Phase transition and critical phenomenon in traffic flow model with velocity-dependent sensitivity

The traffic flow model with optimal velocity is extended to take into account the velocity-dependent sensitivity. The dependence of the jamming transition upon the sensitivity is investigated in the extended optimal velocity model. The phase transition among the freely moving phase, the coexisting phase and the homogeneous congested phase is studied by computer simulation. Order parameter S which is different from zero below the critical point is shown. The phase diagrams are obtained for the sensitivity parameters depending upon the car velocity. It is shown that the phase boundaries and the critical point depend largely upon the sensitivity parameters. The scaling properties of the headway, the car velocity and the jam’s propagation velocity are found near the critical point. It is shown that the scaling exponents are independent upon the velocity-dependent sensitivity.

[1]  Gábor Csányi,et al.  Scaling behaviour in discrete traffic models , 1995 .

[2]  Helbing.  Gas-kinetic derivation of Navier-Stokes-like traffic equations. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[4]  Robert Herman,et al.  Kinetic theory of vehicular traffic , 1971 .

[5]  Cuesta,et al.  Phase transitions in two-dimensional traffic-flow models. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Dirk Helbing.  Derivation and empirical validation of a refined traffic flow model , 1996 .

[7]  Nagatani.  Bunching of cars in asymmetric exclusion models for freeway traffic. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  Komatsu,et al.  Kink soliton characterizing traffic congestion. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  Nagatani.  Jamming transition in the traffic-flow model with two-level crossings. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  S. L. Paveri-Fontana,et al.  On Boltzmann-like treatments for traffic flow: A critical review of the basic model and an alternative proposal for dilute traffic analysis , 1975 .

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

[12]  Hui,et al.  Two-dimensional traffic flow problems with faulty traffic lights. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  Kerner,et al.  Deterministic spontaneous appearance of traffic jams in slightly inhomogeneous traffic flow. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[15]  K. Nagel,et al.  Deterministic models for traffic jams , 1993, cond-mat/9307064.

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

[17]  Takashi Nagatani,et al.  Kinetic segregation in a multilane highway traffic flow , 1997 .

[18]  Middleton,et al.  Self-organization and a dynamical transition in traffic-flow models. , 1992, Physical review. A, Atomic, molecular, and optical 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.