Cellular Automata and Situated Cellular Agents for Crowd Dynamics Modeling and Simulation

Universita degli Studi di Milano-BicoccaDipartimento di Informatica, Sistemistica e Comunicazione

Dottorato di Ricerca in Informatica XXI CicloAnno Accademico 20072008

CELLULAR AUTOMATA AND SITUATED CELLULARAGENTS

FOR CROWD DYNAMICS MODELING ANDSIMULATION

Stefano RedaelliPh.D. Dissertation

Supervisor: Prof. Stefania BandiniTutor: Prof. Flavio De Paoli

Ph.D. Coordinator: Prof. Stefania Bandini

When He had come back to Capernaumseveral days afterward, it was heard that He was at home.

And many were gathered together,so that there was no longer room, not even near the door;

and He was speaking the word to them.(Mark 2:1-2)

A Laura, Gigi e Simone.

CONTENTS

1 Introduction 7

2 Theories about crowds 112.1 Sociological Theories . . . . . . . . . . . . . . . . . . . . . . 112.2 The contribute of Elias Canetti . . . . . . . . . . . . . . . . 152.3 Pedestrians Observed Behavior . . . . . . . . . . . . . . . . 172.4 Cognitive Psychology: Spatial Knowledge . . . . . . . . . . 192.5 Social Psychology . . . . . . . . . . . . . . . . . . . . . . . . 24

2.5.1 Groups . . . . . . . . . . . . . . . . . . . . . . . . . . 242.5.2 The role of Emotions . . . . . . . . . . . . . . . . . . 27

2.6 Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3 Approaches to crowd modeling and simulation 353.1 Forcebased approach . . . . . . . . . . . . . . . . . . . . . 37

3.1.1 Magnetic force . . . . . . . . . . . . . . . . . . . . . . 383.1.2 Social force . . . . . . . . . . . . . . . . . . . . . . . . 40

3.2 CAbased approach . . . . . . . . . . . . . . . . . . . . . . . 423.2.1 Benefit cost . . . . . . . . . . . . . . . . . . . . . . . . 463.2.2 Bidirectional . . . . . . . . . . . . . . . . . . . . . . 483.2.3 Floor field . . . . . . . . . . . . . . . . . . . . . . . . 49

3.3 MASbased approach . . . . . . . . . . . . . . . . . . . . . . 513.3.1 Dynamic navigation . . . . . . . . . . . . . . . . . . . 533.3.2 Pedis . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.3.3 Social Distance . . . . . . . . . . . . . . . . . . . . . 563.3.4 MultiAgent Cellular Automata Systems . . . . . . 58

3.4 Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 603.5 Situated Cellular Agents . . . . . . . . . . . . . . . . . . . . 63

3.5.1 SCAagent actions and formal language description 673.5.2 The SCA model for pedestrian dynamics . . . . . . . 693.5.3 Experiments on SCA for pedestrians . . . . . . . . . 73

3.6 Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4

4 From theory to SCA 814.1 Logic description of Canettis basic crowd concepts . . . . . 82

4.1.1 A DL Language for Ontological Knowledge Repre-sentation . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.1.2 Elias Canettis Crowd . . . . . . . . . . . . . . . . . . 854.1.3 The mesolevel structure . . . . . . . . . . . . . . . 904.1.4 Two kinds of crowds . . . . . . . . . . . . . . . . . . 93

4.2 From the ontology to SCA . . . . . . . . . . . . . . . . . . . 964.2.1 The pedestrian agents and the limits of the SCA . . 1014.2.2 The aggregated level: a SCAoriented model . . . . 103

4.3 Redefinition of SCA into SCA4CROWD . . . . . . . . . . . 1094.3.1 The agent type ped . . . . . . . . . . . . . . . . . . . 1104.3.2 Other agent types . . . . . . . . . . . . . . . . . . . . 112

4.4 Modeling phenomena of crowd dynamics . . . . . . . . . . . 1134.4.1 The aggregation phenomenon . . . . . . . . . . . . . 1144.4.2 The dispersion phenomenon . . . . . . . . . . . . . . 120

4.5 Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 125

5 Towards a workstation for crowd simulation 1275.1 Platforms for crowd simulation . . . . . . . . . . . . . . . . 1285.2 SCA4CROWD: from the ontology to functional architecture 135

5.2.1 SCA4CROWD: the environment . . . . . . . . . . . 1365.2.2 SCA4CROWD: the pedestrian agents . . . . . . . . 1405.2.3 SCA4CROWD: interface and visualization . . . . . 1425.2.4 SCA4CROWD: considerations about analysis tools . 145

5.3 Guidelines for setting experiments on Open and ClosedCrowds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1505.3.1 The design of an Open Crowd simulation scenario . 1505.3.2 The design of a Closed Crowd simulation scenario . 154

6 Complementary Extensions 1596.1 The introduction of emotions . . . . . . . . . . . . . . . . . . 159

6.1.1 A SCAbased model of the work of Adamatzky . . . 1606.1.2 A SCA4CROWD model: the case of stadium . . . . . 1626.1.3 Considerations . . . . . . . . . . . . . . . . . . . . . . 165

6.2 Genetic Programming for smart pedestrian behaviors . . . 1656.2.1 Some notions of Genetic Programming . . . . . . . . 1666.2.2 Modeling Evacuees Behavior with GP . . . . . . . . 1686.2.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . 1706.2.4 Considerations . . . . . . . . . . . . . . . . . . . . . . 172

7 Conclusions 175

ACKNOWLEDGEMENTS

I want to thank all the people that have made this work possible andthat have patiently given to me their support and their time. In particu-lar all the colleagues of the Laboratory of Artificial Intelligence (Lintar)and the Complex System and Artificial Intelligence Research Center(CSAI). A special thanks to Prof. Stefania Bandini for her guide andher contagious enthusiasm. I want to thank Prof. Flavio De Paoli forhis precious advices and Dr. Sara Manzoni for the support given to meand for the hours of work spent together. Another thanks goes to JuliaWeekes for her exceptional helpfulness. I would like to thank also thepeople of the Department of Informatics, Systems and Communication(Disco) that shared with me these years and part of my path. I like toremember in particular all the other Ph.D. students of the XXI cycle andmy friends Stefano and Elisabetta.

CHAPTER 1

INTRODUCTION

The research context of this work refers to the application of bottomupapproaches to model and simulate the dynamics of pedestrian crowds.The study of crowd behavior is an important research field whose po-tential exploitations are oriented to support the design and manage-ment of public spaces and events towards the improvement of security,safety and comfort requirements. Due to the mobility increment and theavailability of fast means of transportation, the management of publicevents (e.g. community celebrations, entertainment events, parties orsocial gatherings) or naturally crowded places (e.g. stations, subways,arenas) is becoming crucial. Multi-functional structures, such as stadi-ums or sport centers, can host many kinds of attendants, from footballsupporters, to rock star fans, while urban squares might constitute thescenarios of events of a different nature such as fairs, political demon-strations, protest marches, musical festivals, markets etc, that attractpeople with diversified aims. Therefore, the interest in these researchesis motivated by the necessity to actively contribute to the design of safeenvironments in cities designed around the needs of mobility, securityand access to services in respect and consideration of human behaviorand habits.

