Agent-based Modeling of Indoor Evacuation Behavior
under Stressful Psychological State
Lu Tan and Hui Lin
Institute of Space and Earth Informaiton Science, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China
Keywords: Agent-based Modelling, Building Evacuation, Social Force, Stress, Emotional Contagion.
Abstract: This paper presents an agent-based model focusing on occupant’s locomotion under stress, so as to study the
impact of psychic stress on evacuation efficiency. In our model, the occupant’s stress is determined by
factors including the moving velocity and distance to the exit, the psychological feature of stress resistance
capability, and emotional contagion. The occupant’s evacuation behaviour in a stressful psychological state
is attained as an emergent function of stress-related desire intensity and interaction force based on the
Helbing social force model. Through a series of simulations using the proposed model, it is concluded that
the increase in the occupants’ stress level does reduce the evacuation efficiency; the emotional contagion
performs either a panic effect or a calm-down effect which affects the evacuation efficiency negatively or
positively; intensive emotional contagion will significantly affect the occupant’s stress level and lead to
remarkable variation in evacuation time; population structure has an influence on the evacuation efficiency
in respect to the occupant’s capability of stress resistance. The conclusions indicate that proper control of
psychic stress during emergency evacuation is critical for improving evacuation efficiency.
1 INTRODUCTION
When an emergency occurs in a building, the
occupants have to evacuate within a very limited time,
which results in a stressful psychological state (Wood,
1979). Such stress will remarkably affect the
occupants’ behaviours and movements. For example,
occupants usually increase the speed of their actions
and become less patient due to the time pressure.
Also, the stressful psychological state would affect
accurate information processing and decision making
for quick exiting (Proulx, 1993; Pelechano and
Malkawi, 2008). These impacts are supposed to have
influence on evacuation efficiency. Therefore, the
goal of this paper is to present an agent-based model
focusing on occupant’s locomotion when being in a
stressful state, so as to study the impact of psychic
stress on the evacuation efficiency.
2 RELATED WORKS
There has been much work done for computational
simulation of evacuation behaviour using different
method. Earlier researches mainly focus on the
physical aspect of evacuation behaviour, such as the
fluid-dynamic model (Hughes, 2002), cellular
automata (CA) (Kirchner and Schadschneider, 2002,
Nishinari et al., 2003), and the social force model
(Helbing et al., 2000, Helbing and Molnar, 1995).
These models are prominent in simulating the
individual’s physical movement, but consider very
simple, if any, psychological factors.
As the necessity of considering psychological
factors has been highlighted (Zheng et al., 2009;
Kobes et al., 2010), more efforts are put into
incorporate mental state and emotional interaction
(Papelis et al., 2011; Zoumpoulaki et al., 2010).
Meanwhile, agent-based models are getting famous
for simulating heterogeneous population with
different social roles and psychological features
(Pelechano, 2005; Pan, 2006; Wu and Lin, 2012).
However, these researches mainly focus on the
impact on decision making such as route choice
(Ozel, 2001), while the impact on locomotion seems
to be neglected. Besides, the modelling of stress
growing and the effect of emotional contagion is still
inadequate in current simulation of evacuation
behaviour, although several works have been carried
out in the field of psychology (Proulx, 1993; Bosse
et al., 2009).
166
Tan L. and Lin H..
Agent-based Modeling of Indoor Evacuation Behavior under Stressful Psychological State.
DOI: 10.5220/0004190901660171
In Proceedings of the 5th International Conference on Agents and Artificial Intelligence (ICAART-2013), pages 166-171
ISBN: 978-989-8565-38-9
Copyright
c
2013 SCITEPRESS (Science and Technology Publications, Lda.)
In this paper, we focus on the stress impact on
occupant’s locomotion during building emergency
evacuation. The modelling of psychic stress is
incorporated with the concept of social force based
on the Helbing model (Helbing et al., 2000) so as to
obtain an improved simulation of indoor evacuation.
