A common approach to modelling traffic flow is to consider the stream of vehicles from a macroscopic point of view. This leads to the same type of partial differential equations (PDEs) as in continuum mechanics. An example is sedimentation of small particles in a liquid.

Thus, the PDEs modelling traffic flow and sedimentation are of the same type. When considering traffic flow at junctions and networks, shifting number of lanes or changing surface conditions, the coefficients in the model PDE become discontinuous functions of the spatial variable. Stefan Diehl in the group has during a long time done research on such equations with the specific application to continuous sedimentation.

An example of the problems that appear at junctions is provided by the master's thesis Mathematical Modelling of Traffic Flow at Bottlenecks by Cathleen Perlman, 2008.

A short overview of the modelling of traffic flow is given by Stefan Diehl's docent lecture in 2006 (in Swedish): Modellering av trafikflöde.

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Last modified: 2009-03-16

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