The crowding phenomena that can be observed in our daily life inour cities often represent a compromise between competition for sharedspaces and obliged collaboration imposed by physical constraints, notnecessarily explicit social rules and norms that govern the behavior ofpeople in public places, personal perceptions and emotions. The num-ber and heterogeneity of these elements give an idea of the complexityof this study. For this reason crowding problems are research inter-ests of multiple disciplines (physics, sociology, ethology, social and be-havioral psychology, building design, urban planning, security manage-

8 INTRODUCTION

ment, among others) that constitute a broad heterogeneous field involv-ing several kinds of knowledge and competencies, ranging from acad-emic and scientific ones to technological and engineering contributions.

Within this scenario computer science can give its contribution inproviding computational models and simulation tools usable also fromexperts of other disciplines. Crowd modeling applications help design-ers supporting them in making decisions about the dimensioning ofdoors and other facilities in normal and evacuation situations. More-over, simulations can constitute a support to the study of pedestrianbehavior allowing the envisioning of different behavioral models in re-alistic environments thanks to the possibility of performing inmachinaexperiment testing and also sociological or psychological theories. Con-ceptual and computational models, and computerbased tools, openednew perspective in all the disciplines which tackle crowd behavior, al-lowing the simulation of expected behaviors, the creation of whatifscenarios, numerical and statistical elaborations of collected data, thevisualization of meaningful situations etc.

In spite of the great attention given to the crowding phenomena, thisfield of research still suffers from a lack of unifying theories and of ashared methodological framework, although thanks to new possibilitiesgiven by recent modeling and technological achievements, and thanksto a major understanding of the necessity of a multi-disciplinal effort,it constitutes a promising path for research. The general literature onpedestrian crowds and related behaviors is spread on a vast, heteroge-neous and multidisciplinary territory and the proposed theories oftenlack formalization. Pedestrian crowds have been the object of observa-tion and empirical study, and although several successful experiences inthe modeling of crowds and related emergent phenomena have been car-ried out, little methodological work can be found in the literature, andthere are no general guidelines for the adoption of specific modeling ap-proaches given to a pedestrian modeling scenario. The nonadoption ofa shared and clear language to define all the concepts involved in thecrowd phenomena makes it more difficult to give a unique and formalanswer to the question what is a crowd?.

According to these preliminary remarks, the aim of this work is therealization of a computational model based on a formal and sharablelanguage for the representation of a crowd dynamics phenomena. Thewords crowd dynamics define the study of how and where crowdsform and move [Sti00], and concern all the phenomena (e.g. crowd ag-gregation, dispersion and selforganized movement) where pedestriansare not considered only as single individuals, but as part of a group.

9

In chapter 2 a multi-disciplinal state of the art is introduced takinginto consideration the point of view and insights of disciplines such associology, cognitive sciences and social psychology in order to displaythe complexity of this field of study and collect the available knowledgeabout crowds and pedestrian behavior.

Chapter 3 focuses on the computer science contribution to the studyof crowds, and in particular it gives an overview of the modeling ap-proaches already available. The considered models are based on themicrosimulation of pedestrian crowds, where pedestrians are influ-enced by the environment but are also able to cause local changes thatmight have an influence on the behaviors of other pedestrians. In thesemodels the simulation of a human crowd emerges from the modeling ofsingle individuals that compound it inside the context where the crowdacts. One particular approach, the Situated Cellular Agent (SCA), ispresented as sufficiently suitable and flexible to represent the pedes-trian movement and dynamics into a very general context of study.However, the chapter ends considering that all the presented model-ing approaches can manage the dynamics of pedestrians well as singleindividuals, while they can represent the crowd dynamics phenomenaefficiently only in very particular scenarios. In fact, nowadays, a modelwhich is able to represent all the basic crowd dynamics phenomena (i.e.aggregation, dispersion and group movement) is still an open issue inthis research context.

Chapter 4 shows the results of the effort of applying the SCA ap-proach to the modeling of the crowd dynamics phenomena. The workstarts from the choice of a referring theory about crowds that could pro-vide a map of the involved concepts and a presentation of the crowddynamics phenomena with a clear semantics. The next step was thedescription of these concepts in a formal language in order to facilitatethe passage from the theory to the computational model. The applica-tion of the SCA pedestrian model to describe concepts of crowd dynam-ics showed some critical areas, and the introduction of some extensionsto the SCAbased model were necessary. The chapter ends with theformal description of the new SCAbased model specific for crowd dy-namics and with the presentation of the model applied to the case ofaggregation and dispersion phenomena.

Chapter 5 shows how the work is proceeding towards the develop-ment of a software tool for the simulation of the pedestrian and crowddynamics phenomena. The chapter contains some considerations aboutthe implementation choices, the functionalities of the interface and theenvisioning tool, and what are the elements to consider in order to cre-

10 INTRODUCTION

ate the setting for an experiment into a crowd dynamics scenario.Chapter 6 introduces two research paths that start from the advan-

tages offered by the using of a SCAoriented model, and meets the needof a deeper study on specific scenarios (e.g. people in an emergencysituation or the case of a crowd of supporters at a stadium). The firstpath is a study of the possibility of introducing emotions into the deci-sion process of pedestrian agents; while the second one is the applica-tion of genetic programming algorithms (i.e. a well known evolutionaryapproach which extends the genetic model of learning to the space ofprograms) in order to evolve the best behavior for pedestrians in anevacuation scenario and in the case of a totally unknown environment.These two complementary studies are at the beginning, but they havealready presented some interesting results which are discussed in thischapter.

Some conclusions end this thesis on chapter 7.

CHAPTER 2

THEORIES ABOUT CROWDS

Crowds have been studied under the perspective of many disciplines. Inthis section the studies on crowd will be presented under the point ofview of some of these, with the aim of providing an overview of the rele-vant aspects that have to be taken into consideration when approachinga study on pedestrian and crowds (a deeper presentation of some aspectsof this state of the art can be found in [Fed07]).

2.1 SOCIOLOGICAL THEORIES

The firsts considerations about crowds can be found in the Italian Schoolof Criminology, early explanations of crowd phenomena claimed thatcrowd members were to be considered mad, insane or crazy. Under thisperspective crowds were supposed to be composed of an accumulationof disintegrated social elements, people that were rejected by societyand that for this reason were hostile to it (i.e. see Lombroso, LUomoDelinquente, 1876 and Scipio Sighele, The Criminal Crowd, 1891).

Gabriel Tarde directly inspired by the works of Sighele and Lom-broso wrote The Crimes of Crowds (1888) but it is in Le lois de limitation(1890) where he defines the mechanism of imitation as the basis of hu-man behavior and introduces the concept of Group Mind an idea des-tined to have a great success in the future studies of Collective Psychol-ogy, and fundament of the European origins of crowd s studies.

