2023/02/22 by Hamza Ennaji, Ennaji, Hamza, Noureddine Igbida +3 · 2 citations
Engineering · #Analysis of PDEs (math.AP) #Evacuation and Crowd Dynamics #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Traffic Prediction and Management Techniques #Traffic control and management
paper · pdf · doi:10.48550/arxiv.2302.11315
openalex publication_date 2023/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a new variant of mathematical prediction-correction model for crowd motion. The prediction phase is handled by a transport equation where the vector field is computed via an eikonal equation \Vert ∇φ\Vert=f, with a positive continuous function f connected to the speed of the spontaneous travel. The correction phase is handled by a new version of the minimum flow problem. This model is flexible and can take into account different types of interactions between the agents, from gradient flow in Wassersetin space to granular type dynamics like in sandpile. Furthermore, different boundary conditions can be used, such as non-homogeneous Dirichlet (e.g., outings with different exit-cost penalty) and Neumann boundary conditions (e.g., entrances with different rates). Combining finite volume method for the transport equation and Chambolle-Pock's primal dual algorithm for the eikonal equation and minimum flow problem, we present numerical simulations to demonstrate the behavior in different scenarios.