Continuous limit of a crowd motion and herding model

Jan-Frederik Pietschmann, Peter Alexander Markowich, Martin Burger*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


In this paper we study the continuum limit of a cellular automaton model used for simulating human crowds with herding behaviour. We derive a system of non-linear partial differential equations resembling the Keller-Segel model for chemotaxis, however with a non-monotone interaction. The latter has interesting consequences on the behaviour of the model's solutions, which we highlight in its analysis. In particular we study the possibility of stationary states, the formation of clusters and explore their connection to congestion. We also introduce an efficient numerical simulation approach based on an appropriate hybrid discontinuous Galerkin method, which in particular allows flexible treatment of complicated geometries. Extensive numerical studies also provide a better understanding of the strengths and shortcomings of the herding model, in particular we examine trapping effects of crowds behind nonconvex obstacles.

Original languageEnglish (US)
Pages (from-to)1025-1047
Number of pages23
JournalKinetic and Related Models
Issue number4
StatePublished - Dec 1 2011


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