A three-phase fundamental diagram from three-dimensional traffic data

Maria Laura Delle Monache, Karen Chi, Yong Chen, Paola Goatin, Ke Han, Jing Mei Qiu, Benedetto Piccoli

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


This paper uses empirical traffic data collected from three locations in Europe and the US to reveal a three-phase fundamental diagram with two phases located in the uncongested regime. Model-based clustering, hypothesis testing and regression analyses are applied to the speed– flow–occupancy relationship represented in the three-dimensional space to rigorously validate the three phases and identify their gaps. The finding is consistent across the aforementioned different geographical locations. Accordingly, we propose a three-phase macroscopic traffic flow model and a characterization of solutions to the Riemann problems. This work identifies critical structures in the fundamental diagram that are typically ignored in first-and higher-order models and could significantly impact travel time estimation on highways.

Original languageEnglish (US)
Article number17
Pages (from-to)1-20
Number of pages20
Issue number1
StatePublished - Mar 2021

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Mathematical Physics
  • Logic
  • Geometry and Topology


  • Gap analysis
  • Macroscopic models
  • Multi-phase models
  • Traffic data


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