Stochastic and coarse-grained two-dimensional modeling of directional particle movement

We study the evolution of interacting groups of pedestrians in two-dimensional geometries. We introduce a microscopic stochastic model that includes floor fields modeling the global flow of individual groups as well as local interaction rules. From this microscopic model we derive an analytically-tractable system of conservation laws that governs the evolution of the macroscopic pedestrian densities. Numerical simulations show good agreement between the system of conservation laws and the microscopic model, though the latter is slightly more diffusive. We conclude by deriving second-order corrections to the system of conservation laws. •Develop an agent-based stochastic model for interacting groups of pedestrians.•Model includes global individual group flow and local interaction rules.•Derive the continuum limit, a system of analytically tractable conservation laws.•Simulations show good agreement between stochastic and continuum models.•Derive second-order corrections to the system of conservation laws.