Simulation of the Emotion Dynamics in a Group of Agents in an Evacuation Situation.
Conference Proceeding: From Grid Environment to Geographic Vector Agents, Modeling with the GAMA simulation platformConference of the International Cartographic Association; 01/2011
Simulation of the emotion dynamics in a group
of agents in an evacuation situation
Le Van Minh1,2, Carole Adam3, Richard Canal1,4, Benoit Gaudou5,6,
Ho Tuong Vinh1,4, Patrick Taillandier6
1Institut de la Francophonie pour l’Informatique (IFI), Hanoi, Vietnam
2Danang University (UDN), Danang, Vietnam
3RMIT University, Melbourne, Australia
4UMI 209 UMMISCO, Institut de Recherche pour le D´ eveloppement (IRD), Bondy,
5Universit´ e de Toulouse, Toulouse, France
6Institut de Recherche en Informatique de Toulouse (IRIT), UMR CNRS 5505,
email@example.com, firstname.lastname@example.org, email@example.com,
Abstract. Nowadays, more and more emergency evacuation simulations
are used to evaluate the safety level of a building during an emergency
evacuation after an accident. The heart of this kind of simulations is
the simulation of human behavior because simulation results depend for
a big part on how this behavior is simulated. However, human behav-
iors in a real emergency situation are determined by a lot of cognitive
mechanisms. In order to make the simulation more realistic, plenty of fac-
tors (e.g. innate characteristics, perception of the environment, internal
rules, personality and even emotions) that affect human behaviors must
be taken into account. This paper focuses on the influence of emotions,
and more precisely on the influence of their dynamics and propagation
from an agent to another. The main contribution of this work is the de-
velopment of a model of emotions taking into account their dynamics and
their propagation and its integration in an evacuation simulation. The
first results of the simulation show the benefits of considering emotion
Keywords: emotion, emotional agent, emotion propagation, emergency
Nowadays, the computing power available on any personal computer allows one
to create simulations including thousands of agents, as for example in simula-
tions of the traffic in a city, or simulations of the emergency evacuation from a
building... In order to make the simulation as realistic as possible, each agent
in the simulation is designed to operate autonomously (which means that the
agent is not controlled by any central agent and he makes his decisions using his
own cognitive resources) and to interact with others agents.
Many researches show that adding emotions (e.g. joy, fear, anger, hope...)
into these agents provides huge benefits because emotions improve the quality
of agents’ behaviors and then the quality of the whole simulation . Indeed
emotions play a very important role in human beings’ life by influencing the
decision-making process, the reasoning and the interaction with others [6,8].
Therefore, we should not ignore emotions when creating a virtual human simu-
The recent studies in the domain of artificial agents allow one to give each
agent ways to express pertinent emotions  and to reason about not only his
own emotions but also about others agents’ ones . Critical issues remain con-
cerning the “transmission” of emotions among the agents in the simulation, the
emergence of a common emotion in the group of agents and the effect of this
emotion on each individual.
We thus propose in this paper a model of emotions taking into account both
the emotions dynamics (when they appear and how their intensity level evolves
over time) and the emotions propagation (how they are “sent” and “received”
and how a received emotion influences the receiver). In this paper we focus
on fear (with various intensity levels) and test our model by implementing it
into agents used in a simulation of emergency evacuation in a burning shopping
This paper is organized as follows. Section 2 presents a brief state of the art
on emotions. In Section 3, we present our model of emotions, emotions dynamics
and propagation. Furthermore, in Section 4, we present the implementation of
our model and discuss in Section 5 the first results of our simulation.
2State of the art
2.1Simulation of pedestrian evacuation
Plenty of simulations of emergency evacuation have been developed [18,20,19].
Most of them concentrate on human behaviors, and more particularly on their
movement, in an emergency situation. The typical model of this kind of simu-
lations is the pedestrian evacuation model developed by Crooks on the RepastJ
platform 7. In this simulation, agents representing human beings leave their
office when the fire appears. This simulation is focused on the human movement
and the role of the obstacles on the passage to the door: e.g. the wall of the
room, the table...
