=Paper=
{{Paper
|id=None
|storemode=property
|title=Towards an Agent-Based Proxemic Model for Pedestrian and Group Dynamic
|pdfUrl=https://ceur-ws.org/Vol-621/paper02.pdf
|volume=Vol-621
|dblpUrl=https://dblp.org/rec/conf/woa/ManentiMVOS10
}}
==Towards an Agent-Based Proxemic Model for Pedestrian and Group Dynamic==
https://ceur-ws.org/Vol-621/paper02.pdf
Towards an Agent-Based Proxemic Model
for Pedestrian and Group Dynamic
Lorenza Manenti, Sara Manzoni, Giuseppe Vizzari Kazumichi Ohtsuka, Kenichiro Shimura
Complex Systems and Artificial Intelligence research center Research Center for Advanced Science & Technology
University of Milano–Bicocca University of Tokyo
viale Sarca 336/14, 20126 Milano Komaba 4-6-1, Meguro-ku, Tokyo, 153-8904, JAPAN
{lorenza.manenti,sara.manzoni,giuseppe.vizzari}@disco.unimib.it tukacyf@mail.ecc.u-tokyo.ac.jp
shimura@tokai.t.u-tokyo.ac.jp
Abstract—Models for the simulation of pedestrian dynamics on this topic is still quite lively and far from a complete
and crowds of pedestrians have already been successfully applied understanding of the complex phenomena related to crowds
to several scenarios and case studies, off-the-shelf simulators can of pedestrians in the environment, models and simulators have
be found on the market and they are commonly employed by
end-user and consultancy companies. However, these models are shown their usefulness in supporting architectural designers
the result of a first generation of research efforts considering and urban planners in their decisions by creating the possibility
individuals, their interactions with the environment and among to envision the behaviour/movement of crowds of pedestrians
themselves, but generally neglecting aspects like (a) the impact in specific designs/environments, to elaborate what-if scenarios
of cultural heterogeneity among individuals and (b) the effects and evaluate their decisions with reference to specific metrics
of the presence of groups and particular relationships among
pedestrians. This work is aimed, on one hand, at clarifying and criteria.
some fundamental anthropological considerations on which most The Multi-Agent Systems (MAS) approach to the modeling
pedestrian models are based, and in particular Edward T. Hall’s and simulation of complex systems has been applied in very
work on proxemics. On the other hand, the paper will briefly different contexts, ranging from the study of social systems [3],
describe the first steps towards the definition of an agent- to biological systems (see, e.g., [4]), and it is considered
based model encapsulating in the pedestrian’s behavioural model
effects capturing both proxemics and influences due to potential as one of the most successful perspectives of agent–based
presence of groups in the crowd. computing [5], even if this approach is still relatively young,
compared, for instance, to analytical equation-based modeling.
I. I NTRODUCTION The MAS approach has also been adopted in the pedestrian
Crowds of pedestrians are complex entities from different and crowd modeling context, especially due to the adequacy of
points of view, starting from the difficulty in providing a the approach to the definition of models and software systems
satisfactory definition of the term crowd. The variety of in which autonomous and possibly heterogeneous agents can
individual and collective behaviours that take place in a crowd, be defined, situated in an environment, provided with the
the composite mix of competition for the shared space but also possibility to perceive it and their local context, decide and
collaboration due to, not necessarily explicit but often shared try to carry out the most appropriate line of action, possibly
(at least in a given scenario), social norms, the possibility to interacting with other agents as well as the environment itself.
detect self-organization and emergent phenomena they are all The approach can moreover lead to the definition of models
indicators of the intrinsic complexity of a crowd. Nonetheless, that are richer and more expressive than other approaches that
the relevance of human behaviour, and especially of the were adopted in the modeling of pedestrians (that respectively
movements of pedestrians, in built environment in normal and consider pedestrians as particles subject to forces, in physical
extraordinary situations (e.g. evacuation), and its implications approaches, or particular states of cells in which the environ-
for the activities of architects, designers and urban planners ment is subdivided, in CA approaches).
