Pedestrian Simulation for Urban Traffic Scenarios

3 PEDESTRIANS IN URBAN TRAFFIC
Pedestrian behavior with regard to the interplay between
road users and pedestrians is dependent on walking velocities
of pedestrians and the road crossing behavior. This section
discusses relevant literature in this field.
The modeling of pedestrians for simulation of road networks
has been discussed in [10], proposing a model based
on the vehicle model of VISSIM [15]. The work has the focus
of creating a model with realistic flow-velocity-density
relationships. The shortcoming of this approach is the lack of
two-way traffic, which is important for pedestrians.
Different studies on pedestrian walking velocities have
been performed. A review is provided in [11]; in the following
we briefly summarize the most important insights. A
pedestrian p chooses velocity vp with respect to its physical
constitution and whether p walks on a sidewalk or crosses
a road. Crossing velocity is dependent on whether p is crossing
with or without right of way. Additionally, aggressiveness
increases velocity. This is modeled with help of an aggressiveness
factor AF. These major findings have been derived
from several studies monitoring different inner city crossings
at different places [11].
When p attempts to cross a road and is not able to do so due
to road traffic, aggressiveness of p increases. Aggressiveness
affects the walking velocity increasingly, when p finally is
able to cross the road. Referring to [9], this may result in a
maximum velocity increment of 0.5m · s −1 .
The lowest velocities are walked on sidewalks. When
crossing a road, pedestrians tend to speed up. The more hazardous,
the faster. When crossing with right of way, pedestrians
are slower than without right of way. The slowest crossing
velocities are walked on crosswalks. At pedestrian lights, the
waiting time until p is able to cross, increases aggressiveness
and thus velocity.
Each of these cases has to be separated with respect to
the physical constitution of p. Men are slightly faster than
women. The elderly are slower than adults and children. Finally,
different localities lead to different velocities [11].
When a pedestrian p decides to cross a road, p determines
the estimated crossing time [13]
ECT = w
+ AF (1)
vp
where w is the width of the road. The distribution of ECT
among pedestrians has been investigated in [2]. A mean ECT
of ECT ≈ 7s at a road with w = 9.1m and a mean velocity
of v = 1.2m · s −1 leads to a mean AF of AF ≈ −0.58s. This
means, that pedestrians tend to underestimate the time needed
to cross a road.
These findings build the basis for our model of pedestrian
movements.
Figure 1. Positioning of pedestrian way objects on intersections.
4 PEDESTRIAN MODEL
The interaction between road users and pedestrians is one
of the central aspects of this work. At first, pedestrians need
to find their way through the simulation graph (subsection
4.1). Interaction with road users will only take place, when
pedestrians cross roads. Thus, a mesoscopic simulation model
for pedestrians is introduced in this section. It consists of one
model for sidewalk movements (subsection 4.2) and another
model for crossing roads at pedestrian crossings (subsection
4.3).
4.1 Routing
The calculation of fastest ways in a graph data structure is a
well known problem. In this work, precalculated routes from
each NIa to each NIb can be used as well as online calculated
routes with help of the A* search algorithm and a probabilitybased
routing mechanism [3]. The result of each algorithm is
a list of EIs and a list of NIs, defining the route to be walked.
In the beginning, it is randomly chosen, which side of the
road a pedestrian stands on. Then, a heuristic algorithm calculates
where to cross the roads during the walk through the
calculated route. Crossing can be done on EIs if there is a sufficient
gap. Additionally, NIs store pedestrian ways, allowing
for crossing and pedestrian interaction. Figure 1 shows an intersection.
NI is connected to three EIs : EI1...EI3. Each
dashed line shows the position of a pedestrian way.
A pedestrian has to cross a road, e.g., whenever the following
EI is connected to the current EI into a direction which
is oppositely to the side of the road of the pedestrian. The
pedestrian plan of road crossings privileges pedestrian crossings
and traffic lights (both stored in NIs) over crossing the
road without right of way. Additionally, NIs are used to cross
a road, when crossing on an EI was planned, but not possible.
The models for movement and crossing on EIs and NIs are
different. The following sections 4.2 and 4.3 discuss both.
4.2 Sidewalk Movement
With regard to computational efficiency, pedestrians are
simulated with a very simple model when walking on sidewalks.
Let N b a (µ,σ) = min(max(N (µ,σ),a),b) be Gaussian
distributed random number with µ and σ bounded to the
interval [a···b]. Each pedestrian distinguishes his base velocities
for sidewalks α, for crossing with right of way β and