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Reconstruction of density and cost potential field of Eikonal equation: Applications to discrete pedestrian flow models

Author

Listed:
  • Li, Xiao-Yang
  • Lin, Zhi-Yang
  • Zhang, Peng
  • Zhang, Xiao-Ning

Abstract

The paper formulates a cost potential field on a lattice network through reconstruction of density in a pedestrian’s visible region, which is based on the numerical solution to Eikonal equation. This leads to a lattice gas and a many-particle models by which a pedestrian’s movement essentially depends on a speed-density relationship or fundamental diagram. In the former model, the pedestrian moves to a neighbor with a probability depending on the density distribution and the cost-optimal path of the potential field. In the latter, he/she moves directly along the cost-optimal path in a speed given by the fundamental diagram. Numerical experiments show that the two models are able to reproduce typical phenomena such as the evacuation through an exit and the formation of lanes in the pedestrian counterflow. The numerical results quantitatively agree with observations in the fundamental diagram, evacuation time, and capacity through an exit.

Suggested Citation

  • Li, Xiao-Yang & Lin, Zhi-Yang & Zhang, Peng & Zhang, Xiao-Ning, 2023. "Reconstruction of density and cost potential field of Eikonal equation: Applications to discrete pedestrian flow models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 629(C).
    • Handle: RePEc:eee:phsmap:v:629:y:2023:i:c:s0378437123007239
    DOI: 10.1016/j.physa.2023.129168
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