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In crowded environments, pedestrians moving in opposite directionssegregate into lanes of individuals moving in the same direction. It is believed that this formation of lanes that facilitates the flowresults from the individuals acting on their behalf, responding to localstimuli, without the intention of benefiting the crowd as a whole. Wegive evidence that this is true by developing and analyzing a simplemathematical model. Our results suggest that the simple behaviorof moving out of the way to avoid imminent collisions leads to theformation of  lanes of individuals moving in the same direction

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