Virtual pedestrians risk modeling

International INTERNATIONAL Journal of Civil Engineering JOURNAL and OF Technology CIVIL (IJCIET), ENGINEERING ISSN 0976 – 6308 AND
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ISSN 0976 – 6316(Online), Volume 5, Issue 10, October (2014), pp. 32-42 © IAEME
TECHNOLOGY (IJCIET)
ISSN 0976 – 6308 (Print)
ISSN 0976 – 6316(Online)
Volume 5, Issue 10, October (2014), pp. 32-42
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IJCIET
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VIRTUAL PEDESTRIANS’ RISK MODELING
Meriem MANDAR1, Azedine BOULMAKOUL2
1ENSAK, Bd Béni Amir, BP 77, Khouribga – Morocco
2FSTM, Department of computer sciences, LIM/IDS Lab. Faculty of Sciences and Technologies of
Mohammedia – Morocco
32
ABSTRACT
All people move almost as pedestrians on the road network, but this activity is not as good as
it should be. The loss of millions of lives and injury of others doesn't suffice architects, urban
designers and policy makers to reconsider, radically, the design of the urban network, and to improve
the use of priorities rules. In this paper, we present an exposition risk indicator for road accidents
which can measure both pedestrians and vehicles risk exposition. For this purpose, we use our
pedestrian's dynamics fuzzy ant model based on artificial potential field [1], and for vehicles
dynamics both IDM [2] and MOBIL [3] models. Simulation results for both pedestrians and vehicles
traffic confirm predictions given by the first-order traffic flow theory. The current software solution
will be integrated for pedestrians' accidents analysis in urban transportation networks.
Keywords: Virtual Pedestrian Model, Intelligent Agent, Simulation, Accident Risk, Transportation
Theory.
I. INTRODUCTION
Each year millions people lose their lives on roads over the world. The majority of these
victims are pedestrians hit by motor vehicles in various situations. These situations could be
analyzed and classified in terms of the way pedestrians and/or vehicles behave and their relative
settings on the road network. Pedestrians are exposed to accident risk either when standing or
walking on the pavement or when crossing the road. The numbers of accidents depends on the local
transport policy and the resources devoted to pedestrian safety. While the injury seriousness is a
function of speed, the vehicles design, the road design and the vulnerability of the pedestrian,
without taking into consideration those of the pedestrian's dynamics, since waling is not yet
considered as an essential and necessary part of the overall transportation system.
Differences between the design of the planner and that of the user induce the dysfunction
observed in the system failure caused by the high number of accidents. Assaily has reported that 70-

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
80% of deaths on the roads, between 15 and 59 years old are men [4]. However, according to
Waylen and McKenna, the frequency and severity of accidents are higher among girls than boys.
This observation can be explained based solely on risk exposure [5]. Indeed, observations show that
there are gender differences’ in engagement in risk behaviour, as well as in the ability of risk
assessment according to age groups (children, adolescents and adults) [6]. In addition to attitudes
towards risk and their evaluation, any use of the road must also have a set of rules governing the
interactions of the road environment [7]. The transgression of these rules causes dangerous
behaviour that can lead to accidents. This act is even more among men than women for both drivers
and pedestrians [8].
The road accident risk is used to be estimated as a rate of accident involvement per unit of
time spent on the road network. Researchers are based on data collected by means of questionnaires
or field observations [9]. In most cases, there is lack of information about the micro-environments
met by pedestrians in those collected data, e.g. whether it concern a busy road or not, whether the
crossings are made at junctions or mid-block locations, and so on. Hence only macroscopic risk
indicators can be measured, which are heavily dependent on the often poor quality of accident data
for pedestrians. Our aim is to develop a methodology for assessing the risk exposure of pedestrians
in urban areas.
As non-crossing accidents generally represent a small proportion of pedestrian accidents [10],
we assume that pedestrians are at risk only when crossing a road. We consider characteristics
including traffic volume and speed without any distinction between different types of vehicles.
Pedestrians may have different types of behaviour at crossings, by having many different routes in
their trip, each one of these routes may entail different crossing types depending on their speeds. A
trade is made between pedestrian's perception of the risk they are exposed to, and between speeds
sequences, to let them finally choose an appropriate crossing behaviour, while taking into account
the needed time for crossing and their desire to feel comfortable.
This paper is structured as follows. After a short introduction, section 2 presents pedestrian’s
exposure concept. The third section presents some related works, while fourth one presents our fuzzy
ant pedestrians model based on artificial potential fields. Later section five presents the
measurements of pedestrians’ exposure to accident risk. Finally we describe obtained results given
by chosen traffic light simulation scenarios for vehicles' dynamics.
33
II. PEDESTRIAN EXPOSURE
It is important to understand the concept of pedestrian exposure and its relationship to
pedestrian risk. There is no best measure of pedestrian exposure. However, according to the specific
needs and objectives, some measures are better suited than others, such as the study of risk exposure
between populations and its evolution over time.
When defining exposure, it is necessary to specify who is exposed and to which element. The
term “exposure” originates from the field of epidemiology and is described as the situation when an
agent is subject to potentially hazardous situation or substance. Exposure can also be considered as a
trial event where a harmful outcome might occur. For example we are exposed to the possibility of
getting injured by a vehicle each time we cross a street. Risk is a function of exposure and hazard. It
refers to the occurrence probability of a hazardous event after a set of trials representing exposure
units. In our purpose, exposure specifies the situation of the exposure to accident risk. Pedestrian
exposure is therefore defined as a pedestrian’s rate of contact with potentially harmful vehicular
traffic [11].