These first studies on crowds do not consider the crowd as a collec-tion of independent individuals, but as a unique entity endowed witha single mind. The theory of the emotional contagion1 explains themechanism of the emotional suggestion to which the individual un-

1The theory of emotional contagion is deeper exposed in section 2.5.2

12 THEORIES ABOUT CROWDS

dergoes when in a crowd. Under the point of view of firsts social inves-tigators on crowds, this suggestion causes the vanishing of individualpersonality and intention.

In Tardes perspective (1890), the crowd acts guided by the conta-gion effects with less morality and intelligence than what would do theindividuals that constitute it. In that sense, the crowd, represents themanifestation and the destruction of the social. Due to the extreme so-ciality the crowd destroys the normal process of the imitation principle2.

Few years after Tardes work (in 1895), Gustave LeBon writes Psy-chologie des Foules [Bon02]. Strongly influenced by Tardes ideas, LeBonconsiders that crowds are composed of normal individuals that aretransformed in the crowd by a collective psychological process that inspite of their character, profession, intelligence and culture force thembehaving as they were possessed by a collective mind. The transfor-mation of the single individuals in a crowd, in the thought of LeBon,implies anonymity (individuals believe in the unaccountability of theirbehavior), a sense of invincibility and the disappearance of consciouspersonality. LeBon believes that these characteristics are the cause ofthe contagion, as to say the effect of extreme suggestibility to which sin-gle individuals are subjected when they are part of a crowd, and to theextraordinary behaviors of crowd members. The transformation of in-dividuals into a crowd brings also to the emergence of an unconsciouspersonality dominated by instincts and primitive beliefs. This state ofthings is called by LeBon collective mind or law of Mental Unity. Otherconsequences of the collective mind are the increased suggestibility thatis the source of impulsiveness, irritability, incapacity of judgement, ex-aggeration of feelings.

The theory of the crowd as an entity emotionally unstable, obtuseand violent has been discussed in the XX century by the works ofthe American sociological tradition, especially with the contribution ofMead and Parsons that brought the origin of action back to the individ-ual will.

The so called Chicago School was influenced by the Europeanthought but mainly it was influenced by American Pragmatism ofPeirce, Dewey and James (for further reading see [Col94]). RobertEzra Park published in 1904 The Crowd and the Public(Masse und Pub-likum). Park states that in the crowd individuals are influenced by animpulse that is the product of what he calls social interaction. This im-

2Borch underlines that although Tarde is cautious and does not want to derive socialand society from individual actors, that does not mean that Tardes attempt is to denyany active role to the individual.

2.1 SOCIOLOGICAL THEORIES 13

pulse is, by his definition, common, uncritical, collective and anarchical.Park adopts the concepts of social unrest and circular reaction to explaincollective behavior (see [McP89]). In the opinion of Park, unrest and cir-cular reaction are the elementary forms of collective behavior. Socialunrest is transmitted from an individual to another so the discontentof an individual x is transmitted to an individual y and then reflectedagain back on x producing what he defines a circular reaction. This lastconsists in a mutual infection of thoughts and feelings (a sort of con-tagion). The Chicago School attempts to bring back on the individualthe explanation of crowd phenomena (that is why this line of thought iscalled Micro-Interactionism).

Pupil of Park is Blumer. Blumer is known for his theory of SymbolicInteractionism. People act in relation to the meanings that things (sit-uations, behaviors etc,) have for them. The meanings are derived fromsocial interaction and are then modified through personal interpreta-tion. Blumer [Blu93] classifies crowds as a form of collective action,and, like his master Park, kept on thinking that group activity can beconsidered as a collective behavior (individuals are acting together). Hebelieves that individuals force them to behave following an interpreta-tive interaction, as to say, a response not to the behavior of the others,but to what is their interpretation of the behavior of the others (sym-bolic interactionism) (see [McP89]). Collective behavior in an (acting)crowd, in Blumers theory, develops in five steps:

Exciting Event: it is related to the social unrest, people cede thecontrol to that event.

Milling: people reproduce ones another behavior (pure circularbehavior), walking, talking etc.

Common Object: emerges a common orientation, a common tar-get/object for the people.

Collective Excitement: it eliminates peoples capacity to useimagination and interpretation to change the object of attention.When this happens the transformations of individuals in a crowdhas happened.

Common Impulse: Emerges a common interpretation or disposi-tion to behave (images that are fruits of the process of suggestionand imitation).

It can be said that Blumer synthesizes the ideas of LeBon and Parkand that he contributed to affirm the transformation theory of crowds.


His works were also introduced in police and military crowd controlmanuals.

Other authors follow this idea of crowd where its membersloose their individuality assuming a sort of collectiveidentity. Zim-bardo [Zim69], although critic to precedent traditions, believes that anindividual normally is in a state of individualization, control and ratio-nal behavior and calls deindividuation the state of the individual in thecrowd. This state is reached through a process that includes a loweringof selfobservation and of selfevaluation.

On the other side there is the individualistic tradition, and FloydAllport can be consider one of its assertors. He believes that the indi-vidual in the crowd behaves just as he would behave alone only more so(in [Rei]). In the opinion of Allport people in a crowd already share thesame attitudes and the excitement derives from the number of peoplethat are present.

The first book on collective behavior is constituted by the work ofTurner and Killian [TK87]. The two sociologists admit that the crowdis characterized by a component of irrationality, although they describecrowd behavior as fundamentally rational. Turner in a seminal work of1964 (in [MS99]), speaks about the illusion of unanimity referring tothe behavior of individuals in a crowd, this last characterized by whatTurner calls differential expressions. In the opinion of Turner, in fact,inside a gathering do exist many variations, but since his work therehas not been any attempt to systematically measure these variations.

A renewal of interest in the crowds is found only in the seventies,after social march and demonstrations of those years. Smelser formu-lates his Value Added Theory (in [Lev89]) while many researches focal-ized especially on panic situations. Richard Berk [Ber74] following theidea of rationality applied the game theory to crowd studies, in orderto demonstrate that also in panic situations can be detected a ratio-nal behavior of individuals. Meaningful in this field are the researchesand observations of McPhail [McP91] that enriches his considerationswith many data collected directly on the field. McPhail, after a series ofobservations of assemblage of people, comes to the conclusion that tra-ditional stereotypes as emotionality and unanimity of crowd must bedismissed as they do not constitute an adequate schema for the descrip-tion of crowds, neither in extreme panic situations. McPhail asserts thatsince LeBon the crowd has been separated from the sociological context,in relation to the first works on crowds of Reicher [Rei]. Reicher insertshis work inside the so called Social Identity theory, that states that be-haviors of individuals in a crowd depend on the stereotypes that each

2.2 THE CONTRIBUTE OF ELIAS CANETTI 15

individual has formed of himself. The individual in fact will act follow-ing what he believes the stereotype, the selfcategorization to which hebelongs, would act in that situation, for this reason the individual willimitate only the action of the other individuals that he recognizes asbelonging to his category.

The table 2.1 resumes the most evident differences between the twomain approaches to crowd: the Single CollectiveIdentity Theory andthe Individualistic Theory.

