When pedestrians walk along a corridor in both directions, a frequently observed phenomenon is the segregation of the whole group into lanes of individuals moving in the same direction. While this formation of lanes facilitates the flow and benefits the whole group, it is believed that results from the actions of the individuals acting on their behalf, without considering others. This phenomenon is an example of self-organization and has attracted the attention of a number of researchers in diverse fields. We introduce and analyze a simple model. We assume that individuals move around a multi-lane circular track. All of them move at the same speed. Half of them in one direction and the rest in the opposite direction. Each time two individuals collide, one of them moves to a neighboring lane. The individual changing lanes is selected randomly. We prove that the system self-organizes. Eventually, each lane is occupied with individuals moving in only one direction. Our analysis supports the belief that global self-organization is possible even if each member of the group acts without considering the rest.
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