Chaotic jam and phase transition in traffic flow with passing

Area of Science:

• Traffic flow dynamics
• Nonlinear physics
• Complex systems modeling

Background:

• Understanding traffic jams is crucial for transportation efficiency.
• Existing models often simplify or omit the impact of vehicle passing behavior.
• The transition dynamics of traffic flow under varying conditions require further investigation.

Purpose of the Study:

• To develop a lattice hydrodynamic model that incorporates the passing effect in one-dimensional traffic flow.
• To analyze the impact of the passing constant (gamma) on traffic jam transitions.
• To investigate the emergence of chaotic density waves and their relationship with jam dynamics.

Main Methods:

• Development of a lattice hydrodynamic model.
• Analysis of traffic flow transitions under different passing constants (gamma).
• Linear stability analysis to derive the neutral stability line.
• Nonlinear analysis to derive the modified Korteweg-de Vries equation.

Main Results:

• A critical passing constant (gamma) determines the nature of traffic jam transitions.
• For gamma > critical value, transitions occur from uniform flow to chaotic density waves, then to kink density waves, with increased delay.
• The chaotic region expands with increasing gamma, and the neutral stability line aligns with the uniform flow to density wave transition.
• The modified Korteweg-de Vries equation accurately describes kink jams for small gamma.

Conclusions:

• The passing effect significantly influences traffic jam transitions, leading to complex dynamics like chaotic density waves.
• The lattice hydrodynamic model provides a framework for understanding these complex traffic phenomena.
• The findings offer insights into traffic flow control and management strategies.