Since the human behaviors in the real world are much more complex than
those of the agents in the simulation (e.g. the planned tasks of a person are
often updated in case of a stressful situation), many researchers have proposed
to introduce additional factors to make the agents’ behavior more human-like.
readers candownload themodelon the website
In particular, Musse and Thalmann described a hierarchical model of virtual
crowds for real-time simulations . In their simulation, the human behaviors
executed by simulated agents are classified in three types: innate or scripted
behaviors, behaviors defined by rules and behaviors controlled by external fac-
tors. Furthermore, Hollmann et al.  improved the human behaviors model in
urgent situations by adding the two following attributes: available time and es-
timated required time. When these two variables reach a particular threshold,
the agent changes his behavior (e.g. he accelerates in order to get to the goal
location, changes the goal location or even ignores some of the planned tasks to
concentrate on the ultimate goal).
As mentioned previously, emotions play an important role in human behav-
iors in particular in emergency situations. We choose to integrate emotions in
evacuation simulations. Therefore the first question is how to define and describe
2.2Theories of Emotions
In the 19th century, James and Lange proposed a physiological theory of emotion
. Their theory indicates that the human autonomous nervous system creates
physiological events like heart rate and respiration in response to various human
experiences. The emotions are the sentiments that appear as results of this phys-
iological change. According to this theory, humans can express their emotions
via their physiological states and can guess the emotions of others based on this
kind of expression.
While this physiological theory advocates that emotions result from physi-
ological factors, many scientists defend the idea that cognitive factors are very
important in the process of emotion triggering. They propose various so called
cognitive theories. In the domain of cognitive theories of emotions, Arnold 
and Lazarus  argue that human beings always evaluate what they perceive
and the emotion triggered by this perception is thus the result of an appraisal
process. They proposed the theory called cognitive appraisal theory. In parallel
to these purely psychological researches, Ortony, Clore and Collins  define a
typology of emotions (known as the OCC typology) depending on the type of
stimulus appraised and various appraisal variables. They distinguish three kinds
of stimuli: events, actions of agents, aspects of objects. The 20 emotions defined
are deeply related to mental attitudes, this eases their integration into artificial
In , Cabanac proposed a four-dimension model of consciousness. In this
model, every state of consciousness is described in 4 dimensions: the qualita-
tive dimension, the intensive dimension, the hedonic dimension and the time
dimension. He then proposed a definition of emotions based on his model of
consciousness. “Emotion is any mental experience with high intensity and high
In , Bosse et al. proposed a model of emotion contagion. In their model, the
propagation of emotions depends on six factors: the current level of the sender’s
emotion, the current level of the receiver’s emotion, the extent to which the
sender expresses the emotion, the receiver’s openness or sensitivity for emotions,
the strength of the channel from the sender to the receiver and the tendency to
adapt emotions upward or downward .
2.3 Existing models of emotional agent
In , Parunak et al. propose a Model of Emotions for Situated Agents called
DETT. “DETT (Disposition, Emotion, Trigger, Tendency) is an environmentally
mediated model of emotion that captures the essential features of the widely-
used OCC (Ortony, Clore, Collins) model of emotion” . Contrarily to most
agents architectures using the OCC typology, in DETT emotions are triggered
by the perception module (rather than being the result of an internal reasoning).
In , Zoumpoulaki et al. propose a multi-agent framework for emergency
evacuation. The multi-agent model presented in the paper is a combination of
the BDI (Belief, Desire and Intention) architecture  for the agent’s reasoning
process, the OCEAN (Openness, Conscientiousness, Extraversion, Agreeableness
and Neuroticism) as model of personality and the OCC model for emotions. This
kind of framework can be used to simulate emotions in controllable situations,
but in the case of an extremely serious emergency, when the situation becomes
truly chaotic, we argue that people do not have enough time to make reasoned
decisions but rather make decisions based on simple heuristics such as emotions.
