Threshold Queueing to Describe the Fundamental Diagram of Uninterrupted Traffic

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Queueing because of congestion is an important aspect of road traffic. This paper provides a novel threshold queue that models the empirical shape of the fundamental diagram. In particular, we show that our threshold queue with two service phases captures the capacity drop that is eminent in the fundamental diagram of modern traffic. We use measurements on a Danish highway to illustrate that our threshold queue is indeed capable of capturing the fundamental diagram of real-world traffic systems. We furthermore indicate the modelling power of our threshold queue via a sensitivity study showing that our model is able to capture a wide range of shapes for the fundamental diagram.
Original languageEnglish
Pages (from-to)585-596
Number of pages12
JournalTransportation science
Issue number2
Publication statusPublished - 26 Mar 2019


  • Threshold queue
  • Hysteresis
  • Capacity drop
  • Fundamental diagram
  • Matrix Analytic Methods
  • Level-dependent quasi-birth-and-death process
  • 22/4 OA procedure


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