are apparent (see, e.g., [1] and [2]), especially given recent The main aim of this work is to present the motivations,
dramatic episodes such as terrorist attacks, riots and fires, fundamental research questions and directions, and some pre-
but also due to the growing issues in facing the organiza- liminary results of an agent–based modeling and simulation
tion and management of public events (ceremonies, races, approach to the multidisciplinary investigation of the complex
carnivals, concerts, parties/social gatherings, and so on) and dynamics that characterize aggregations of pedestrians and
in designing naturally crowded places (e.g. stations, arenas, crowds. This work is set in the context of the Crystals project,
airports). Computational models of crowds and simulators are a joint research effort between the Complex Systems and
thus growingly investigated in the scientific context, but also Artificial Intelligence research center of the University of
adopted by firms1 and decision makers. In fact, even if research Milano–Bicocca, the Centre of Research Excellence in Hajj
1 see, e.g., Legion Ltd. (http://www.legion.com), Crowd Dynamics Ltd.
and Omrah and the Research Center for Advanced Science
(http://www.crowddynamics.com/), Savannah Simulations AG (http://www. and Technology of the University of Tokyo. In particular, the
savannah-simulations.ch). main focus of the project is on the adoption of an agent-based
pedestrian and crowd modeling approach to investigate mean- A. Perceived Distance and Proxemic Behavior
ingful relationships between the contributions of anthropology, Proxemic behavior includes different aspects which could it
cultural characteristics and existing results on the research be useful and interesting to integrate in crowd and pedestrian
on crowd dynamics, and how the presence of heterogeneous dynamics simulation. In particular, the most significant of
groups influence emergent dynamics in the context of the Hajj these aspects being the existence of two kinds of distance:
and Omrah. The last point is in fact an open topic in the physical distance and perceived distance. While the first de-
context of pedestrian modeling and simulation approaches: pends on physical position associated to each person, the latter
the implications of particular relationships among pedestrians depends on proxemic behavior based on culture and social
in a crowd are generally not considered or treated in a very rules. The term proxemics was first introduced by Hall with
simplistic way by current approaches. In the specific context respect to the study of set of measurable distances between
of the Hajj, the yearly pilgrimage to Mecca that involves over people as they interact [8]. In his studies, Hall carried out
2 millions of people coming from over 150 countries, the analysis of different situations in order to recognize behavioral
presence of groups (possibly characterized by an internal struc- patterns. These patterns are based on people’s culture as they
ture) and the cultural differences among pedestrians represent appear at different levels of awareness.
two fundamental features of the reference scenario. Studying In [9] Hall proposed a system for the notation of proxemic
implications of these basic features is the main aim of the behavior in order to collect data and information on people
Crystal project. sharing a common space. Hall defined proxemic behavior
The paper breaks down as follows: the following section and four types of perceived distances: intimate distance for
describes some basic anthropological and sociological theories embracing, touching or whispering; personal distance for
that were selected to describe the phenomenologies that will interactions among good friends or family members; social
be considered in the agent-based model definition. Section III distance for interactions among acquaintances; public distance
will present the current state of the art on pedestrian and used for public speaking. Perceived distances depend on some
crowd models, with particular reference to recent develop- additional elements which characterize relationships and inter-
ments aimed at the modeling of groups or improving the actions between people: posture and sex identifiers, sociofugal-
modeling of anthropological aspects of pedestrians. Section IV sociopetal (SFP) axis, kinesthetic factor, touching code, visual
briefly describes the first steps towards the definition and code, thermal code, olfactory code and voice loudness.
experimentation of a model encompassing basic anthropolog- It must be noted that some recent research effort was aimed
ical rules for the interpretation of mutual distances by agents at evaluating the impact of proxemics and cultural differences
and basic rules for the cohesion of groups of pedestrians. on the fundamental diagram [10], a typical way of evaluating
Conclusions and future developments will end the paper. both real crowding situations and simulation results.
II. I NTERDISCIPLINARY R ESEARCH F RAMEWORK B. Crowds: Canetti’s Theory
Elias Canetti work [11] proposes a classification and an
The context of research regards very large events where a
ontological description of the crowd; it represents the result
large number of people may be gathered in a limited spatial
of 40 years of empirical observations and studies from psy-
area, this can bring to serious safety and security issues for
chological and anthropological viewpoints. Elias Canetti can
the participants and the organizers. The understanding of the
be considered as belonging to the tradition of social studies
dynamics of large groups of people is very important in the de-
that refer to the crowd as an entity dominated by uniform
sign and management of any type of public events. The context
moods and feelings. We preferred this work among others
is also related to crowd dynamics study in collective public
dealing with crowds due to its clear semantics and explicit ref-
environments towards comfort services to event participants.
