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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 872807, 7 pages
Research Article

A Mathematical Model of the Formation of Lanes in Crowds of Pedestrians Moving in Opposite Directions

School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA 30332-0160, USA

Received 5 May 2015; Accepted 9 June 2015

Academic Editor: Tetsuji Tokihiro

Copyright © 2015 Guillermo H. Goldsztein. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In crowded environments, pedestrians moving in opposite directions segregate into lanes of individuals moving in the same direction. It is believed that this formation of lanes that facilitates the flow results from the individuals acting on their behalf, responding to local stimuli, without the intention of benefiting the crowd as a whole. We give evidence that this is true by developing and analyzing a simple mathematical model. Our results suggest that the simple behavior of moving out of the way to avoid imminent collisions leads to the formation of lanes of individuals moving in the same direction.