3 AGENT-BASED MODELLING
3.1 Modelling Framework
The main motivation of our work is that the stressful
psychological state caused by an emergency will
impact occupant’s moving behaviour and evacuation
efficiency. Figure 1 shows the framework of the
proposed model. The stress level, which is raised by
the emergency situation, affects the intensity of
movement desire and interaction force with others.
The movement in turn impacts the occupant’s stress
level according to the moving efficiency and the
occupant’s capability of stress resistance. In our
model, the occupant’s movement is treated as a set
of basic movement rules based on the theory of
social force. The stress level is modelled as an
emergent function of self-generated stress and the
influence by emotional contagion.
Figure 1: Interaction of occupant’s movement and psychic
stress.
3.2 Basic Movement Rules
In the proposed agent-based model, the geometric
space is represented as finer grids (Song et al.,
2006). The grid size is approximately 16.7cm ×
16.7cm. Each occupant is simulated as an agent
which occupies 3 × 3 grids. The basic movement
rules of agent are developed based on social force
(Helbing et al., 2000). At each time step, the agent
selects one of the eight possible directions to move
into with different transition probabilities (Figure 2).
Figure 2: Possible transitions for an agent and associated
probability P
i,j
.
The transition probability P
,
is determined by
the agent’s desired movement, interaction with the
surrounding agents and constructions, as well as the
inertia force. So it is given by:
P
,
ND
,
∑
F
,
I
,
δ
,
(1)
Here D
,
is the intensity of the agent’s movement
desire in direction i, j, which reflects the influence
by self-adaptive force. F
,
is the influence of the
interaction force, which might be either negative or
positive. I
,
is the enhancement on the agent’s
previous movement direction as a result of inertia.
δ
,
denotes the availability of direction i, j. The
direction is available (δ
,
1) if the intensity of
desired movement overcomes the interaction force
and the agent occupies enough space after the
movement, saying more than six grids. Otherwise,
the direction is unavailable ( δ
,
0). N is the
normalization factor to ensure
∑
P
,,
1.
As for indoor evacuation, the agent’s desired
movement should be towards the exit. In this model,
since there are eight potential moving directions, the
desired movement is projected to the three closest
directions, as shown in Formula (2) and Figure 3(a).
D
,
D cos
θ
,
(2)
Here D
,
is the projection of desired movement D
in direction i, j. θ
,
is the angle between D
,
and D.
The interaction force, which includes repulsion
and friction, is simulated through the overlapping
grids among agents and between the agents and the
constructions. The impact of interaction force on the
transition possibility is shown in Figure 3(b)
corresponding to formula (3).
F
,
F cos
γ
μFsin
γ
(3)
Here F
,
is the change of transition probability in
direction i, j resulting from interaction force. F is
the average interaction force of the overlapping
agents. Parameter μ is the friction coefficient. γ is
the angle between F and F
,
.
Figure 3: (a) Projection of the desired movement. (b)
Interaction force generated by overlapped grid.
F
1, 1
F
0, 1
F
1, 0
F
1, -1
F
-1, 1
F
-1, 0
F
-1, -1
F
0, -1
F
Ƴ
1,0
D
D
1, 0
D
0, -1
D
1, -1
Ɵ
1,0
(a) (b)
Agent-basedModelingofIndoorEvacuationBehaviorunderStressfulPsychologicalState
167
3.3 Coping with Stress
According to the previous researches, it is important
to model the following observations to simulate
human behaviour in stressful situation:
(1) The stress level depends on the occupant’s
perception of current situation (Proulx, 1993).
Moving with higher velocity and getting close to the
exit indicate a safer situation and reduce the stress.
(2) The increase in stress level is related to
individual’s capability of stress resistance. People
who differ in personality features might have
different psychological reaction in case of an
emergency evacuation. Those who have not been
properly trained are more likely to feel stressed due
to time pressure (McGrath, 1970, Pelechano, 2005).