Single CollectiveIdentity IndividualisticTheory Theory

Group Mind Social IdentityLoss of Presence of

individual personality individual personalityInstinctive Rational

Table 2.1: Main differences between Single CollectiveIdentity Theoryand Individualistic Theory

2.2 THE CONTRIBUTE OF ELIAS CANETTI

In 1960 Elias Canetti wrote Crowds and Power ([Can84]) after 40years of gestation. He can be inserted in the tradition of studies thatconsiders the Crowd as a single entity, a unity dominated by uniformfeeling (contagion theory). He was impressed by great popular protestmarches and movements after the murder of Walter Rathenau, Germanminister of foreign affairs, in Frankfurt. Its analysis comprehends avery original and specific classification of Crowds and many considera-tions under different perspectives, from the psychological to the anthro-pological. He is author of what can be defined an ontology of crowds.

In Canettis opinion within the crowd there is equality and the crowdloves density, it never feels too dense. The maximum feeling of den-sity is perceived in the moment of the discharge, that is a particularevent characterizing the crowd formation. The fear of being touchedis another interesting concept that Canetti identifies. Single individualsavoid physical contact, in fact in normal situations they are afraid ofbeing touched, but the discharge transforms this fear into its opposite,creating a Crowd. The Crowd is the only situation where this happens.When the individual abandon itself to the Crowd he is no more afraid


of being touched and the crowd becomes a dense and compact uniquebody. The discharge, the metaphysical concept introduced by Canetti,is an event that transforms all the gathered individuals into the Crowd,an entity, this last, where all personal differences (gender, class, ageetc.) are dropped and, for the author, we can not speak of Crowd beforethis event. Big is the belief that come out of the illusion of being equalforever. Inside a Crowd can be found crowd crystals, groups governedby rigid rules.

Canetti also adds that one of the main characteristic of a Crowd isthe existence of a target. A target can be a place to reach or a situationto fulfil (e.g. arriving to a safe place or defeating a common enemy).In Canettis opinion another Crowd characteristics is the impulse to de-struction. Houses and objects are the things that a crowd destroys moreeasily because the sound of the destruction helps the crowd. Destruc-tion is an attack to all the boundaries and fire attracts more people.This last characteristics are mainly referred to what Canetti calls OpenCrowd considered by Canetti as the real crowd, the crowd at its max-imum potential. Canettis main distinction is between Open Crowdsand Closed Crowds. Open Crowds originates where before there wasnot anything. Then people feel the urge to join the crowd from eachside, may be not even knowing what is happening there, they need tofind themselves with other people, they are attracted by the crowd. Inthis phase the movement of the ones is communicated to the others andeverybody has a target, that can simply be the place where the crowdis. This phenomenon can occur spontaneously. Closed Crowds are op-posite to Open Crowds. They are crowds that renounce to grow in favorof duration. The Closed Crowd fills a place that has been assigned to it(i.e. a stadium, a theatre) and though it has established and identifiableboundaries (i.e. of concrete) that do not allow a not ruled ingress andthat present a controlled access (people are counted). Open Crowd islimited in growing and it can not grow after a limit (i.e. when the sta-dium is full). It respects boundaries and usually it has a ceremony foradmission (i.e. the payment of a ticket). Closed Crowds accept disper-sion in the perspective of reconstitution (i.e. next weeks match or show).Eruption instead is the sudden transformation of a Closed Crowd in anOpen Crowd. Social and institutional rules tend to capture the crowd.The crowd excites easily (is irritable, angry, sensitive) against designedenemies, whatever a single individual, or more individuals, separatedfrom the crowd, that will be interpreted as against the crowd. Panicinstead is identified by Canetti as the cause of the disintegration of thecrowds. A fire in a theater creates a fight for life and against others. In-

2.3 PEDESTRIANS OBSERVED BEHAVIOR 17

dividual violence against the others is perceived as obstacle on the wayto the exit. In panic the individual does not feel part of the crowd any-more and his boundaries become clear again to him. The most commoncause of panic diffusion into a crowd is the fulfilment of the commontarget, and as a consequence, the loss of common motivations.

For further information about Canettis theory see chapter 4.

2.3 PEDESTRIANS OBSERVED BEHAVIOR

In relation to pedestrians have been collected some data from differ-ent researches that can undergo the definition of ethological observa-tion in consideration only to what concerns the moving observable be-havior of pedestrians. Some observation campaigns could determinesome general rules that pedestrian follow when moving in a genericenvironment and these rules of behavior seem to be independent fromculture and other factors. Helbing et al. [HFMV02] lists some of theserules of pedestrian movement in normal situation, between the others:pedestrian feel aversion to taking detours or moving opposite to the de-sired walking direction; even if the direct way is crowded; pedestrianschoose the fastest route to their next destination, but not the shortestone (they choose the more comfortable route); pedestrians walk withan individual desired speed which corresponds to the more comfort-able (least energyconsuming); the mean value of pedestrian speed isapproximately 1.34m/s; pedestrians keep a certain distance to otherpedestrians and borders (of street walls and obstacles); the distance de-creases with growing pedestrian density, and the more a pedestrian isin a hurry; pedestrian density increases around particularly attractiveplaces; self organization effects occurs in pedestrian crowds.

Other interesting observations related to pedestrian behavior can befound in the Equator Project Data [LS02]. Some of the skills that pedes-trians seem to have are: human beings are aware of the flow, they areable to avoid getting stacked on a tile; pedestrians queue when the den-sity of people around them is really too high; if the pedestrian density isquite high one do not try to overtake permanently, on the contrary oneadapt ones linear speed to the flow3. The minimum space occupied bya pedestrian is usually fixed at 0.5 square meter.

3Other data reported in the Equator Data Project are that usually daily walkingtrips do not last more than 6 minute while 50 percent of the people walk less than1.4km per day. Pedestrian traffic seem to decrease up to 60 percent in case of rainyweather while daily cycles influence pedestrian density that present its peak time inthe morning or at lunch time but it may changes also in relation to the kind of zone (i.e.offices or residential)


Besides this needed space required by a pedestrian to walk, peopletry to establish other distances among them. E. T. Hall [Hal59] differen-ziates four sort of distances among people:

1. The intimate distance ranges from body contact approximately40-50cm. The infringement of intimate distance zone by anotherperson causes disconfort and could be perceived as a dangerousintrusion.

2. The personal distance ranges approximatey from 40-50cm to150cm. The personal distance includes a close phase 50-90cmpermitting one person to touch the other and a far phase thatdoes not permit this (90-150cm is the medium arms length).

3. The social distance ranges approximatey from 150cm to 3m.It is the casual interaction distance between acquaintances andstrangers. It is common for business meeting, classrooms and im-personal social affairs.

4. The public distance (above 300cm) is observed betweenstrangers. This distance is also called a public speaking distance.

Moreover pedestrians have demonstrated to have the following abil-ities:

Monitoring: is the capacity to guess the behavior of other peopleto avoid collision, or to evaluate their state of mind (being in ahurry, angry etc.).