erence to concepts of loss of individuality, crowd uniformity,
Large people gatherings in public spaces (like pop-rock con-
spatio-temporal dynamics and discharge as a triggering entity
certs or religious rites participation) represents scenarios where
generating the crowd, that could be fruitfully represented by
the dynamics can be quite complex due to different factors (the
computationally modeling approaches like.
large number and heterogeneity of participant people, their
The normal pedestrian behaviour, according to Canetti, is
interactions, their relationship with the performing artists and
based upon what can be called the fear to be touched principle:
also exogenous factors like dangerous situations and any kind
of different stimuli present in the environment [6], [7]). The “There is nothing man fears more than the touch
traditional and current trend in social sciences studying crowds of the unknown. He wants to see what is reaching
is still characterized by a non-dominant behavioral theory on towards him, and to be able to recognize or at least
individuals and crowds dynamics. Several open issues are still classify it.”
under study, according multiple methodological approaches “All the distance which men place around them-
and final aims. However, in order to develop both empirical selves are dictated by this fear.”
and theoretical works on crowd studies, we claim that the A discharge is a particular event, a situation, a specific
theoretical reference framework has to be clarified. This is the context in which this principle is not valid anymore, since
main aim of this section. pedestrians are willing to accept being very close (within
t=0 t=1 t=2
Fig. 2. A diagram showing a sample effect of movement generated through
the coordinated change of state of adjacent cells in a CA. The black cell is
occupied by a pedestrian that moves to the right in turn 0 and down in turn
1, but these effects are obtained through the contemporary change of state
among adjacent cells (previously occupied becoming vacant and vice versa).
A. Pedestrians as particles
Several models for pedestrian dynamics are based on an
analytical approach, representing pedestrian as particles sub-
Fig. 1. A diagram exemplifying an analytical model for pedestrian movement: ject to forces, modeling the interaction between pedestrian
the gray pedestrian, in the intersection, has an overall velocity v that is the and the environment (and also among pedestrians themselves,
result of an aggregation of the contributions related to the effects of attraction
by its own reference point (a), and the repulsion by other pedestrians (b and in the case of active walker models [15]). Forces of attrac-
c). tion lead the pedestrians/particles towards their destinations
(modeling thus their goals), while forces of repulsion are
used to represent the tendency to stay at a distance from
touch distance). Canetti provided an extensive categorization other points of the environment. Figure 1 shows a diagram
of the conditions, situations in which this happens and he exemplifying the application of this approach to the repre-
also described the features of these situations and of the sentation of an intersection that is being crossed by three
resulting types of crowds. Finally, Canetti also provides the pedestrians. In particular, the velocity of the gray pedestrian
concept of crowd crystal, a particular set of pedestrians which is determined as an aggregation of the influences it is subject
are part of a group willing to preserve its unity, despite to, that are the attraction to its reference point (the top exit)
crowd dynamics. Canetti’s theory (and precisely the fear to be and the repulsion from the other pedestrians. This kind of
touched principle) is apparently compatible with Hall’s prox- effect was introduced by a relevant and successful example
emics, but it also provides additional concepts that are useful of this modeling approach, the social force model [16]; this
to describe phenomena that take place in several relevant approach introduces the notion of social force, representing the
crowding phenomena, especially from the Hajj perspective. tendency of pedestrians to stay at a certain distance one from
Recent developments aimed at formalizing, embedding and another; other relevant approaches take inspiration from fluid-
employing Canetti’s crowd theory into computer systems (for dynamic [17] and magnetic forces [18] for the representation
instance supporting crowd profiling and modeling) can be of mechanisms governing flows of pedestrians.
found in the literature [12], [13] and they represent a useful While this approach is based on a precise methodology and
contribution to the present work. has provided relevant results, it represents pedestrian as mere
particles, whose goals, characteristics and interactions must
III. R ELATED W ORKS be represented through equations, and it is not simple thus to
incorporate heterogeneity and complex pedestrian behaviours
It is not a simple task to provide a compact yet compre- in this kind of model. It is worth mentioning, however, that
hensive overview of the different approaches and models for an attempt to represent the influence of groups of pedestrians
the representation and simulation of crowd dynamics. In fact, in this kind of model has been recently proposed [19].
