Try playing around with the simulation of pedestrian movement on the
boards below:
(a) cross-directional model
(b) 4-directional model
If you look closely at the lower right corner of any lattice of cells below, you see 3 small buttons. Click the top one to randomly populate the grid. Click the middle button to clear the grid (click twice for best results). Click the bottom one to run and to pause the simulation of the Ped CA model. You may also add peds to or remove peds from the board by clicking on or dragging over selected cells.
Cross-directional
model (pedestrians going to the right and up):
The lattice, or floor area, is randomly filled with about 30% of its
cells occupied by pedestrians. The peds move in two distinct steps.
First, lane changes are made. Next, forward steps to the right are
made. The forward movement wraps around the lattice when peds reach
the end of the walkway as they would in the uni- and bi-directional cases
over a circular track, and in the cross- and 4-directional cases over a
torus.
One pedestrian moving to the right is gray and one moving down is black
to aid in keeping track of a particular pedestrian moving in either cross-direction.
The peds are assigned a desired maximum speed shown by the color of
the occupied cell. The desired speed can not always be reached because
of blocking by other pedestrians. In the models direction of movement
is identified in the color scheme:
4-directional model
Two pedestrians moving right-left are gray and two moving up-down are
black to aid in keeping track of a particular pedestrians moving in either
bi- or cross-direction.
The cross- and 4-directional pedestrians are about equally proportioned
by direction in this demonstration. In order to avoid unrealistic
and permanent jams, opposing pedestrians who find themselves nose to nose
or one cell apart are allowed to exchange places with a 50% probability
of success - just as in real life such maneuvers are only fairly successful
on the first try.
Shock waves or avalanches may easily be observed. The peds often
jam, but pick their way through the jam according to the rules used for
exchanging places. Shock waves are an important phenomenon captured
by CA models that other simulation methods find difficult to emulate.
Note also that the original random configuration of peds transforms into
a self-organized configuration as the simulation progesses. This
phenomenon of self-organization is another important characteristic of
CA models. Computer experiments are ongoing to further capture ped
phenomena that occur in actuality. Further work in lane formation
is being undertaken as well, as shown in the next two examples below.
More about CA models:
The board layout is derived from the web site by Andreas Ehrencrona that
has a good explanation of Cellular
automata (CA) and the Life CA Game (with the author's permission).
I have adaptied that "Life" model CA JAVA code to my pedestrian CA model
originally written in C/C++. The ped model for uni-directional flow
was presented at the Transportation Research Board Annual Meeting in 1998.
The bi-directional flow model was presented at the TRB 1999 Annual Meeting
and
the ISTTT Conference held in Jerusalem in July 1999. Other bi-directional
papers are in review. The 4-directional pedestrian model presented here
has been submitted to the TRB 2000 Annual Meeting. The pedestrian
models Jeff Adler of RPI and I have created exhibit emerging fundamental
pedestrian flows from localized pedestrian rules.
Also try Exploring
Emergence and Artificial
Life Online for further explanations and examples of CA. Check
out TRANSIMS
for research ongoing with CA vehicular traffic simulations pioneered by
Kai Nagel. Also, the models of Craig
Reynolds and Dirk
Helbing, though not CA models, may be of interest because their models
deal with self-organization of individual, autonomous agents.
Click to go back to homepage, to bi-directional
modeling, or to go to the Iterated Prisoners'
Dilemma simulations.
Victor Blue (July 26, 1999). Send email with comments to: vicblue@ulster.net
Going to the right - blue
Going to the left - red
Going up
- green
Going down - violet.
This condition of people picking their way through a crowd without
forming lanes would occur at a busy crosswalk, on a subway platform, or
in a lobby, shopping mall, or concourse of any kind. It is an important
and difficult case to model, but CA allows a rather tractable approach.