Yielding: is the attitude to change trajectory to avoid a collisionwith somebody else. The distance at which one starts detouring islonger as the density is slower. If both start detouring at the sameside, a kind of oscillation might appear.

Streaming: when density is quite high, people are likely to followthe ones who walk in the same direction as them.

Daamen [Daa04] studied the behavior of pedestrians inside a transitstation where are present many activities beside walking that may in-fluence the general flow of passengers (pedestrians are performing spe-cial activities like waiting, buying tickets, shopping) while passengersunder time pressure have high speeds and force their way through thecrowd. Daamen observes that waiting passengers move with no specificdestination or trajectory and very slowly while the patterns of arrivingand leaving passengers are mostly determined by the public transport

2.4 COGNITIVE PSYCHOLOGY: SPATIAL KNOWLEDGE 19

timetable and that determines a large variance in flow. One momentthe area is empty, the next is overcrowded.

Regarding human movement in potential dangerous situations itis a common prejudice that people start adopting a behavior of selfpreservation instead than of altruism. That is traduced in nervousnessand in the undertaking of blind actions during which people move con-siderably faster than normal. It is thought that individuals start push-ing and that interactions among individuals become physical. Whilemoving becomes uncoordinated escape from a source of danger is sloweddown by fallen or injured people and also people tend to do what otherpeople do (see [HFMV02]). This point of view is not commonly sharedbecause other studies shows utterly different results and conclude thateven if people feel a strong fear human nature in disasters is more afunction of social factors than individual selfinterest and people rarelyloose control while instead they generally follow community expecta-tions [Cla02] [Qua47].

The table 2.2 resumes the main behavior and abilities of pedestriansin a crowd situations. The two columns report the behavior of singleindividuals and the behavior of pedestrians as a collective entity.

Individual Behavior Collective BehaviorCollision avoidance QueueingAwareness of crowd Streaming

Direction keepingTrajectories planningSeparation keeping

Table 2.2: The main pedestrian behavior and abilities

2.4 COGNITIVE PSYCHOLOGY: SPATIAL KNOWL-EDGE

The movement of pedestrians strongly depends to their perception andrepresentation of space. Human perception of space is a critical issue,in fact no two individuals know exactly the same thing about a placeand do not reason in the same way about space and places like under-lines Montello [Mon01]. To understand the way humans perceive spacemeans also to know how to represent space in virtual environments.But what is human knowledge of space?


Kuipers [Kui88] divides knowledge of space into different levels:

Sensor motor level: also defined as knowledge in the world, thislevel requires physical and sensorial access to the environment.It is constituted by view-action sequences (i.e. stimulus responsepatterns) and implies interaction with the environment (look forand find a target; move towards a target).

Representation of the space in memory: representing the prob-lem and reasoning on the basis of representation requires spa-tial memory and a representation of the environment requiresspatial inference. This can be considered to as knowledgein the head and can be divided in procedural level (sensori-motor schemata that combine various viewaction sequences);topologicalorientational level (contains places and their connec-tions); metrical level (contains information on distances and direc-tions and information that can be local or global, this last informa-tion can refers to orientation) and absolute space representation.

Arentze et al. underline [AHT01] that humans acquire spatialknowledge and beliefs directly via sensor motor system that operateswhile they move in the world and that many kinds of knowledge areimplied in the development of a knowledge about a specific space. Firstknowledge about landmarks is acquired, then knowledge about routesconnecting these landmarks is acquired and finally a survey knowledgecombines knowledge about different routes.

Landmark is an important concept, Presson and Montello [PM88]define a landmark as any distinct object or feature that is noticed andremembered. A second meaning (that can be defined relational or func-tional) considers a landmark a spatial cue associated with a location,target object or behavioral contingency. More generally, the role oflandmarks in our knowledge of space consist in their being featuresthat are relatively better known and define the location of other pointsbut in the spatial information content are really important the quali-tative relations as to say close to, connects to etc. These issues are allimportant if it necessary to consider different expertise of pedestriansthat move in an environment that they may know or they might do notknow.

Spatial Problems and WayFinding: Cognitive psychology takesinto consideration also spatial problems that normally an individual hasto solve: grasp an object; follow a wall; find the shortest route; taking


a shortcut; build a spatial configuration under constraints and wayfinding.

Weisman [Wei81] identifies 4 classes of environmental variablesthat influence wayfinding in an unknown building: visual access; ar-chitectural differentiation; signs; plan configuration.

Mark et al. [MFC+99] instead propose an hypothetical informationflow model for spatial and geographical cognition that is articulated in:acquisition of geographical knowledge; mental representation of geo-graphical knowledge; knowledge use and communication of geographi-cal information.

Space Concepts: Which aspects of space (spatial information con-tent) are needed to be represented? Spatial concepts can be divided asfollowing (see [Ber98]):

Topological: the space under consideration is a set of points. En-tities are conceptualized in terms of regions. Each region definesthree subsets of space that are its interior; its boundary and its ex-terior. The relation between two regions can be disjoint, externallyconnected, partially overlapping, equal, proper part, tangential.Hierarchies are often described as graphs and the whole space isdescribed by the root node of the tree.

Orientational: orientation refers to the orientation of somethingin relation to another specific object, orientation often coincideswith an order. A point is located with respect to other points andthe tree possible relations it can have to another point are major,equal or minor.

Metrical: metrical space is characterized by distance, a functionthat assigns to every two entities A and B of the space a realnumber. This function satisfies the axioms of positive definiteness,symmetry and triangle inequality (the sum of the distance of twosides of a triangle is major than the other side).

Relational and Positional: Relational and positional representa-tion of space refers to relations between entities. Spatial Relationscan be vectorial, topological, orientational and logical. Relationsare usually binary because the concepts that one wants to expressare always with two arguments while a positional representationconsists of elements of the space under consideration which actas positions (location) and entities located at certain of these posi-tions.


Mental Maps and Cognitive Collages: Humans are thoughtto form cognitive maps of their environments for use in navigation.Lynch [Lyn60] developed a set of generic components which he hypoth-esized are used to construct cognitive maps of urban environments:

Paths: channels by which people move along in their travels(roadsand sidewalks).

Edges: edges, are all other lines not included in the path group(walls, seashores).

Nodes: sections of the environment with similar characteristics,for example, a group of streets are points or strategic spots wherethere is an extra focus. Examples of nodes include a busy intersec-tion or a popular city center.

Districts: logically and physically distinct sections of the city,usually relatively substantial in size, which have an identifyingcharacter about them.

Landmarks: external physical objects that act as referencepoints. Landmarks can be a store, mountain, school, or any otherobject that aids in orientation.

Another theory instead speaks of cognitive collages (Tverskyin [MFC+99]). This theory introduces the term to stress the factthat mental representations (that drives judgement and wayfindingprocesses) are fragmented and multimedia. It seems that spatial knowl-edge does not have the metric qualities that maps have. The organiza-tion of space undergoes though to: economic categories; geographicalboundaries; functional grouping (of different kinds).

