Congested crossing pedestrian traffic flow: Dispersion versus transport in crowded areas

This study investigates the complex dynamic interactions between two typed populations coexisting within a shared space. We propose both theoretical and numerical study to analyze scenarios where one population (population [Formula: see text]) must traverse a territory occupied by another (population [Formula: see text]), necessitating strategies to mitigate overcrowding caused by spatial limitations. To capture these interactions, we model population [Formula: see text] using a linear transport equation, while population [Formula: see text] is described by a granular diffusion model á la sandpile to represent its internal dynamics and tendency to decongest. Through numerical simulations, we explore how different movement strategies of the traversing population (population [Formula: see text]) — including directed motion towards a specific destination, internal dispersion to minimize crowding, and uniform dispersal across the space — affects the behavior of population [Formula: see text].