entire scientific interdisciplinary workshops and conferences
are focused on this topic (see, e.g., the proceedings of the B. Pedestrians as states of CA
first edition of the International Conference on Pedestrian and
A different approach to crowd modeling is characterized by
Evacuation Dynamics [14] and consider that this event has
the adoption of Cellular Automata (CA), with a discrete spatial
reached the fifth edition in 2010). However, most approaches
representation and discrete time-steps, to represent the simu-
can be classified according to the way pedestrians are repre-
lated environment and the entities it comprises. The cellular
sented and managed, and in particular:
space includes thus both a representation of the environment
• pedestrians as particles subject to forces of attrac- and an indication of its state, in terms of occupancy of the
tion/repulsion; sites it is divided into, by static obstacles as well as human
• pedestrians as particular states of cells in a CA; beings. Transition rules must be defined in order to specify the
• pedestrians as autonomous agents, situated in an environ- evolution of every cell’s state; they are based on the concept of
ment. neighborhood of a cell, a specific set of cells whose state will
be considered in the computation of its transition rule. The models exploiting a cellular space representing spatial aspects
transition rule, in this kind of model, generates the illusion of agents’ environment. A MAS is a system made up of a
of movement, that is mapped to a coordinated change of set of autonomous components which interact, for instance
cells state. To make a simple example, an atomic step of a according to collaboration or competition schemes, in order
pedestrian is realized through the change of state of two cells, to contribute in realizing an overall behaviour that could not
the first characterized by an “occupied” state that becomes be generated by single entities by themselves. As previously
“vacant”, and an adjacent one that was previously “vacant” introduced, MAS models have been successfully applied to the
and that becomes “occupied”. Figure 2 shows a sample effect modeling and simulation of several situations characterized
of movement generated by the subsequent application of a by the presence of autonomous entities whose action and
transition rule in the cellular space. This kind of application interaction determines the evolution of the system, and they
of CA-based models is essentially based on previous works are growingly adopted also to model crowds of pedestrians [1],
adopting the same approach for traffic simulation [20]. [28], [29], [30]. All these approaches are characterized by
Local cell interactions are thus the uniform (and only) way the fact that the agents encapsulate some form of behaviour
to represent the motion of an individual in the space (and inspired by the above described approaches, that is, forms
the choice of the destination of every movement step). The of attractions/repulsion generated by points of interest or
sequential application of this rule to the whole cell space reference in the environment but also by other pedestrians.
may bring to emergent effects and collective behaviours. Some of the agent based approaches to the modeling of
Relevant examples of crowd collective behaviours that were pedestrians and crowds were developed with the primary goal
modeled through CAs are the formation of lanes in bidi- of providing an effective 3D visualization of the simulated
rectional pedestrian flows [21], the resolution of conflicts in dynamics: in this case, the notion of realism includes ele-
multidirectional crossing pedestrian flows [22]. In this kind ments that are considered irrelevant by some of the previous
of example, different states of the cells represent pedestrians approaches, and it does not necessarily require the models
moving towards different exits; this particular state activates a to be validated against data observed in real or experimental
particular branch of the transition rule causing the transition situations. The approach described in [31] and in [32] is char-
of the related pedestrian to the direction associated to that acterized by a very composite model of pedestrian behaviour,
particular state. Additional branches of the transition rule including basic reactive behaviours as well as a cognitive
manage conflicts in the movement of pedestrians, for instance control layer; moreover, actions available to agents are not
through changes of lanes in case of pedestrians that would strictly related to their movement, but they also allow forms
occupy the same cell coming from opposite directions. of direct interaction among pedestrians and interaction with
It must be noted, however, that the potential need to objects situated in the environment. Other approaches in this
represent goal driven behaviours (i.e. the desire to reach a area (see, e.g., [33]) also define layered architectures including
certain position in space) has often led to extend the basic cognitive models for the coordination of composite actions
CA model to include features and mechanisms breaking the for the manipulation of objects present in the environment.
strictly locality principle. A relevant example of this kind Another relevant approach, described in [34], is less focused
of development is represented by a CA based approach to on visual effectiveness of the simulation dynamics, and it
pedestrian dynamics in evacuation configurations [23]. In supports a flexible definition of the simulation scenario also
this case, the cellular structure of the environment is also without requiring the intervention of a computer programmer.
characterized by a predefined desirability level, associated to However, these virtual reality focused approaches to pedestrian
each cell, that, combined with more dynamic effects generated and crowd simulation were not tested in paradigmatic case
by the passage of other pedestrians, guide the transition studies, modeled adopting analytical approaches or cellular
of states associated to pedestrians. Recent developments of automata and validated against real data.