In the sequel we consider situations of extreme emergency; that is why we have
only simple agents feeling extreme emotions (like fear). Their behavior is mainly
directed by the emotion they are feeling and the emotions received from other
3Proposed model of emotional agent
3.1A two-dimensional model of emotion in the emergency
As described in the previous section, we consider an emotion as a particular
mental state which is triggered by the individual appraisal of various stimuli.
Stimuli in our case will be either events of the environment, or behaviors of the
other agents, both being perceived by the agent. The subject appraises these
stimuli according to his knowledge and his current emotions.
From the psychological four-dimensional model proposed by Cabanac 
and the multi-agent framework integrating personality and emotion proposed
by Zoumpoulaki et al. , it appears that the more emotions are simulated,
the more realistic the simulation becomes but the more complicated relevant
results will be extracted from the simulation, which leads to difficulties in the
evaluation phase when we evaluate the role of emotions and of their propagation
in the emergency situation. In order to emphasize the effect of emotions and
of their transmission, we propose a simple model of emotion -a two-dimension
model of emotions- which allows us to have simulation results that remain sim-
ple to analyze. Our model is the reduction of Cabanac’s four-dimensional model
Fig.1. Decay of the emotion
 by ignoring the qualitative dimension (Axis x) and the hedonic dimension
(Axis z). We consider that the emotion triggered in every emergency evacuation
is the fear. We concentrate on this emotion and the two dimensions represent its
intensity and the duration of the emotion. Thus, the emotional model proposed
is a two-dimensional model with 2 axes: the emotion intensity (Axis y) and the
emotion duration (Axis t).
“Axis y” represents the intensity of the emotion. In our proposition, the
value of y(t) is continuous and always positive. If y(t) < ? (a very small thresh-
old), the emotion disappears. The initial value of y(t) (i.e. when the emotion
is triggered) is calculated by the appraising process. We suppose that an agent
has the capability to calm down over time and thus reduce the intensity of
his emotion. Then the value of y(t) decreases gradually following the formula
y(t) = y(t − 1)/α,(α > 1) (1) (with α is the decay coefficient).
“Axis t” represents the duration of the emotion. Due to the decay equation
(1), the intensity of the emotion will follow the evolution presented in Figure 1,
in the ideal case where there is no other stimulus.
3.2 Architecture of the emotional agent
We present in Figure 2 the architecture of our emotional agent.
Simplifications. In the sequel, we consider the three following simplifications.
They allow us to simplify conceptually and computationally our model and thus
improve the simulation performance and make the simulation more effective.
Simplification 1. The current emotion of the agent does not have any influence
on the process of perception. The current emotion is taken into account only in
the process of evaluation of the perception outputs (emotional appraisal) that
Simplification 2. There is only one emotion in the agent at one moment. This
also means that only one emotion can be taken into account in the appraisal
process and that this process can create only one emotion.
Fig.2. Model of the emotional agent
Simplification 3. The agent acts immediately once the emotion appears. The
agent does not update his knowledge base before performing an action.
Description of the architecture. We describe here the main process of the
1. Perception of the stimuli (Perception component in the Figure 2): first,
the agent perceives the stimulus (coming from Arrow 1). In this work, the type
of emotion simulated is the fear. Therefore, only the stimuli which contribute
to fear are perceived, the rest is ignored. According to the source of the stimuli,
the agent classifies the stimulus into 1 of 2 possible types.
a. Indirect stimulus: This type of stimuli is caused by the environment. They
do not trigger directly an emotion. They can only affect the intensity of existing
emotions. For example: a child who is alone in the middle of the graveyard, under
the heavy rain; if this child is scared, any additional noise will increase the level
of his fear.
b. Direct stimulus: This type of stimuli is caused by events of the environment
or by the behavior of other agents. Each stimulus provokes one type of emotion
with a specific intensity.