(3) The social function of emotional contagion
will affect occupant’s stress level (Bosse et al., 2009,
Hoogendoorn et al., 2010, Tsai et al., 2011). In
addition to the physical interaction, people also
interact emotionally. The expressions and receptions
of emotional state within the crowd might help
occupants to calm down or result in an even more
stressful psychological state.
Therefore, the self-generated stress level is
modelled as a function of the occupant’s moving
speed and the distance to the exit
S
t
k
expW
v
t
W
d
d
t
/d
(4)
Here S
t
is the self-generated stress level of
agent i at time t. v
t
is the agent’s current average
moving speed in desired direction. d
t
is the
agent’s distance to the exit and d
is the
maximum distance to the exit. W
and W
are
respectively the weight of influence by the moving
speed and the distance to the exit. k
is the stress
increase coefficient which depends on the agent’s
psychological feature of stress resistance. Higher k
means the agent is more vulnerable to emergency
and will be more stressed under the same situation.
Meanwhile, the stress state propagates among the
crowd through emotional contagion. According to
(Bosse et al., 2009), emotional contagion is related
to five critical aspects, namely the level of sender’s
emotion, the level of receiver’s emotion, sender’s
emotion expression, receiver’s emotion openness,
and the strength of the channel from sender to
receiver. Therefore, the weighed combined stress
level an agent received from the others is
S
∗
t
∑
W
S
∈
t
(5)
Where W
δ
α
/
∑
δ
α
∈
is the weight of
influence by agent j.δ
is the expressiveness of agent
j and α
is the channel strength from agent j to i.
Considering the agent’s openness ε
and its self-
generated stress S
t
, the stress level of agent i at
each time step is given by
S
t
S
t
S
∗
t
S
t
∑
ε
δ
α
∈
(6)
As a reaction to the psychic stress, occupants
tend to have a stronger desire to move towards the
exit, thus enhancing the interaction among
occupants. In particular, the occupant under stressful
state will push hard when blocked by others instead
of waiting in queue because of the strong desire to
move on, which will lead to inefficient outflow. This
further aggregates the blocking, and eventually
triggers even more stress and enhance the movement
desire and interaction force. Therefore, the stress-
related desire intensity and interaction force are
defined as
D
t
D
expS
t
/k
(7)
F
t
F
expS
t
/k
(8)
Here D
t
is the intensity of desired movement
of agent i at time t . D
is the initial intensity of
desired movement, and k
is the increase coefficient
of desire intensity against the stress level. F
t
is the
interaction force of agent i with other agents and
constructions at time t. F
is the initial interaction
force, and k
is the increase coefficient of
interaction force against the stress level.
4 SIMULATION RESULTS
AND ANALYSIS
Here we study a simple but quite common situation,
namely the evacuation of 200 occupants from a large
room with one exit such as a lecture hall or dance
hall. The room size is 15m × 15m and the width of
the exit door is 1m. Parameters are set as different
values to study their impacts on evacuation time.
4.1 Impact of Interaction Force
and Desire Intensity
In our model, the agent’s movement is a direct result
of movement desire and interaction force.
Movement desire is a positive factor that leads the
agent towards the exit, while the interaction force
ICAART2013-InternationalConferenceonAgentsandArtificialIntelligence
168
including repulsion, friction and extrusion are
negative factors opposing the movement. Figure 4 is
the curve of evacuation time against the division
between the interaction force and desire intensity. It
is observed that the evacuation time increases
evidently as the value of F/D is getting larger. In
particular, the evacuation time is shorter when F/D is
less than 1.6. Then it increases dramatically when
F/D ranges from around 1.6 to 2.6, and fluctuates
slightly when F/D reaches 4.4. This indicates that
evacuation rate is reduced when the occupants are
getting crowded and the interaction force becomes
dominant. When it is extremely overcrowded, the
evacuation time reaches a maximum value and does
not change a lot as the interaction force increases.
