Abstract
In this paper, a reactive dynamic user equilibrium model is extended to simulate two groups of pedestrians traveling on crossing paths in a continuous walking facility. Each group makes path choices to minimize the travel cost to its destination in a reactive manner based on instantaneous information. The model consists of a conservation law equation coupled with an Eikonal-type equation for each group. The velocity-density relationship of pedestrian movement is obtained via an experimental method. The model is solved using a finite volume method for the conservation law equation and a fast-marching method for the Eikonal-type equation on unstructured grids. The numerical results verify the rationality of the model and the validity of the numerical method. Based on this continuum model, a number of results, e.g., the formation of strips or moving clusters composed of pedestrians walking to the same destination, are also observed.
Original language | English |
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Pages (from-to) | 1541-1555 |
Number of pages | 15 |
Journal | Acta Mathematica Scientia |
Volume | 29 |
Issue number | 6 |
DOIs | |
Publication status | Published - 1 Nov 2009 |
Keywords
- 76M12
- conservation law
- density-velocity relationship
- Eikonal-type equation
- fast marching method
- finite volume method
- pedestrian flows
- unstructured grids
ASJC Scopus subject areas
- Mathematics(all)
- Physics and Astronomy(all)