A Macroscopic Approach to the Lane Formation Phenomenon in Pedestrian Counterflow

We simulate pedestrian counterflow by adopting an optimal path-choice strategy and a recently observed speed-density relationship. Although the whole system is symmetric, the simulation demonstrates the segregation and formation of many walking lanes for two groups of pedestrians. The symmetry breaking is most likely triggered by a small numerical viscosity or "noise", and the segregation is associated with the minimization of travel time. The underlying physics can be compared with the "optimal self-organization" mechanism in Helbing's social force model, by which driven entities in an open system tend to minimize their interaction to enable them to reach some ordering state.