Constructing set-valued fundamental diagrams from jamiton solutions in second order traffic models.

• Author(s) / Creator(s)

  • Flynn, M.R.
  • Rosales, R.R.
  • Kasimov, A. R.
  • Seibold, B.

• Fundamental diagrams of vehicular traffic flow are generally multi-valued in the congested flow regime. We show that such set-valued fundamental diagrams can be constructed systematically from simple second order macroscopic traffic models, such as the classical Payne-Whitham model or the inhomogeneous Aw-Rascle-Zhang model. These second order models possess nonlinear traveling wave solutions, called jamitons, and the multi-valued parts in the fundamental diagram correspond precisely to jamiton-dominated solutions. This study shows that transitions from function-valued to set-valued parts in a fundamental diagram arise naturally in well-known second order models. As a particular consequence, these models intrinsically reproduce traffic phases.

• Date created

  2013-01-01

• Subjects / Keywords

  • Traveling wave
  • Second order
  • Fundamental diagram
  • Jamiton
  • Sensor data
  • Payne-Whitham
  • Aw-Rascle-Zhang
  • Effective flow rate
  • Traffic model

• Type of Item

  Article (Published)

• DOI

  https://doi.org/10.7939/R3NS0MB4J

• License

  Attribution 4.0 International