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Jamming transition in a two-dimensional traffic flow model.

¹Division of Thermal Science, College of Engineering, Shizuoka University, Hamamatsu 432-8561, Japan.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

|April 24, 2002

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This study explores phase transitions in two-dimensional traffic flow, revealing distinct phases like free movement and congestion below a critical point. The critical point value is influenced by the proportion of eastbound cars.

Area of Science:

Physics
Traffic Flow Dynamics
Statistical Mechanics

Background:

Traffic flow models are crucial for understanding urban mobility and congestion.
Extending one-dimensional models to two dimensions captures more complex traffic behaviors.

Purpose of the Study:

To investigate phase transitions and critical phenomena in a two-dimensional traffic flow model.
To analyze the impact of car proportions on critical points and traffic phases.

Main Methods:

Numerical and analytical investigations of a two-dimensional lattice hydrodynamic traffic model.
Application of linear stability theory and nonlinear analysis.
Derivation of the time-dependent Ginzburg-Landau (TDGL) equation.

Main Results:

Related Experiment Videos

Identified three distinct phases: freely moving, coexisting, and uniformly congested, occurring below the critical point.
Observed no phase transition above the critical point.
Determined that the critical point value decreases with an increasing fraction of eastbound cars (for c<=0.5).
Calculated neutral stability lines, phase separation lines, spinodal lines, and the critical point using the TDGL equation.

Conclusions:

The two-dimensional traffic flow model exhibits critical phenomena analogous to physical systems.
The proportion of different vehicle types significantly influences traffic phase transitions and critical behavior.