this approach introduce even more sophisticated behavioural
elements for pedestrians, considering the anticipation of the IV. A S IMPLE AGENT-BASED P ROXEMIC M ODEL
movements of other pedestrians, especially in counter flows This section will describe a first step towards an agent–based
scenarios [24]. model encompassing abstractions and mechanisms accounting
Another relevant recent research effort that must be men- based on fundamental considerations about proxemics and
tioned here is represented by a first attempt to explicitly basic group behaviour in pedestrians. We first defined a very
include proxemic considerations not only as a background general and simple model for agents, their environment and
element in the motivations a behavioural model is based upon, interaction, then we realized a proof–of–concept prototype to
but rather as a concrete element of the model itself [25]. have an immediate idea of the implications of our modeling
choices. In parallel to this effort, a set of experiments were
C. Pedestrians as autonomous agents conducted (in June 2010) to back-up with observed data some
Recent developments in this line of research (e.g. [26], [27]), intuitions on the implications of the presence of groups in
introduce modifications to the basic CA approach that are specific scenarios; two photos of one of the experiments
so deep that the resulting models can be considered much are shown in Figure 4. In particular, this experiments is
more similar to agent–based and Multi Agent Systems (MAS) characterized by two sets of pedestrians moving in opposite
p g
r
(a) (b)
Fig. 3. Basic behavioural rules: a basic proxemic rule drives an agent to move away from other agents that entered/are present in his/her own personal space
(delimited by the proxemic distance p) (a), whereas a member of a group will pursue members of his/her group that have moved/are located beyond a certain
distance (g) but within his/her perception radius (r) (b).
directions in a constrained portion of space. In the set of representing the maximum displacement per time unit.
pedestrians, in some of the experiments, some individuals were More complex environments could be modeled, for instance
instructed to behave as friends or relatives, tying to stay close by means of a set of relevant objects in the scene, like points of
to each other in the movement towards their goal. It must interest but also obstacles. These objects could be perceived by
be noted that this kind of situation is simple yet relevant agents according to their position and perceptual capabilities,
for the understanding of some general principle on pedestrian and they could thus have implications on their movement.
movement and on the implications of the presence of groups Objects can (but they do not necessarily must be) in fact be
in a crowd. In the context of the project a set of observations considered as attractive or repulsive by them. The effect of the
will be carried out in order to extend and improve the available perception of objects and other pedestrians, however, is part
data for model calibration and validation. of agents’ behavioural specifications. For this specific applica-
tion, however, the perceptive capability of an agent a are sim-
The simulated environment represents a simplified real built ply defined as the set of other pedestrians that are present at the
environment, a corridor with two exits (North and South); time of the perception in a circular portion of space or radius
later different experiments will be described with corridors of rp centered at the current coordinates of agent a. In particular,
different size (10m wide and 20 m long as well as 5m wide each agent a ∈ A is provided with a perception distance pera ;
and 10 m long). We represented this environment as a simple the set of perceived agents is defined as Pa = p1 , . . . , pi where
euclidean bi-dimensional space, that is discrete (meaning that p
d(a, i) = (xa − xi )2 + (ya − yi )2 ≤ pera .
coordinates are integer numbers) but not “discretized” (as Pedestrians are modeled as agents situated in an envi-
in a CA). Pedestrians, in other words, are characterized by ronment, each occupying about 40 cm2 , characterized by a
a position that is a pair hx, yi that does not not denote a state representing individual properties. Their behaviour has a
cell but rather admissible coordinates in an euclidean space. goal driven component, a preferred direction; in this specific
Movement, the fundamental agent’s action, is represented as example it does not change over time and according to agent’s
a displacement in this space, i.e. a vector. The approach is position in space (agents want to get out of the corridor from
essentially based on the Boids model [35], in which however one of the exits, wither North or South), but it generally
rules have been modified to represent the phenomenologies changes according to the position of the agent, generating a
described by the basic theories and contributions on pedes- path of movement from its starting point to its own destination.
trian movement instead of flocks. Boundaries can also be The preferred direction is thus generally the result of a stochas-
defined: in the example Eastern and Western borders cannot tic function possibly depending on time and current position of
be crossed and the movement of pedestrians is limited by the the agent. The goal driven component of the agent behavioural
pedestrian position update function, which is an environmental specification, however, is just one the different elements of
responsibility. Every agent a ∈ A (where A is the set the agent architectures that must include elements properly
of agents representing pedestrians of the modeled scenario) capturing elements related to general proxemic tendencies
is characterized by a position posa represent by a pair of and group influence (at least), and we also added a small
coordinates hxa , yx i. Agent’s action is thus
q represented by random contribution to the overall movement of pedestrians,
a vector ma = hδxa , δya i where |ma | = δx2a + δy2a < M as suggested by [36]. The actual layering of the modules
where M is a parameter depending on the specific scenario contributing to the overall is object of current and future work.