According to this, in the following simulations the
values of D
, F
, k
, k
are set to 0.1, 0.15, 0.5,
0.25 to keep the value of F/D within a reasonable
range so as to study the impact of stress level on
evacuation time.
Figure 4: Curve of evacuation time against F/D.
4.2 Impact of Stress Level
In order to observe the impact of stress level on
evacuation efficiency, we exclude the influence from
emotional contagion among occupants by setting the
parameters of the emotion openness ε , emotion
expressiveness δ, and the channel strength α to zero.
Figure 5 shows the change of crowd’s average
stress level plotted against evacuation time with
different stress increase coefficient k
. It is shown
that large k
value results in higher average stress
level. It is also observed that at the beginning of
evacuation the stress level is rather high, and it is
more evident when k
is large. The reason for this is
that stress level is an emergent function of moving
velocity and distance to the exit. At the beginning,
far distance from the exit causes most of the stress.
As the agents are getting closer to the exit, velocity
becomes the dominant factor that impacts stress
level. When it becomes crowded around the exit, the
stress level increases due to inefficient move.
The resulting variation of stress level is supposed
to have an influence on evacuation efficiency.
Figure 6 shows the change of evacuation time
against stress increase coefficient k
. In general,
higher k
value reduces the evacuation rate and
results in longer evacuation time. As we mentioned,
the growth of stress will lead to an increase in both
desire intensity and interaction force, and it is the
division between desire intensity and interaction
force that critically affects the evacuation efficiency.
If the k
value is large, the stress level will be more
likely to reach the point where the interaction force
becomes dominant and evacuation efficiency is
reduced because of inefficient outflow.
Figure 5: Curve of the crowd’s average stress against
stress increase coefficient.
Figure 6: Curve of evacuation time against stress increase
coefficient.
4.3 Impact of Emotional Contagion
In order to study the impact of emotional contagion,
two types of agents were designed. Agent A has
stronger stress resistance capability ( k
0.1),
while Agent B has inadequate stress resistance
capability ( k
0.5). Two typical scenarios are
simulated (Table 1). In scenario 1, Agent A acts as
receiver fully opened to the emotional stress
expressed by the sender Agent B. In scenario 2, the
roles of Agent A and Agent B are reversed.
Figure 7 shows the crowd’s stress level at a
particular time. The number of Agent A and Agent
B are the same and the scope of emotional contagion
is one meter. Comparing with the simulation without
emotional contagion, overall stress level is higher in
Scenario 1 because of the stressful emotion sent out
by Agent B, while it is much lower in Scenario 2
because of the calm-down effect by Agent A.
400
450
500
550
600
650
1.0 2.0 3.0 4.0 5.0
Average time steps
F/D
μ
=0.2I=0.2
F/D=1.6
F/D=2.6
F/D=4.4
0
0.2
0.4
0.6
0.8
0 100 200 300 400
Average stess level
Time ticks
k
s
= 0.1
k
s
= 0.4
k
s
= 0.7
k
s
= 1.0
D
0
=0.10 k
D
=0.50
F
0
=0.15 k
F
=0.25
ε = δ = α =0
400
450
500
550
600
650
0.00.20.40.60.81.0
Average time steps
k
s
values
D
0
=0.10 k
D
=0.50
F
0
=0.15 k
F
=0.25
ε = δ = α =0
Agent-basedModelingofIndoorEvacuationBehaviorunderStressfulPsychologicalState
169
The resulting variation of stress level apparently
has an influence on evacuation time (Figure 8). It is
shown that evacuation time is reduced evidently in
Scenario 2. Meanwhile, the gap becomes remarkably
as the channel is strengthened, which indicates
stronger emotional contagion within the crowd and
more impact on the overall stress level.
Table 1: Parameters setting of the two scenarios.
