Automatic fitting procedure for the fundamental diagram

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The fundamental diagram of a road, including free-flow capacity and queue discharge rate, is very important for traffic engineering purposes. In the real word, most traffic measurements come from stationary loop detectors. This paper proposes a method to fit Wu's fundamental diagram to loop detector data. Wu's fundamental diagram is characterised by five parameters, being free-flow speed, wave speed, free-flow capacity, queue discharge rate and jam density. The proposed method entails fixing the wave speed and the free-flow speed. The method consists of two steps. We first use a triangular fundamental diagram to separate the congested branch from the free-flow branch. Then, the remaining three parameters of Wu's fundamental diagram are fitted on each branch using a least-square fit. This method is shown to be robust for cases tested in real life, and hence very noisy, data.
Original languageEnglish
Number of pages16
JournalTransportmetrica B: Transport Dynamics
Publication statusPublished - 2016


  • Fundamental diagram
  • fitting
  • freeway
  • wave speed
  • free-flow speed
  • capacity drop
  • calibration


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