34
III. RELATED WORKS
In general, accident risk is represented by the probability of accident per unit time of
exposure for a specific crossing section. Most of pedestrian’s causalities in road crashes happens
along trips in urban areas, and specifically while road crossing. Many factors may contribute to
collision or risk potentiality such as physical characteristics of the street and behavioral issues of
both pedestrians and drivers. The consideration of these factors in the analysis of pedestrians risk
exposure while crossing can produce a pedestrian-oriented planning of road design, traffic control
and crossing facilities [12].
It is difficult to measure directly pedestrians’ exposure to accident risk, because it would
involve tracking people’s movements at times. Several metrics are used in literature to measure
pedestrian exposure in both micro and macro level, such as the product of pedestrian and vehicle
volumes at an intersection and pedestrian distance traveled and pedestrian trips made but pedestrian
volumes are the most frequently used. In situations where travel-based measures of exposure are not
available, population-based measures are sometimes used for exposure approximation. The choice of
exposure measure strongly impacts the resulting calculation of risk.
Pedestrians’ accidents risk is often examined in macroscopic level [13] by several indicators
such as road collisions number in population of pedestrians [14-15], walking distance travelled [16]
and spent time [17], trips number [18] or road crossings number [19]. Macroscopic indicators may be
appropriate for a whole estimation of pedestrians’ exposure and for calculating aggregate risk
indicators. However, they suffer from the lack of details and do not take into account the
implications of the crossing behavior and the interaction between pedestrians and vehicles [20].
Comparing to macroscopic level, pedestrians exposure analysis in microscopic one have been given
in only a few studies. The indicators developing in latter are based either on the number of
pedestrians crossing a road section at given time intervals [21], or the product of vehicles and
pedestrians number crossing a road section during time intervals[22].
Unlike macroscopic indicators, microscopic ones take into account pedestrians characteristics
as well as traffic and road conditions. They may estimate more accurately pedestrians’ exposure at
specific locations. Indeed, even if urban system offer to pedestrians many facilities, their crossing
decision are made dynamically and spontaneously based on both their perceptions of vehicles gaps
and aims to minimize walking distances and time. Therefore, the largest percentage of pedestrians
road accidents occur outside specified crossing locations [23]. This crossing practice of pedestrians
may affect the analysis of pedestrians risk exposure since a relatively unsafe crossing choice or an
unexpected event may potentially increase it, and is not fully examined in existing research.
IV. FUZZY ANT PEDESTRIANS MODEL USING ARTIFICIAL POTENTIAL FIELDS
Our model is based on one of the most successful conceptual framework in swarm
intelligence; which is Ant Colony Optimization paradigm. It is inspired by the pheromone trail
laying and following behavior of ants. Such behaviors allow ant colonies to find shortest paths
between their colonies and food sources. Ants communicate indirectly by the mine of chemical
pheromone trails. The more ants visit shorter paths the higher the pheromone density remains for a
longer time. However, the pheromone evaporates with time [1]. Like ants, pedestrians move in a two
dimensional map, and use the same principle of creating trails, but in a virtual way.
Pedestrians are treated as particles moving on artificial potential fields having the form of a
hill in which they're rolling toward their goals while being repulsed from obstacles. The goal point
acts as an attractive force on the pedestrians and the known obstacles act as repulsive ones. The
superposition of all forces has an impact on pedestrians' routes by guiding them toward the goal
point while simultaneously avoiding obstacles.

