Lane formation in bidirectional pedestrian streams is based on a stimulus-response mechanism and strategies of navigation in a fast-changing environment. Although microscopic models that only guarantee volume exclusion can qualitatively reproduce this phenomenon, they are not sufficient for a quantitative description. To quantitatively describe this phenomenon, a minimal anticipatory collision-free velocity model is introduced. Compared to the original velocity model, the new model reduces the occurrence of gridlocks and reproduces the movement of pedestrians more realistically. For a quantitative description of the phenomenon, the definition of an order parameter is used to describe the formation of lanes at transient states and to show that the proposed model compares relatively well with experimental data. Furthermore, the model is validated by the experimental fundamental diagrams of bidirectional flows.
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