Phase Diagram in Multi-Phase Traffic Model

A multi-phase traffic model is presented to take into account the complex motion of vehicles. The multi-phase model is one of the extended optimal velocity model. The optimal velocity (OV) function is modified to have multi turning points. The original OV model with a single turning point exhibits two-phase traffic, while the model with n(n⩾2) turning points displays n+1 phase traffic. The multiple phase transitions occur by varying the density. The phase transitions depend highly on the sensitivity (the inverse of delay time). The neutral stability line is obtained by using the linear stability analysis and is consistent with the jamming transition points. The phase diagrams are presented for the multiple jamming transitions.

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

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

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

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

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

[9]  Boris S. Kerner,et al.  Complexity of Synchronized Flow and Related Problems for Basic Assumptions of Traffic Flow Theories , 2001 .

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

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

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

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

[14]  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.

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

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

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

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

[19]  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.

[20]  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.

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

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

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

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