Fig. 4. Experiments on facing groups: several experiments were conducted on real pedestrian dynamics, some of which also considered the presence of
groups of pedestrians, that were instructed on the fact that they had to behave as friends or relatives while moving during the experiment.
In the scenario, agents’ goal driven behavioural component These basic considerations, also schematized in Figure 3-
is instead rather simple: agents heading North (respectively A, lead to the definition of rules support a basic proxemic
South) have a deliberate contribution to their overall movement behaviour for pedestrian agents.
mga = h0, M i (respectively mga = h0, −M i). in which the environment is populated with two variable
We realized a sample simulation scenario in a rapid pro- sized sets of pedestrians heading North and South; they are
totyping framework2 and we employed it to test the simple not characterized by any particular relationship binding them,
behavioural model that will be described in the following. with the exception of a shared goal, i.e. they are not a group
In the realized simulator, the environment is responsible for but rather an unstructured set of pedestrians.
updating the position of agents, actually triggering their action
choice in a sequential way, in order to ensure fairness among B. Group Dynamic Rules
agents. In particular, we set the turn duration to 100 ms and In this situation, we simply extend the behavioural spec-
the maximum covered distance in one turn is 15 cm (i.e. the ification of agents by means of an additional contribution
maximum velocity for a pedestrian is 1.5 m/s). representing the tendency of group members to stay close to
A. Basic Proxemic Rules each other. First of all, every pedestrian may be thus part of a
Every pedestrian is characterized by a culturally defined group, that is, a set of pedestrians that mutually recognize
proxemic distance p; this value is in general related to the their belonging to the same group and that are willing to
specific culture characterizing the individual, so the overall preserve the group unity. This is clearly a very simplified,
system is designed to be potentially heterogenous. In a normal heterarchical notion of group, and in particular it does not
situation, the pedestrian moves (according to his/her preferred account for hierarchical relationships in groups (e.g. leader
direction) maintaining the minimum distance from the others and followers), but we wanted to start defining basic rules for
above this threshold (rule P1). More precisely, for a given the simplest form of group.
agent a this rule defines that the proxemic contribution to the Every pedestrian is thus also characterized by a culturally
overall agent movement mpa = 0 if ∀b ∈ Pa : d(a, b) ≥ p. defined proxemic distance g determining the way the pedes-
However, due to the overall system dynamics, the mini- trian interprets the minimum distance from any other group
mum distance between one pedestrian and another can drop member. In particular, in a normal situation a pedestrian moves
below p. In this case, given a pedestrian a, we have that (according to hie/her preferred direction and also considering
∃b ∈ Pa : d(a, b) < p; the proxemic contribution to the overall the basic proxemic rules) keeping the maximum distance from
movement of a will try to restore this condition (rule P2) the other members of the group below g (Rule G1). More
(please notice that pedestrians might have different thresholds, precisely, for a given agent a, member of a group G, this rule
so b might not be in a situation so that his/her P2 rule is defines that the group dynamic contribution tothe overall agent
activated). In particular, given p1 , . . . , pk ∈ Pa : d(a, pi ) < p movement mga = 0 if ∀b ∈ Pa ∩ (G − {a}) : d(a, b) < g.
for 1 ≤ i ≤ k, given c the centroid of posp1 , . . . , pospk , However, due to the overall system dynamics, the maximum
the proxemic contribution to the overall agent movement distance between one pedestrian and other members of his
mpa = −kp ·c − posa , where ka is a parameter determining the group can exceed g. In this case, the it will try to restore this
intensity of the proxemic influence on the overall behaviour. condition by moving towards the group members he/she is
able to perceive (rule
G2). In particular, given p1 , . . . , pk ∈
2 Nodebox – http://www.nodebox.org Pa ∩ (G − {a}) : d(a, pi ) ≥ g for 1 ≤ i ≤ k, given c
Individual pedestrians
heading South
Pedestrian group
heading South
Pedestrian group
heading North
Individual pedestrians
heading North
Fig. 5. Screenshots of the prototype of the simulation system.
the centroid of posp1 , . . . , pospk , the proxemic contribution to facing each other must manage to “turn around” each other
the overall agent movement mga = kg · c − posa , where ka is to preserve their unity but at the same time advance towards
a parameter determining the intensity of the group dynamic their destination.
influence on the overall behaviour.
