Boundary Effects and Non-Equilibrium States in Pedestrian Dynamics - Experiments and Modelling
The collective dynamic of pedestrians is a lively field of research. From a theoretical point of view it's a complex system with interesting self-organization phenomena and collective effects. It has an important application for the design of pedestrian facilities, ranging from Level of Service concepts to guarantee the compliance with safety regulations. The number of models for pedestrian dynamics has grown in the past years, but the experimental data to test them and to distinguish between these models is still to a large extent controversial and contradictory.
The project is funded by the German Research Foundation (DFG) and the contract
numbers are KL 1873/1-1 and SE 1789/1-1.
Grant period: 2007 − 2012
The experiments include 99 different runs distributed over five days with up to 250 test persons. The objectives are to resolve the discrepancies in the literature concerning flow-density measurements and to provide a reliable data base for model development. Most of the data are provided on the website of the "Departement of Computer Simulation for Fire Safety and Pedestrian Traffic".
- Number of pedestrians: N = 17 - 110
- Corridor width: b = 0.7, 0.85 and 1.0 m
- Uni - bidirectional flow
- Closed and open boundaries
The video shows the velocity-density dependence of pedestrian streams. With increasing density the velocity decreases.
On the right at t=0:25 you can observe the formation and dissolution of a jam wave.
- Bottleneck width b: 0.8, 0.9, ..., 2.5 m
- Bottleneck length l: 0.1, 2.0, 4.0 m
- Corridor width bc: 4.0, 5.0, 6.0 m
- Number of pedestrians N: 50, 100, ..., 250
- Distance to the entrance d: 1.0, 2.0, 3.0, 4.0 m
Pedestrian flow through bottlenecks of different widths. Flow increases linearly with the width.
For data capturing we developed the tool item PeTrack which allows extracting the trajectories with high accuracy from video recordings. The procedure includes calibration, recognition, tracking and height detection, see video:
Video recording and resulting trajectories
For the modelling of pedestrian movement we use the continuous space approach as well as cellular automata. To reduce the numbers of free parameter we try to model pedestrian movement by considering the details of the locomotors system, like the moving of pedestrians in steps. The animation shows the movement of self driven objects with size depending on the step length. The objects adapt their velocity in dependence of the distance to the pedestrian in front, which models the dynamically varying space requirement of moving pedestrians.
The model reproduce the velocity-density dependence and the formation of jam waves.
Shape of pedestrians
To model the movement in two dimensions we use ellipses with velocity dependent semiaxes. With this approach we are able to reproduce the fundamental diagram in a narrow and a wide corridor with one parameter set.
- Top left: Circles with constant size: density inside the bottleneck is too low.
- Top right: Circles with velocity dependent size: Space requirement lateral to the movement direction is too high. Only two lanes appear inside the bottleneck.
- Bottom left: Ellipses with velocity depended size: Density and velocity in front and inside the bottleneck agree very well with the experiment. Three lanes appear inside the bottleneck.
- Bottom right: Experiment.
- Schadschneider, W. Klingsch, H. Klüpfel, T. Kretz, C. Rogsch und A. Seyfried, Evacuation Dynamics: Empirical Results, Modeling and Applications. In: R. A. Meyers (ed.) Encyclopedia of Complexity and System Science, Springer, 5, 3142-3176 (2009)
- U. Chattaraj, A. Seyfried und P. Chakroborty, Comparison of Pedestrian Fundamental Diagram Across Culture, Advances in Complex Systems (ACS), 12, 393-405 (2009)
- M. Chraibi, A. Seyfried und A. Sachdschneider, Generalized centrifugal force model for pedestrian dynamics, Physical Review E, 82, 046111 (2010)
- Steffen und A. Seyfried, Methods for measuring pedestrian density, flow, speed and direction with minimal scatter, Physica A, 389, 1902-1910 (2010)
- M. Boltes, A. Seyfried, B. Steffen und A. Schadschneider, Automatic Extraction of Pedestrian Trajectories from Video Recordings. In: W. W. F. Klingsch, C. Rogsch, A. Schadschneider und M. Schreckenberg (eds), Pedestrian and Evacuation Dynamics 2008, Springer, p. 43-54 (2010)
- M. Chraibi, A. Seyfried, A. Schadschneider und W. Mackens, Quantitative Description of Pedestrian Dynamics with a Force-based Model. In: IEEE/WIC/ACM International Joint Conference on Web Intelligence and Intelligent Agent Technology, IEEE Computer Society, 3, 583-58 (2009)
A. Seyfried, A. Portz und A. Schadschneider, Phase Coexistence in Congested States of Pedestrian Dynamics. In: S. Bandini, S. Manzoni, H. Umeo und G. Vizzari (eds), Cellular Automata, Springer, LNCS 6350, 496-505 (2010)