Scenario 1 Scenario 2
Agent A Agent B Agent A Agent B
k
0.1 k
0.5 k
0.1 k
0.5
ε
1.0 ε
0.0 ε
0.0 ε
1.0
δ
0.0 δ
1.0 δ
1.0 δ
0.0
Figure 7: Stress level at the 100th time tick: (a) without
emotional contagion, (b) Scenario 1 and (c) Scenario 2.
Figure 8: Evacuation time under Scenario 1 and Scenario
2 with different channel strength.
Figure 9 is the curve of the evacuation time
against the scope of emotional contagion. It is
observed that the evacuation time is further
increased in Scenario 1 and reduced in Scenario 2 as
the scope of emotional contagion is enlarged. The
reason is that with wider emotional contagion scope,
one would have emotional interaction with more
agents. Therefore, the emotional influence by the
surrounding population is enhanced, which leads to
stronger panic effect in Scenario 1 and calm-down
effect in Scenario 2.
Figure 10 shows the change of evacuation time
corresponding to different population structure,
where the scope of emotional contagion is set as one
meter. It is noted that the population structure has an
evident influence on evacuation time in respect to
occupant’s stress resistant capability. In fact, the
overall stress level rises up with higher percentage
of Agent B which has more rapid stress increase
rate, or lower percentage of Agent A which has
slower stress increase rate. This results in increasing
evacuation time in Fig. 10(a) and decreasing
evacuation time in Fig. 10(b), even without
emotional contagion ( α
α
0). Meanwhile,
when emotional contagion is taken into account, the
increasing number of emotional senders leads to
additional panic effect in Scenario 1 and calm-down
effect in Scenario 2. Therefore, comparing with the
simulation without emotional contagion, the
evacuation time generally increases more rapidly as
the percentage of Agent B increases in Scenario 1
and decreases more rapidly as the percentage of
Agent A increases in Scenario 2.
Figure 9: Impact of the emotional contagion scope on the
evacuation time.
Figure 10: Impact of the population structure on the
evacuation time.
5 CONCLUSIONS
In this work we introduced the stress impact in the
modelling of occupants’ locomotion i building
evacuation. From the results of the simulations using
the proposed model, the following conclusions can
be drawn: (1) The increase in occupant’s stress level
during emergency evacuation does lead to
overcrowding and reduce the evacuation efficiency.
(2) Emotional contagion critically affects the
crowd’s stress level and the evacuation time. The
contagion of higher stress level might aggravate the
crowd’s overall stress and reduce evacuation
efficiency, while the contagion of lower stress level
performs a calm-down effect and improves
evacuation efficiency. (3) The variation of
evacuation time is related to the intensity of
400
420
440
460
480
500
520
540
560
0.10.20.30.40.50.60.70.80.91.0
Average time steps
α values
Scenario 1
εA=1, δA=0
εB=0, δB=1
Scenario 2
εA=0, δA=1
εB=1, δB=0
ICAART2013-InternationalConferenceonAgentsandArtificialIntelligence
170
emotional contagion. If the emotional contagion
channel is weak and the scope is small, the influence
of emotional contagion on occupants’ stress level is
limited and the evacuation time will not be
significantly affected. (4) The evacuation efficiency
is affected by population structure in terms of
occupant’s capability of stress resistance. With the
increase in the number of occupants who are
vulnerable to emergent situation, the crowd’s overall
stress level rises up more rapidly and the evacuation
efficiency will be reduced. Therefore, it is essential
to control the crowd’s stress level for an efficient
building evacuation.
Although the model is developed on the basis of
some critical observations of human behaviour in
emergency situation, a comprehensive validation is
still in need. Therefore, we are now working towards
developing more complex simulation scenarios so as
to further evaluate the proposed model. It is
expected that such a model incorporating psychic
stress will be able to reflect more reliable indoor
evacuation in emergent situation.
ACKNOWLEDGEMENTS
The work described in this paper is supported by
National Natural Science Foundation of China (grant
no. 41171146 and 41101370).
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