Representation of Space: The problem of representation of spacethat takes into account perception an cognitive capabilities of pedestri-ans has been considered by Penn A. and Turner A. [PT02] in their workof Space syntax.

Space sintax derives from a set of analytic measures of configurationthat have been shown to correlate well with how people move throughand use buildings and urban environments. Space syntax representsthe open space of an environment in terms of the interdivisibility ofpoints and space. Kerridge [PT02] proposes agents4 with limited envi-ronmental perception of their immediate vicinity, by superimposing a

4A definition of agent will be given later in chapter 3


grid on space and organizing obstructions so that and agent can employlocal behavioral rules.

Space syntax methods were first developed to compare the similar-ities and differences between built environments at building interiorscale and urban neighborhood scale. The plan of an environment is rep-resented as a map in which all longest lines of sight are drawn. The mapis translated into graph in which a line is represented by a node and in-tersections between lines are shown as links between nodes. Measuresof the graph are made in a way that allow to assign them back as vari-ables associated with the location of each line in the original map. Thiskind of representation captures only the geometry of the configurationof space in the environment. The ability to predict movements with thisrates depends to the accuracy of assignment of degree of importance tothe attractors. Many studies revealed a lots of failures in this approach.Space syntax aims at describing some areas in a city in the sense of in-tegration and segregation. A location is more integrated if all the otherplaces can be reached from it after going thorough a small number ofintermediate places5. With such parameters the movement pattern ina city can be understood and predicted. For example, the better a line islocal integrated, the busier it will be.

Other methods of representations replace the line map with a graph.Graph discretisations are used most commonly for simulations with theaim to simulate wayfinding situations in a large scale context, usuallyanother form of space discretisation, a grid, is used when the focus isa building, or a square. Another classical representation of space isinstead a uniform grid of identical cells.

For Michael Batty [Bat01b] spatial models at any scale imply in-teractions based on movements of people, goods, ideas, between two ormore locations which are usually classified as origins and destinations.Michael Batty remarks that these movements cover processes operat-ing at different time scales and different speeds, from slow (in years) tofast (in minutes and seconds) and at a human scale, interactions occurin different sized areas, each implying different dynamics, purposes andgoals.

5Connectivity is the number of lines connected to a line; control value of a line ex-presses the number of choices each line represents for its immediate neighbors as a lineto move to; depth can be defined as the number of steps from a considered node to all theother nodes. Thus a node can be said to be deep or shallow; integration of a node is ex-pressed by a value that indicates the degree to which a node is integrated or segregatedfrom a system (global integration) or from a part of a system (local integration).


2.5 SOCIAL PSYCHOLOGY

Social Psychology is a discipline that sometimes overlaps with sociol-ogy, in fact, some of the considerations, theories and researches aboutcrowd that have been presented in the section related to sociology, canbe considered also as social psychological studies. In this section socialpsychological theories will be taken into consideration mainly for whatregard the behavior of a group and emotions. These two topics are par-ticularly interesting for the work developed in this dissertation.

2.5.1 GROUPS

The study of the behaviors of groups is important because people rarelymove alone and rarely they act without taking into consideration theobjectives of group to which they belong. Also in very crowded situ-ation people move in groups or two, three or more persons. In manycrowded situations people take part as a member of structured group(i.e. supporters of a football team, families, school childrens) and be-have in relation to the role that they have inside the group (e.g. seefigure 2.1). Moreover people can spontaneously aggregate in groups oras a consequence of the rise of a leader in the crowd.

Figure 2.1: People walking aggregated in a group.

2.5 SOCIAL PSYCHOLOGY 25

But what is a group? Kurt Lewin [LLW39] defines a group as a re-ality that is not reducible to the individuals that compound it. In theopinion of Lewin a group is a determinate system of interdependencebetween: the members of the group; other elements that are part of thefield; the environment (context) that surrounds the group; the finalities,norms, perceptions about the external environment; differences in roles,status and so on. Forsyth [For83] defines a group as something that isconstituted by two or more persons that have a social interaction and be-tween whom exists a mutual influence. A group is also characterized bysome specific norms. Some of these are established by the group and for-malized, other are informal. Sherif [She36] states that the group normis an original product of the group and is interiorized by the subjectsthat compound the group. Baron and Byrne [BB97] explain that sin-gle subjects change their behavior to accomplish the social norms of thegroups and factors that influence conformism in small groups are normsformation (the more is shared the more is resistant to the change); con-formity to the major part of the group (group influence acceptation) andthe obedience to the authority6 (for classics studies on the obedience toauthority see Milgram [Mil63]).

A group has a structure that allows the relations inside the group tobe stable. The members of a group share common objectives that helpthe group to stay together, and have the perception to be part of thegroup. Members of a group have in fact a criteria to differentiate whobelongs to the group and who does not. A group moreover is charac-terized by cohesion, tension, ideology, (with a particular degree of ho-mogeneity). But why people joint into groups? Many reasons can beidentified. The group transmits a sense of security to single individu-als and it also recognizes a role and a status to the individual, for thisreason the belonging to a group can enforce self estimation and positivesocial identity. A group satisfies social necessities of a person but alsoallows to reach objectives impossible for single individuals.

A group is ruled by specific norms that can be of different kinds:

Connected to the Performance: what results or production hasto be produced or which actions have to be performed;

Connected to Appearance: i.e. kinds of clothes that has to bewore, when you have to appear occupied, when it is allowed torelax, loyalty towards the other members of the group;

6The conclusions of Milgam were that obedience to authority that can also lead tocommit some crimes does not imply a lack of morality in the obedient person. Milgramdescribes the state of the obedients as an agentic state in which they see themselves asagents of the experimenter, of the authority. This state it is difficult to interrupt.


Informal Rules: with whom to joint or to go to eat, friendshipsinside the group etc.

Assignment of Resources: rules can also regard the assignmentof resources inside the groups (i.e. to specific teams etc).

Relations inside a Group: J.L. Moreno in 1934 develops the So-ciometry (i.e. see [Mor46]), that consists in a metric analysis based upongraph analysis aimed at measuring affective relation inside a groupthrough the construction of weighted graphs called sociograms). So-ciometry is the set of techniques that allows to represent the forces ofattraction (positive tele) and rejection (negative tele) that hold inside agroup. Moreno uses the term tele to indicate the sociogenic unit thatfacilitate the transmission of our social inheritance. A tele is the con-crete that keeps the group together, is the most simple unit of feelingthat is transmitted from an individual to another. Relations are rep-resented by sociogram. A sociogram represents the nature and the in-tensity of the relations that holds between individuals inside a groupthat, under Morenos perspective, choose how to relate with the mem-bers of the group following criteria of: sympathy, perceived competence,assonance and dissonance, roles, representation of the other. Sociometricallows to determine: the structure of a group, the cohesion of a group,leaders and subleaders, opinion leaders, diadic or triadic relations be-tween members of a group etc.