2. Appraisal of the stimuli (Evaluation component in Figure 2): The
results of the perception (Arrow 2) are appraised according to the knowledge of
the agent (Arrow 3) and his current emotion (Arrow 4). There are 2 types of
stimuli so there are also 2 types of evaluation. In the end of this process, the
agent creates an emotion.
a. Evaluation of the indirect stimuli: the agent searches in his knowledge
base for rules relating to the indirect stimuli perceived. If some rules are found,
the agent acquires the global variable (γi). As the stimulus can have either a
positive effect or a negative effect on the agent, this global variable (γi) can
Fig.3. Algorithm to calculate the intensity of the fear
have a positive value or a negative value. With one stimulus, γican be different
from an agent to another one according to his knowledge base: an agent can give
a positive value to γi, whereas another agent can give it a negative value. For
example, consider a child in a dark room; the darkness is the indirect stimulus;
if this child is normal, this stimulus is negative; if this child is blinded; darkness
does not scare him; so this stimulus will not be perceived or will have a neutral
value. After having evaluated all the indirect stimuli, the agent has a set of γi
that he aggregates with: γ =?
b. Evaluation of the direct stimuli: the agent finds in his knowledge base the
rules matching with the direct stimuli perceived. According to rules found, the
agent acquires an additional intensity value (∆y).
c. Computation of the intensity: the intensity of the temporary emotion is
computed by the algorithm presented in the Figure 3.
In the algorithm, “y” represents the intensity of the fear. When “y” reaches
a determined threshold, the agent will change his behavior. The maximal value
of “y” is “ymax” which is defined as an input parameter of the simulation that
limits an overgrowing emotion intensity. In our model, we consider that agents
perceive the other agents’ emotion depending on their sensitivity factor α. This
sensitivity coefficient is a positive constant and varies from an agent to another
one. According to this coefficient, an agent can perceive emotion more easily
3. Computation of behaviors (Behaviors component in Figure 2): once
the new emotion has been created, the agent reacts immediately to the stimulus
from the environment. Initially, the agent finds in his knowledge base the rules
related to the emotion and then executes the corresponding behavior. The agent
executes two kinds of action in one step: he reduces the intensity according to the
formula (1) and reacts to the stimulus. When the agent reacts to the stimulus,
his behavior affects not only the environment but also the other agents. The
other agents perceive thus these behaviors and interpret them as stimuli.
Fig.4. Emotional propagation model
3.3Model of emotion propagation
According to the agent model proposed, an agent appraises the stimuli caused
by the actions of other agents in the process of evaluation. When an agent reacts
to the environment, he expresses his emotion via his behavior. Then, an agent
can recognize the emotion of the other ones according to the behaviors that he
perceives. The emotion of an agent can thus spread over a group of agents. Figure
4 describes the way an agent gives his emotion to others via his behaviors.
4 Implementation of the emotional agent
In this section we present the situation that we want to simulate, the details of
the agents involved in this simulation and how we can improve their behavior
by introducing emotions. The model is implemented on the GAMA platform [2,
4.1Description of the application case: pedestrian evacuation in a
burning shopping center
The simulation aims at representing the scenario described below. In a shopping
center, while people are shopping, the fire appears. Figure 5 presents the overview
of the simulation. The people who see the fire may be scared. They may scream
or change their movement speed. Other agents who perceive these actions may
feel their fear. With this simulation we aim at highlighting the important role of
emotions (in this case, the fear) in an emergency evacuation, and in particular
the fact that the casualty rate can highly be increased, in the case of a panicked
Fig.5. Overview of the simulation
4.2Description of the agents
In our simulation, we use two kinds of agent: agents representing human beings
and agents representing fire. In the sequel we describe in details the implemen-
tation of both kinds of agent.
