VISSIM 5.30-05 User Manual

7 Simulation of Pedestrians
In this equation, v_alpha is the current velocity of the pedestrian, v 0 _alpha is
his desired speed taken from a distribution defined by the user. The crucial
value is the unit vector e_alpha which multiplied with the desired speed
gives the current desired velocity.
Up to now e_alpha in VISSIM always has been pointing into the direction of
the shortest path. With the dynamic potential the idea is that it points into a
direction which is a current estimation for the direction of the quickest path. It
can never be analytically the “true” and correct direction of the quickest path
as such a solution could only in principle be the result of an iterated
simulation. Yet, up to now no such method exists for pedestrians, not even
for small systems unless they are trivially small (e.g. just one pedestrian). As
real pedestrians also err a lot about what at a current point in time is the
direction that will take them in quickest time to their destination, it is not a
principle problem that the true direction of the quickest path can not be
calculated exactly. Therefore assuming hypothetically that the direction of the
quickest path would be available in the simulation and thus the behavior of
all pedestrians would be individually optimal, it would probably not be
realistic.
The meaning of the parameter impact is that an e_alpha s for the direction of
the shortest path and an e_alpha q for the direction of the quickest path are
calculated and then a resulting e_alpha is calculated in which e_alpha s and
e_alpha q have weights according to the value of the parameter Impact.
No matter if e_alpha points into the direction of the shortest path (dynamic
potential deactivated) or the estimated quickest path (dynamic potential
activated 100%) it is always calculated by at first calculating values for the
points of a grid which give either the distance or the estimated remaining
travel time from that particular point to the corresponding destination area.
This grid is what is called potential, another name would be “look-up table”.
As the distance to the destination does not change in the course of a
simulation run, the potential holding the distance values is called static
potential. As, on the contrary, the estimated remaining travel time to the
destination – under consideration of the presence of all other pedestrians –
changes continuously this potential is called dynamic potential. One can
imagine the values of a potential as elevation values and e_alpha then
points into the direction of steepest descent, mathematically it is the
(negative) gradient.
The potentials are calculated by driving a front outward from the boundaries
of the destination area. This can be imagined as tipping some object onto a
water surface and following the out-most wave front, for each point of the
surface noting, at which time after the tipping it was reached. For the
calculation of the static potential the speed of the wave front is everywhere
the same, for the dynamic potential it is slower, if a spot is occupied by a
pedestrian (in fact the relative walking orientation of the pedestrian also has
an impact on the speed of the wave front). Mathematically this is the
numerical solution of the Eikonal equation using a method similar to the Fast
Marching Method.
390 VISSIM 5.30-05 © PTV AG 2011