This basic idea of group influence on pedestrian dynamics, C. Experimental results
also schematized in Figure 3-B, lead to the extension of the We conducted several experiments with the above described
basic proxemic behaviour for pedestrian agents of the previous model and simulator, altering the starting conditions to evalu-
example. We tested the newly defined rules in a similar ate the plausibility of the generated dynamics and to calibrate
scenario but including groups of pedestrians. In particular, two the parameters to fit actual data available from the literature or
scenarios were analyzed. In the first one, we simply substituted acquired in the experiments. In particular, we focused on the
4 individual pedestrians in the previous scenario with a group influence of the proxemic distance p on the overall system
of 4 pedestrians. The group was able to preserve its unity in dynamics. We started considering Hall’s personal distance
all the tests we conducted, but the average travel time for the as a starting point for this model parameter. Hall reported
group members actually increased. Individuals, in other words, ranges for the various proxemic distances, considering a close
trade some of their potential speed to preserve the unity of the phase and a far phase for all the different perceived distances
group. In a different scenario, we included 10 pedestrians and (described in Section II-A). In particular, we considered both
a group of 4 pedestrians heading North, 10 pedestrians and a an average value for the far phase of the personal distance
group of 4 pedestrians heading South. In this circumstances, (1m) and a low end value (75 cm) that is actually the
the two groups sometimes face and they are generally able to border between the far and the close phases of the personal
find a way to form two lanes, actually avoiding each other. distance range. In general, the higher value allowed to achieve
However, the overall travel time for group members actually relatively results in scenarios characterized by a low density of
increases in many of the simulations we conducted. pedestrians in the environment. For densities close and above
In Figure 5 two screenshots the of the prototype of the one pedestrian per square meter, the lower value allowed to
simulation system that was briefly introduced here. Individual achieve a smoother flow.
agents, those that are not part of a group, are depicted in A summary of the achieved results is shown in Figure 6.
blue, but those for which rule P2 is activated (they are afraid In particular, these data refer to the simulation of a 10 m
to be touched) turn to orange, to highlight the invasion of long and 5 m wide corridor. We varied the number of agents
their personal space. Members of groups are depicted in violet altering the density in the environment; to keep constant the
and pink. The two screenshots show how two groups directly number of pedestrians in the corridor, the two ends were joined
Fundamental
diagram
-‐
velocity
V. C ONCLUSIONS AND F UTURE W ORKS
1.00
The paper has presented the research setting in which an
0.90
innovative agent–based pedestrian an crowd modeling and
0.80
simulation effort is set. Preliminary results of the first stage of
0.70
the modeling phase were described. Future works are aimed,
Velocity
0.60
0.50
on one hand, at consolidating the preliminary results of this
0.40
first scenarios (performing a calibration of the model and
0.30
validation of the results, that is currently under way), but
0.20
also extending the range of simulated scenarios characterized
0.10
by relatively simple spatial structures for the environment
0.00
(e.g. bends, junctions). On the other hand, we want to better
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
formalize the agent behavioural model and its overall archi-
Density
tecture, but also extending the notion of group, in order to
Low
personal
distance
High
personal
distance
capture phenomenologies that are particularly relevant in the
context of Hajj (e.g. hierarchical groups, but also hierarchies
Fundamental
diagram
-‐
flow
of groups). Finally, we are also working at the integration of
1.40
these models into an existing open source framework for 3D
1.20
computing (Blender3 , also to be able to embed these models
and simulations in real portions of the built environment
1.00
defined with traditional CAD tools.
0.80
Flow
ACKNOWLEDGMENTS
0.60
This work has been partly funded by the Crystal Project.
0.40
The authors would like to thank Dr. Nabeel Koshak for
0.20
his expertise on the Hajj pilgrimage description and on the
0.00
requirements for second generation modeling and simulation
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
systems; the authors would also thank Prof. Ugo Fabietti for
Density
his suggestions about the anthropological literature that was
considered in this work.
Low
personal
distance
High
personal
distance
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