In this model, the fuzzyfication of pedestrians' utility concerns only spatial perception
(obstacles, preferred direction, amount of pheromone for dynamic floor, etc.). Our goal in this
approach is to have a simple model integrating fuzzy modeling and the Ant Colony paradigm and
artificial potential fields’ concept. This model ensures an easy and effective navigation to pedestrians
by attracting them automatically to their objectives while repulsing them from obstacles in their
ways. Certainly, other cognitive and behavioral factors will be considered in our future work. This
work is scheduled to consider dangerousness of crossing intersections by pedestrians. Perception of
vehicle speed by pedestrians and other psychological factors can be integrated. The software
architecture of the simulator allows this extension. For theoretical foundation, the fuzzy general
utility proposed here, may be interpreted as a fuzzy probability, extending the crisp probability
transition given by Ant Colony paradigm.
V. MEASUREMENT OF PEDESTRIANS EXPOSURE TO ACCIDENT RISK
35
1. Crossing roads: Risks and Skills
We assume that the pedestrians are exposed to risk when they cross the road. This
assumption is almost realistic given the low accident rate out roads [10]. In addition, pedestrians
crossing trajectories can have different shapes. The choice of trajectory is usually a compromise
between the perception of risk by the pedestrian and his ability to cross with the most possible
comfort. On the walkway, the path usually takes the form of a line perpendicular to the road. And out
of it, when passing, pedestrians tend to cut corners and select oblique lines [24]. Regardless of the
path and choose the section of road, pedestrians are trying to adjust their speed according to the
situation they are exposed. The exposure for given entities is usually defined as the product of their
speed and duration of exposure.
Figure 4: Trajectory of pedestrians crossing a road
In a situation of crossing lanes, pedestrians must both perceive the elements provided by the
mobile components of their environment (others pedestrians, motorists, motorcyclists, etc.) in a
spatiotemporal volume. And secondly understand their meanings and be able to project their status in
the near future. However, previous experience and knowledge can act as filters to select relevant
information.

Figure 5: General pedestrians crossing process
This crossing activity can be divided into some elementary steps (Fig. 5) starting from the
selection of the place and time of crossing, after exploring the visual space and selecting relevant
information to help estimating the potential impact time. And finishing by walking activity during
which the pedestrians face the risk of accident. This decomposition process involves many
prospective cognitive and walking processes, where pedestrians must use specific skills.
36
2. Case 1
An exposure may be defined as an event occurring at some location. Many monitoring
instruments can generate continuous readings giving the concentration at a particular location at
almost any instantaneous time. Thus the exposure of organism i located at position (x , y , z ) is given
by:
( ) ( )
0
, , ,
T
i E t = c x y z t dt (11)
Figure 6: Graphical representation of the exposure and dosage received by pedestrians at location
(x , y , z ) and time t with flowc (x , y , z )

In our context, pedestrians are exposed to accident risk in a road segment involved by a flow
of vehicle during crossing time. Thus pedestrians' exposure to accidents risk is defined as:
E t = qv dt (12)
× ×
37
( )
c t
0
V C E = q ×t (13)
Where V q and C t are respectively the vehicles flow and pedestrians crossing time.
We assume that the pedestrian cross a road having a given width D in a rectilinear line, with
a given speed p P n = t ×D
Moreover, the vehicle flow can be expressed in terms of their densities and speeds, which
they reach their maximum value if the density is null, and vanish in the case of maximum density
(see Figure), according to the equation :
= −
max

max
1
r
u u
r

(14)
Therefore the pedestrians' exposure to accidents risk becomes

= × − ×
Exp t
/ max

max
2
max
max
max
1 V
p V V p
V p
V p
t
t
r
r u
r
r u
r u
r
= × × −
(15)
n
max r r
n
Figure 7: Speed variation depending on the
density
r r
max
2
p/V Exp
Figure 8: Variation of the pedestrians accidents
risk indicator according to vehicles density
This exposure follows a parabolic curve. If vehicle density reaches its maximum
value V max r = r , accidents risk is vanished / 0 p V Exp = and pedestrians can cross inter vehicles. Also if
the density of vehicles is zero 0 V r = , pedestrians are not at risk during their crossing, because of the
absence of vehicles. So we have / 0 p V Exp = . The problem arises for intermediate values of the density
of vehicles within a center max 2 V r = r . These changes in the value of exposures to the risk of
pedestrian accidents according to the density of vehicles are illustrated in the following Fig. 2.
Recently, the roads and intersections are being equipped with traffic lights, for pedestrians,
which transition state depends on vehicles states. Pedestrians violate these crossing rules depending
on their gender stereotypes. The most popular violation is passing traffic red light. When someone

