Jam formation in traffic flow on a highway with some slowdown sections

We study the traffic jams appearing on a single-lane highway with a few slowdown sections. At low density, the flow (current) increases linearly with density, while it saturates at some values of intermediate density. In such case that some slowdown sections have the same speed limit, when the flow begins to saturate, a single discontinuous front (stationary shock wave) occurs before a slowdown section or some discontinuous fronts appear before some slowdown sections. For the case of different speed limits, the discontinuous front occurs before the section of strongest slowdown. The saturated flow is given by the maximal value of the current of the strongest slowdown section. The relationship between the densities is derived before and after the discontinuity. The dependence of jam lengths on density is derived numerically and analytically.

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

[2]  Takashi Nagatani.  Chaotic and periodic motions of a cyclic bus induced by speedup. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  M. Evans,et al.  Jamming transition in a homogeneous one-dimensional system: The bus route model , 1997, cond-mat/9712243.

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

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

[6]  H. W. Lee,et al.  Macroscopic traffic models from microscopic car-following models. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[8]  A I Olemskoi,et al.  Synergetic theory for a jamming transition in traffic flow. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  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.

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

[11]  Havlin,et al.  Presence of many stable nonhomogeneous states in an inertial car-following model , 2000, Physical review letters.

[12]  Ihor Lubashevsky,et al.  Towards a variational principle for motivated vehicle motion. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Kai Nagel,et al.  Two-lane traffic rules for cellular automata: A systematic approach , 1997, cond-mat/9712196.

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

[15]  Takashi Nagatani,et al.  Phase Diagram in Multi-Phase Traffic Model , 2005 .

[16]  B. Kerner.  THE PHYSICS OF TRAFFIC , 1999 .

[17]  Shlomo Havlin,et al.  Multifractal chaotic attractors in a system of delay-differential equations modeling road traffic. , 2002, Chaos.

[18]  Takashi Nagatani,et al.  Transition and saturation of traffic flow controlled by traffic lights , 2003 .

[19]  Redner,et al.  Kinetics of clustering in traffic flows. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  Ihor Lubashevsky,et al.  Long-lived states in synchronized traffic flow: empirical prompt and dynamical trap model. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Takashi Nagatani,et al.  Spatio-temporal dynamics of jams in two-lane traffic flow with a blockage , 2003 .

[22]  T. Nagatani,et al.  Bunching transition in a time-headway model of a bus route. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Fan Weicheng,et al.  Simulation of bi-direction pedestrian movement using a cellular automata model , 2003 .

[24]  Dirk Helbing,et al.  Granular and Traffic Flow ’99: Social, Traffic, and Granular Dynamics , 2000 .

[25]  Takashi Nagatani,et al.  Discontinuity at edge of traffic jam induced by slowdown , 2006 .

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

[27]  Henri Huijberts,et al.  Analysis of a continuous car-following model for a bus route: existence, stability and bifurcations of synchronous motions , 2002 .

[28]  A Schadschneider,et al.  Optimizing traffic lights in a cellular automaton model for city traffic. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  S. Maniccam,et al.  Traffic jamming on hexagonal lattice , 2003 .