Groups and leadership: Sometimes groups follow a leader. Theclassical studies state that the leader is an exceptional human beingthat shows specific qualities like ambition, energy, desire to direct, in-tegrity, intelligence, self confidence, knowledge of the role that he or sheoccupies. Nevertheless none of these characteristics can guarantee aleadership and probably the integration of these classic perspectives ina framework that considers leadership as an aspect of a group phenom-enon is needed, in fact the construction and distribution of roles insidethe group leads to the appearance of the leader.

In literature can be found many definitions of leadership. In theopinion of Tannenbaum et al. [TWM61] leadership is a process in whicha person influences the conduct of other people by the profit of sometargets. Gioia [Gio86] states that the essence of the leadership is con-stituted by the ability to offer definitions of reality that can achieve afollowing consensus, while leadership is considered an aspect of person-ality by Stogdill [SC57] and Geier [Gei67].


Groups and movement: In section 2.3 a list of some rules of pedes-trian movement are presented. Now I present what seems to be themovement abilities of people that belong to a group, extracted by ananalysis of what exposed above in this section. Table 2.3 resumes thesecollective abilities that are presented below:

Aggregation: pedestrians can aggregate into groups. This aggre-gation can occur spontaneously or is due to an external event (e.g.the rise of a leader).

Keeping cohesion: when people are part of a group, they canmove towards a common direction, keeping the cohesion inside thegroup. This movement is not similar to a crowd stream, but itimplies an alignment of pedestrian orientation and a maintenanceof a closed distance among the members of the group.

Following the leader: when a group has a leader, he can chosethe direction the group has to take, and the other members areable to follow him.

Group movement abilitiesAggregation

Keeping cohesionFollowing the leader

Table 2.3: The main movement abilities of pedestrians that belong to agroup.

2.5.2 THE ROLE OF EMOTIONS

According to the common sense, the term emotion means a set of affec-tive states, charactetized by a limited duration, a high intensity, an ex-ternal or internal cause, a specific cognitive content. It is a process witha beginning, a duration, and a phase of attenuation. It is expressed byphysiological changes, facial expressions and behaviors typical for eachemotion.

One of the first theory about the emotions it was developed byLange (1885) [Lan85]. According to the author the visceral and somaticchanges are the base of the emotional experience. In the Langes theorythe sequence perception of an event, production of an emotion, conse-quence on the organism, are considered in the inverse sense: emotions


are caused by changes occurring into the viscera. The empirical con-sideration sustaining this theory is that the main emotions (anger, sad-ness, fear, surprise, disgust, happiness) have different somatic expres-sions. Other studies remark the close connection between the corporallanguage and the emotional state. For example, Ekman ( [Ekm82]) inan intercultural study identifies the set of fixed facial expressions foreach the main emotions.

The first to object the thesis of Lange is Cannon (1927) [Can27]. Thetheory of Cannon defines emotions as behavioral states that can be char-acterized by the intensity of their activation. According to Schachterand Singer (1962) [SS62] an emotion need both the perception of a stateof arousal7, and the correct interpretation of the event as an activationof an emotion. Therefore the emotion should be the result of a cognitiveprocess.

Leventhal and Scherer [Sch84] in 1987 propose a theory that unifyall the component influencing an emotional experience. An emotion isdefined as a sequence of state changes occurring into the following subsystems of the organism:

Information processing (evaluation of the situation);

Support (omeostatic control of the internal equilibrium);

Behavior organization (orientation of the actions);

Engine subsystem (action execution);

Supervisor (evaluation about the other subsystems).

All the changes occur synchronously and independently from the others.One of the main original theory are the one proposed by Lazarus in

1966 [Laz66]. The author introduces the concept of coping: the set ofmodality used to answer to the environmental stimuli. Lazarus distin-guishes between two types of coping. The first type is a direct reactionto a stimulus that require a quick answer (e.g. danger or threat situa-tions). The latter one represents a cognitive process that it is an analy-sis about the possible success or the fail of the own actions. The processschema (see figure 2.2) is:

1. The environment produce a stimulus;

2. The stimulus is perceived by the individual and classified;

3. Both cognitive and reactive elements merge into the coping phase.


Figure 2.2: The cicle of interaction: from the environment stimuli to theindividual answer.

In 1984 Russel [FR84] proposes a very famous model for the repre-sentation and classification of the emotions. His model is still one of themore considered. Figure 2.3 shows the model of Russel. Each emotionis represented by a point into a space where the two axes represent thedimension of the pleasantnessunpleasantness (the orizontal axis) andthe dimension of the nervousnessrelaxation (the vertical axis).

The presented theories are some of the most significative ones de-veloped in the second part of XX century. Many other similar theorieshave been developed. In the following a summarizing classification oftheories based on their affinity are presented. This classification is per-formed by DUrso and Trentin (1998) and published in [DT98].

Interpretative theories: (Schachter and Singer [SS62], 1962;Mandler [Man84], 1984) where emotions are composed by arousaland by a cognitive interpretation of the situation.

Theories of cognitive evaluation: (Arnold [Arn60], 1960;Roseman [Ros91], 1991; Scherer [Sch84], 1984; Lazarus [Laz66],1966) where cognitive aspects are part of the experience and of theemotional behavior. The approach of these theories is focused on

7The term arousal means the intensity of the physiological activation of the organ-ism


Figure 2.3: The circular model of Russel.

the detection of the mental content that makes an experience tobe lived by an emotion.

Theories of cognitive representation: (Fehr and Rus-sel [FR84], 1984) where the conceptualized emotional experiencesare scripts stored into the mind. These structures regulate peo-ple expectations in relation to the environment, and the encodingprocess of the significance of the events.

Social aspects of the emotions: When we feel an emotions, we areseldom alone; the other people are around us and there are emotions inthe most relevant moments of our social interactions. Besides its easyto understand how the cultural environment influence our expressionof emotions. Harre [Har86] (1986) asserts that the language and thesociety are decisive for the emotive experience of the individuals. In histhesis he notices how some emotions have change their common inter-


pretation with the change of cultures. For example the pietas: compre-hension, indulgence, permissiveness, was perceives as a virtue in thepast, while nowadays it has a negative meaning. Averill [Ave86] (1986)defines an emotion as a transitory social role. He says that the socialrules have influence on the process of evaluation of the stimuli, on theorganization of the possible answers, and on the control of the behavior.According to Averill the principles regulating the emotions are:

1. The evaluation rules define how a situation are perceived andevalued;

2. The behavioral rules establish how an emotion must be ex-pressed;

3. The prognostic rules regulate the duration and the intensity ofthe emotion;

4. The attribution rules explain the emotion in relation to the so-cial and cultural context.

Emotive contagion: Emotive contagion refers to a form of involun-tary reaction expressing in the imitation of the behavior, the gesturesand the feelings of the other people. Psychologists assert that the emo-tive contagion is the first empatic manifestation. A baby in the earlierpart its life are not able to distinguish the self from the notself. There-fore when he perceives the emotion of some other people he interpretsthe emotion as an internal event. Hatfield [HCR94] (1992) defines theemotive contagion as a set of social and behavioral phenomena com-posed by the following components:

Cognitive conscious process: the individual imagines what hewould feel if he was in the same situation of the other person andtherefore he arrives to feel the same sensations.

