Continuity Equation

  • Martin TreiberEmail author
  • Arne Kesting


The foundations of every macroscopic traffic model are the hydrodynamic relation “flow equals density times speed” and the continuity equation, which describes the temporal evolution of the density as a function of flow differences or gradients. The macroscopic vehicle speed is defined such that it satisfies the hydrodynamic relation, and the continuity equation is directly derived from the conservation of vehicle flows. Thus, both equations are parameter-free and hold for arbitrary macroscopic models. In this chapter, we derive the continuity equation for various road geometries and illustrate it both from the point of view of a stationary observer (Eulerian representation) and a vehicle driver (Lagrangian representation).

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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