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This study introduces disorders into a car-following model to analyze traffic flow. Results show traffic phase transitions are consistently first-order, regardless of speed variations, offering insights into heterogeneous traffic dynamics.

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Area of Science:

  • Traffic Flow Dynamics
  • Statistical Physics
  • Complex Systems

Background:

  • Understanding heterogeneous traffic flow is crucial for transportation.
  • Newell's car-following model is a standard for traffic simulation.
  • Quenched disorders can significantly alter system dynamics.

Purpose of the Study:

  • To investigate the impact of quenched disorders on Newell's car-following model.
  • To analyze heterogeneous traffic dynamics under parameter randomness.
  • To characterize phase transitions in traffic flow.

Main Methods:

  • Introduction of quenched disorders (beta distributions) in free-flow speed, jam density, and backward wave speed.
  • Numerical simulations of the modified car-following model.
  • Analysis of platoon size, vehicle speed, density moments, and gap distributions.
  • Application of mean-field theory for gap distribution derivation.

Main Results:

  • Average platoon size and speed exhibit power-law evolution at low densities.
  • No power-law behavior observed in density moments or distribution, differentiating from sticky gas models.
  • Stationary gap distribution shows no power-law behavior, unlike asymmetric simple exclusion processes.
  • Traffic phase transition (platoon to laminar phase) is first-order, independent of free-flow speed disorder.
  • Transition density is the reciprocal of the average platoon gap in the thermodynamic limit.

Conclusions:

  • Quenched disorders in car-following models lead to specific power-law behaviors at low densities.
  • Traffic phase transitions remain robustly first-order despite parameter heterogeneity.
  • Mean-field theory accurately predicts gap distributions and corroborates simulation findings on phase transitions.