008 .

[17]  孙棣华,et al.  A new traffic model with the consideration of coupling effect with two lanes , 2009 .

[18]  Hai-Jun Huang,et al.  Stability of the car-following model on two lanes. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[20]  K. Hasebe,et al.  Analysis of optimal velocity model with explicit delay , 1998, patt-sol/9805002.

[21]  Takashi Nagatani,et al.  Effect of gravitational force upon traffic flow with gradients , 2009 .

[22]  Takashi Nagatani,et al.  Jamming transitions and the modified Korteweg–de Vries equation in a two-lane traffic flow , 1999 .

[23]  S. Dai,et al.  Effect of the optimal velocity function on traffic phase transitions in lattice hydrodynamic models , 2009 .

[24]  K Konishi,et al.  Coupled map car-following model and its delayed-feedback control. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[25]  Xiaojun Zhao,et al.  Controlling traffic jams by a feedback signal , 2005 .

[26]  Konishi,et al.  Delayed-feedback control of spatial bifurcations and chaos in open-flow models , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[28]  马寿峰,et al.  Influence of lane change on stability analysis for two-lane traffic flow , 2011 .

[29]  Helbing,et al.  Congested traffic states in empirical observations and microscopic simulations , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[31]  Kentaro Hirata,et al.  Decentralized delayed-feedback control of an optimal velocity traffic model , 2000 .

[32]  Akihiro Nakayama,et al.  Equivalence of linear response among extended optimal velocity models. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Chen Xuan,et al.  Study on the two-lane feedback controled car-following model , 2007 .

[34]  Hai-Jun Huang,et al.  An Extended Optimal Velocity Model with Consideration of Honk Effect , 2010 .

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

[36]  Wen-Xing Zhu.  MOTION ENERGY DISSIPATION IN TRAFFIC FLOW ON A CURVED ROAD , 2013 .

[37]  Gao Zi-You,et al.  The stability analysis of the full velocity and acceleration velocity model , 2007 .

[38]  Xianglin Han,et al.  JAMMING TRANSITION IN EXTENDED COOPERATIVE DRIVING LATTICE HYDRODYNAMIC MODELS INCLUDING BACKWARD-LOOKING EFFECT ON TRAFFIC FLOW , 2008 .

[39]  Debashish Chowdhury,et al.  Distributions of time- and distance-headways in the Nagel-Schreckenberg model of vehicular traffic: effects of hindrances , 1998 .

[40]  Hong Kam Lo,et al.  Evaluation framework for IVHS , 1994 .

[41]  Shiro Sawada,et al.  Nonlinear analysis of a differential-difference equation with next-nearest-neighbour interaction for traffic flow , 2001 .