Size: agent size
Perception range: radius within
which an agent can perceive a stimulus GoToTarget(speed:float):
Propagation range: radius within
which an agent can propagate
information to others
Emotion type: type of emotion (in
this model, emotion type is ”fear”)
Emotion intensity: intensity of
Sensitivity ability (α): the sensitivity PropagateInformation():
of an agent. The greater this attribute
is, the more sensible the agent is
Decay ability: the capability to reduce Reflex(): the agent evaluates the
the intensity of emotion. The greater
this coefficient is, the faster the
Global variable: the global effect of
environment on each agent. This
coefficient is set randomly at the
beginning of the simulation
the agent moves randomly
the agent goes to his target
The agent avoids the obstacles
and the other agents
the agent perceives stimuli within
his range of perception
the agent propagates information
within his range of propagation
stimulus in order to choose his
the agent changes his color
Fig.6. Levels of the fear
Fig.7. List of behaviors
Size: size of one piece of fire
Duration: duration of the fire
Propagation range: range within
which the fire can spread at each step
Propagate(): the agent propagates
himself within the range of propagation
4.3Description of the emotion (the fear)
As mentioned above, the emotion that influences the most the behavior of agents
in an emergency situation is the fear. We choose thus to limit the emotions
involved in the simulation to the fear. In our simulation, we distinguish four
levels of fear (depending on the intensity level of the emotion): normal, stress,
fear and panic. Figure 6 presents these levels.
At each level of fear, the agent may execute different behaviors or a behavior
with different manners (e.g. wander with a normal speed when the agent is in
the state normal or wander with a high speed when he is panicked). In our model
we proposed seven behaviors described in Figure 7.
1. Display in color: the agent uses this behavior to show graphically his
current fear level. At each level of fear the agent uses the method Change-
Color(color:Color) to show a particular color (white, light blue, blue, dark blue).
2. Avoid obstacle: this is a fundamental behavior. At every step an agent
moves, he invokes the method AvoidObstacle() to avoid collisions with obstacles
(wall, other agents...)
3. Perceive the stimuli: this is also a fundamental behavior: this method is
invoked at each step. The agent can perceive the fire or get emotional information
from the behavior of other agents.
4. Wander with normal speed: this behavior shows that the agent is in a non-
stressful state. The agent wanders with a normal speed if he is not scared. In
this case, the agent invokes the method Wander(speed : float) with the normal
value of speed.
5. Quit the shopping center with normal speed: this behavior shows that the
agent is aware of a fire. The agent who is scared with the average intensity keeps
his reasoning capabilities: he can thus find a way to escape. The agent invokes
the method GoToTarget(speed : float) with the normal value of speed.
6. Quit the shopping center with great speed: this behavior is similar to the
behavior 5 but in this case, the agent is truly afraid: the value of the speed is
7. Wander with great speed: similar to the behavior 4 but in this case the
speed is higher. This behavior illustrates the case when the fear is so intense that
the agent becomes panicked, loses awareness and thus cannot control himself.
8. Propagate the information: As soon as the agent feels any kind of fear
(stress, fear or panic), he invokes the method PropagateInformation() to spread
this emotional information to other agents.
In this section, we present the tests led on the emergency evacuation model. In
order to evaluate the role of the emotional factor in the emergency evacuation, we
propose two measures that we use to monitor our model: Emotional rate (ER)
is the percentage of people who are in a fear state in a unit of time; Survivor
rate (SR) is the percentage of people who succeed to escape the building. Our
experimentation is separated into three models: a model without emotion, a
model with emotion but without propagation and a model with emotion and
propagation. In each test case, the parameters of the emotional factors are set
with the average value so that the simulation is more like the real event.
5.1Model without emotion
In this test case, we set the values of the propagation range and of the per-
ception range to zero, which means that the human agent cannot perceive the
emotion of other agents. In this case, the human agents are not aware of the
danger. And when the fire propagates in a wide area, these agents do not change
their behavior to survive. In consequence, the survivor rate (SR) is very low.
