The Lighthill–Whitham–Richards Model

  • Martin Treiber
  • Arne Kesting


The continuity equation, which holds for all macroscopic models, describes the rate of change of the density in terms of gradients (or differences) of the flow. The model is closed by specifying flow or local speed. In this chapter we discuss the simpler approach in which the flow is given as a static function of the density, i.e., by a fundamental diagram. The models of this class of first-order models which are also called Lighthill–Whitham–Richards models differ only in the functional form of the fundamental diagram and in their mathematical representation.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institut für Wirtschaft und VerkehrTU DresdenDresdenGermany
  2. 2.TomTom Development Germany GmbHBerlinGermany

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