managed to cross the gap between the two vehicles, others will speed up and follow him, imposing to
vehicles to yield them the road. This leads us to believe that there is an accident risk for vehicles, this
time imposed by pedestrians.
This exposure takes the same form as in the case of pedestrians:
V /P P V Exp = q ×t (16)
Where P q and V t are respectively the pedestrians flow and necessary time for vehicles to pass
a road section. This exposition also follows a parabolic curve. If the density of pedestrians reaches its
maximum value p max r = r , the accidents risk of is zero for vehicles / 0 V p Exp = , as they must
completely stop and wait for the passage of the pedestrians’ crowd. Whereas if the density of
pedestrians is zero 0 p r = , the vehicles are not at risk during their passage / 0 V p Exp = , they can
accomplish their travel in the absence of pedestrians.
The problem also arises for intermediate values of the pedestrians’ density within a center.
This is the case where vehicles are being forced to brake to avoid a potential accident. This reaction
is propagated to all the following vehicles on the road in question. These changes in the value of
exposures to accidents risk for vehicles as a function of pedestrians' density are patterned the same
way as in the case of pedestrians.
38
3. Case 2
The theory of traffic based on the study of trajectories. They allow determining the relevant
traffic flow microscopic and macroscopic quantities. The trajectory ( ) i x t of vehicle (i ) describes the
evolution of his position during the time t. This evolution is obtained by local inductive measures,
either by loops or mean time, local quantities such as road traffic flowq , average speedu and time
headway i h . The latter is calculated over a cross section x by differentiating the passage time of two
consecutive vehicles’ rear bumpers, which can be expressed by [25]:
( ) ( ) ( ) i i i 1 h x t x t x − = − (17)
Figure 9: Representations of headways variables
Many parameters influence the headway, such as driver behavior, vehicle characteristics, and
flow conditions. Its importance stems from the fact that it could determine the capacity of a road

section. Distance headways measure the distance between the rear bumpers of two consecutive
vehicles at time instant t as follow [25]:
i ( ) i ( ) i 1 ( ) s t x t x t − = − (18)
One can note that both headways variables are correlated. In fact, if i 1 v − denotes the speed of
= = =
= × = (20)
39
the leading vehicle, we can obtain: i i 1 i s v h = −
Furthermore, the flow q is a variable varying with time and location. It is generally defined
by the average number of vehicles (n) that pass a cross-section during a unit of time (T). Hence:
1
1
n n
n
i i
q
T h h
=

(19)
Thus the above formulation of pedestrians' exposure to accidents risk could be written as:
c
V C
t
E q t
h
VI. RESULTS AND DISCUSSION
The simulation tool is developed using Visual C++ IDE on windows operating systems. It
has two components: an editor and a simulator. The first let the user to build its simulation map,
either by putting road objects (road, lane obstacle, alert like uphill, and traffic light) for traffic road
simulation. Or in the case of pedestrian's traffic placing obstacles and generators. In both cases, user
places statistics detectors and can modify simulation settings, before starting the simulation. The
results are represented in real time for vehicles case and using ZedGraph graphical library for
pedestrian's case. At the start of simulation, the simulator manager control simulation by its two sub
mangers for both traffic systems: pedestrians and vehicles.
Figure 10: Simulator architecture
For vehicles simulation, we choose a traffic light scenario (Fig. 11). In this case vehicles
must apply a deceleration to prepare to stop at traffic c lights locations. And resume speed once the
light turns green. We placed a detector'D0' before the traffic light to measure the flow of vehicles
according to their densities. We placed a pedestrians’ generator at the top and a given goal at the
bottom. As shown in figure 12, pedestrians are generated and cross the road section to achieve their
common goal. The fundamental diagram obtained in real time simulation shows that vehicular traffic
passes from one fluid to a congested regime.

Figure 11: Chosen simulation scenario Figure 12: Simulation step after 1s25ms
The width of the road section occupies 6 cells each of which is of size 40cms. Moreover, the
speed is similar to all pedestrians and is 1.4 ms-1. One thus obtains that the crossing time for each
pedestrian is 0.285s. We vary vehicles imposed speed on road cross section from 60km/h to
140km/h. One can note that all obtained diagrams follow theoretical variation of the pedestrians
accidents risk indicator according to vehicles density or flow (Fig 8).
40
Figure 13: pedestrians accidents risk indicator
according to vehicles flow for imposed speed
of 60km/h
of 80km/h
of 100km/h
of 120km/h

Figure 17: pedestrians accidents risk indicator according to vehicles flow for imposed speed of
140km/h
41
VII. CONCLUSION
In this paper, we present a measurement of virtual pedestrians and vehicles mutual accidents
risk indicator. Pedestrians' dynamics are modeled using the basic fuzzy ant model [1], to which we
have integrated artificial potential fields. Relation between density and velocity of pedestrian
movement has so far mainly been analyzed using an empirical approach and fundamental relations
found from the fitting of experimental measurements of the main quantities, while vehicles’
dynamics are modeled using Intelligent Driver Model for longitudinal travel, and the MOBIL model
for lane changing. Simulation results confirm predictions given by the first-order traffic flow theory.
Validation of the simulation model toward the real world data is recommended for further study. In
our future work we plan to update developed simulation tools to complete accident risk indicator for
both pedestrian and vehicles, to estimate the risk of crossing intersections.
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