Fig.8. Evolution of the emotion rate and of the number of survivors
5.2 Model with emotion but without propagation
In this test case, the value of the propagation range is zero and the percep-
tion range is set randomly in its definition interval. In this case, the human
agents can themselves perceive the fire which can trigger fear but cannot propa-
gate their emotion to others. Only the people who see the fire may become afraid
and then flee the danger to save their life. The others who do not see the fire
are not scared. This is why the emotional rate (ER) is higher than in the first
test case but still low. With the people who do not realize the danger, it may
be too late to survive because the fire spreads quickly and block the exit. Thus,
in this test case, the survivor rate (SR) is still low. The chart in Figure 8 shows
the progress of the two measures during the simulation.
5.3Model with emotion and propagation
In this test case, the value of the propagation range and of the perception range
are set randomly in their definition interval, which means that the people can
feel the fear by perceiving the stimuli from the environment and can inform the
others about their fear. They can perceive not only the fire but also the behaviors
of the others. In the chart in the Figure 9, at step 40, the emotional propagation
happens, the emotional rate (ER) jumps thus significantly and then the survivor
rate (SR) increases quickly. That is why the survivor rate is higher.
Fig.9. Evolutions of the emotion rate and the number of survivors
After having executed the simulation 100 times and making statistics on the data
obtained, we find that the benefits of the emotional factors in the simulation of
the emergency evacuation is very important. In the chart of the Figure 10, in
the case of emotions with propagation, the percentage of survivors is the highest
We can summarize our model by responding to following questions.
How an emotion appears? The agent perceives stimuli; he evaluates them ac-
cording to his knowledge and his current emotion; then, a new emotion appears.
Which may influence the appraisal process of the stimuli? The stimuli, the empa-
thy of agent and effect of the environment influence on the evaluation of emotion.
The intensity of emotion of each agent is different to each other, although they
perceive the same stimuli at the same time. When the agents perceive the fire,
some may be scare, others may not. This is all because of the empathy.
How can an agent show his emotion? Through his behaviors, an agent shows
his current emotion. In our simulation, these behaviors are: appearance change
(like the human facial expression), the movement speed or other ways to inform
other agents (scream, cry...).
How can the propagation of emotions happen? An agent perceives the others’
behaviors, evaluates them like any environmental stimuli. Then, an emotion
appears. Thus, the emotion spreads over agents.
Fig.10. Evolutions of the emotion rate and the number of survivors
In our research, we found that there is an amplification of the emotional
intensity in the mob. We name it the emotional circle effect. It means that, when
the first agent perceives the fire, he is scared and executes a behavior revealing his
fear; the other agents perceive these behaviors; they are scared in turn and react
to this emotion; the first agent mentioned perceives these behaviors and then the
intensity of his own fear is increased. This type of process is repeated and the
intensity of the fear in the mod jumps significantly. In a real situation, this kind
of phenomenon happens frequently and is not limited to the fear inducing panic
but also for example to the joy: the joy of the spectators in the stadium is much
more intensive than that of the man who watches the match on his television at
Theoretically we proposed a model of emotion based on cognitive theories of
emotion and then a model of emotional agent. According to the theory proposed,
we can improve the emergency evacuation by adding emotional factors.
Practically we described the model of the simulation of the emergency evacu-
ation in a burning shopping center. In addition, according to our simulation, we
succeeded to prove the important role of emotions in the emergency evacuation.
In our research, we simulate only one emotion. The behaviors of agent are
also affected by only one emotion. Simulating a multi-emotion model is thus the
principal perspective of our research. In the multi-emotion model, each stimulus
can trigger more than one emotion and, because many current emotions influence
not only the appraisal process but also the behaviors; the simulation will thus
become more and more complex.
This work was funded by the project EPIS, a French IRD SPIRALES research
program that is developed by research teamwork MSI-IRD UMMISCO.
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