Crowd Flow Modeling
Partial Differential Equations, Spring 2015
This was a project conducted as part of the course Partial Differential Equations (PDEs). For this project, my partner and I were interested in learning about how crowds can be modeled using PDEs. Specifically, we chose to study a type of modeling known as Continuum-Based Crowd Flow Modeling.
Crowd flow modeling is an interesting and important field of modeling because crowd flow models have the potential to provide useful information about how a crowd will behave in a given situation or scenario without having to carry out an actual experiment with human test subjects. This information can then be used by the relevant authorities to help them develop strategies to control or manage a crowd more effectively.
Over the course of our project, we read the original paper by Hughes, who described a continuum-based approach to deriving the necessary PDEs needed to model the flow of pedestrians. We then read an additional paper by which revisited Hughes’ continuum model for pedestrian flow and further refined both the equations that modeled crowd flow as well as the solution method to the PDEs. Using information from these papers, we simulated a 1-dimensional crowd flow situation using Matlab.
Below is a video of our 1-dimensional model predicting the flow of a crowd over time:
Crowd flow modeling is an interesting and important field of modeling because crowd flow models have the potential to provide useful information about how a crowd will behave in a given situation or scenario without having to carry out an actual experiment with human test subjects. This information can then be used by the relevant authorities to help them develop strategies to control or manage a crowd more effectively.
Over the course of our project, we read the original paper by Hughes, who described a continuum-based approach to deriving the necessary PDEs needed to model the flow of pedestrians. We then read an additional paper by which revisited Hughes’ continuum model for pedestrian flow and further refined both the equations that modeled crowd flow as well as the solution method to the PDEs. Using information from these papers, we simulated a 1-dimensional crowd flow situation using Matlab.
Below is a video of our 1-dimensional model predicting the flow of a crowd over time: