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Pedestrian Dynamics: Stop-and-go waves with force-based models

Primary LanguagePython

Model description

This is a 1D model continuous in space which has the goal to reproduce stop-and-go waves.

scenario

Model description is in this article DOI.

Chraibi, M., Tordeux, A., Schadschneider, A. (2016). A Force-Based Model to Reproduce Stop-and-Go Waves in Pedestrian Dynamics. In: Knoop, V., Daamen, W. (eds) Traffic and Granular Flow '15. Springer, Cham. https://doi.org/10.1007/978-3-319-33482-0_22

Model parameters are:

  • v_0: desired speed
  • tau: reaction time
  • a_0: required space of an agent with zero speed
  • a_v: time constant: velocity-dependency on the speed. Space requirement is defined as: a=a_0 + a_v.v

In the dimensionless version of the model (see article) the above mentioned parameter can be reduced to:

v_0 and a_v.

After performing a simplified stability analysis on the model in 1D we find the following relationship:

stability

which indicates for which values of the tuple (v_0,a_v) we can expect having stop-and-go waves.

Requirements

The following python packages are needed

  • matplotlib
  • numpy
  • (optional) pandas: for faster loading of the trajectory files.

It recommended to use a virtual environment before installing:

python3 -m venv .venv
source .venv/bin/activate

To install the required libraries run:

pip install -r requirements.txt

Run simulation

python model.py

The following values are used

  • Length of the system: 200 m
  • Number of pedestrians 133
  • Simulation time: 3000 s
  • v_0=1
  • a_v=0

Note: Run in a separate window tail -f log.txt to display an updated content of the log file.

Plot trajectories

After successfully running the above script, two files should be produced:

  • a trajectory file
  • and a log file

Using the trajectory file we can produce a (x,t) diagram as follows:

python plot-traj.py traj_133_av0.00_v01.00.txt

(Note: the values of the parameter are coded in the name of the file)

The following trajectories are then produced

traj.png

Plot the variation of the velocity

The second file that is produced upon a successful simulation is a log file with some useful speed information (default file name is log.txt).

These can be plotted as well with the following command

python plot_velocity_std.py

which produces this figure

velocity