Emotive conditioned and notconditioned reactions: thecontagion is the result of association processes. For example if afather often hits his son, the only sight of the father could causethe rise of a fearful state in the boy.

Imitation: individuals try always and automatically to imitatethe posture and the facial expressions of the other people in orderto synchronize with them (e.g. see figure 2.4).

Since the year 1940 the social psychologists try to understand thecauses that make an individual more inclined to imitate the emotions ofthe other people.


Figure 2.4: In this famous Gordon Allports photo we can see thespetators of the Irish Bowling Season that imitate the gestures of thelauncher.

One of the aspects are the momentary internal disposition: Itwas proved that happy individuals are more aware of the otherpeople than the unhappy ones.

Another aspect is the cultural environment: Markus and Ki-tayama [MK91] (1991) assert that occidental cultures remark theindividuality and the unicity of each man. People of these culturesare more inclined to feel themselves as an unique individual dis-tant from the others. On the other side other cultures like Chinaand Japan remark the role of the individuals into the community.These people is more subjected to the emotive contagion.

The last aspect is the social context: An individual is more in-clined to comprehend and to feel the emotion of another personwhen between them there is a love relation (e.g. a man and awoman, a mother an a son). Besides Hatfield [HCR94] says thatthe same disposition occurs also between a man and another thathave power on him. But in this case the disposition goes in an

2.6 CONSIDERATIONS 33

unique direction: only the subordinate individual has a particlardisposition in the comprehension of the feelings of his chief.

2.6 CONSIDERATIONS

This heterogeneous overview reflects the complexity of this kind of stud-ies, and underlines also how far we are from an unique and clear de-scription of human behavior in crowding situations. Crowd is a systemcharacterized by phenomena of self-organization that involves the sin-gle individuals that compound it. Single individuals are influenced, butalso influence other individuals. Therefore, the simulation of a humancrowd behavior must emerge from the modeling of single individualsthat compound it inside the context where the crowd acts.

A model of the crowd phenomena must consider a lot of aspects. Atthe level of single pedestrians, a real individual moves in an environ-ment; its movement will have some physical characteristics, such as awalking speed, a tendency to avoid collision with other human beings,a maximum walking range and so on. Anyway, people are not only in-dividuals with mass, speed and orientation. It is clear that modelinga single individual, in a way that reflects or reproduce exactly what areal person would do in a given context, would mean also to define anamount of characteristics that are incredibly complex. A real individualhas an internal world, made of feelings, aspirations, sensations, gusts,believes, relations, perceptions, emotive states etc. that influence itsbehavior in relation to the context. Besides pedestrians interacts withother pedestrians and aggregate into groups and crowds. The emer-gent behavior of these collective entities (i.e. the dynamic of a crowdwhose characteristic phenomena are resumed in the tables 2.2 and 2.3)is another aspect that would be considered in a model with the aim ofstudying crowd phenomena.

CHAPTER 3

APPROACHES TO CROWDMODELING AND SIMULATION

Different modeling techniques have been adopted to represent pedes-trian and crowd dynamics. Pedestrians can be considered for instanceas particles subjected to forces, walking and goaldirected agents, livingreactive beings, socially interacting individuals or emotionally guidedentities.

Empirical studies on crowds often have had the aim of definingguidelines for the design of environments and pedestrian facilities(Pauls [Pau84]) and for planning the operation of systems influencingpedestrian behaviors (Davis and Braakma [DB88]). However, crowds ofpedestrians are characterized by selforganization effects which werenot considered by early modeling approaches, which were thus unable torepresent and reproduce significant phenomena that can emerge fromthe dynamic interaction of groups of moving entities (i.e. persons, inthe case of human crowds) which share a limited space. The most rele-vant approaches tackling this issue are focused on the microsimulationof pedestrian crowds characterized by an active walker approach. Inparticular, in this kind of approach, pedestrians are influenced by theenvironment but are also able to cause local changes that might havean influence on the behaviors of other pedestrians.

For these reasons, this dissertation focuses on the microsimulationapproach.

The aim of this section is to briefly introduce the main approachesto crowd modeling.

Microsimulation models for pedestrian dynamics can be classifiedinto three main classes: forcebased models, models based on CellularAutomata (CA) and models based on Multi Agent Systems (MAS). An

36 APPROACHES TO CROWD MODELING AND SIMULATION

introductive description of these three approaches can be found in thefollowing sections (3.1, 3.2 and 3.3). For each approach some significantmodels are briefly presented. At the end of each presentation a summa-rizing table will show some characteristics of the model, and on someof these characteristics a personal evaluation will be displayed. Theevaluation is expressed on a scale of five steps, from a very low perfor-mance to a very high one. It is based on an interpretation of the citedpresentation papers that can be found in the literature.

The considered table entries are:

1. Spatial representation: if the space is continuous or discrete.

2. Finality: if the model is focused on the representation of somegiven scenarios.

The evalued characteristics are:

3. Heterogeneity: how the model can represent heterogeneous ele-ments and in particular a heterogeneous behavior for pedestriansintroducing different roles and individual characteristics.

4. Environment complexity: how the model is able to managesimulations of the pedestrian movement through complex andstructured environments (an example of a complex environmentcan be seen in figure 3.1).

5. Largescale: the ability to represent a large number of pedestri-ans.

6. Versatility: the independence of the model from a given modeledscenario, and the ease in changing the elements of the environ-ment.

7. Collective behavior: the degree of collective behaviors that themodel seems to be able to represent and manage (see tables 2.2and 2.3 for a list of collective abilities of pedestrians).

The second part of this chapter (see section 3.5) presents in depththe referring modeling approach chosen for this work and shows themotivation of this choice and the results of some experiments performedin order to test the suitability of this approach on some well knownscenarios of pedestrian dynamics.

3.1 FORCEBASED APPROACH 37

Figure 3.1: An example of a structured complex environment. The fig-ure shows a set of rooms (numbered from 3 to 13) connected by a corri-dor (number 2) and positioned around a larger room (number 1) wherethere is the main exit (number 14). The only door connecting the cor-ridor with the set of small rooms and the big room is positioned at theopposite side of the main exit (14). The black points in the figure rep-resent the pedestrians. If the pedestrians in the rooms (e.g. 7 and 13)want to reach the exit (14) they must go toward the opposite cardinaldirection.

3.1 FORCEBASED APPROACH

The forcebased approach includes models where the dynamics of spa-tial features is studied through spatial occupancy of individuals, rep-resented as moving particles subjected to forces: each pedestrian is at-tracted by its goal and repelled by obstacles. One of the most successfulapproaches is Helbings Social Force Model [HM95] [HKM97]. Helbinghas developed a series of models which are built around social forces andare related to ideas derived from fluid flow, particle systems and flock-ing [HBJW05]. Similar approaches are the one of Hoogendoorn [HB00]that exploits gaskinetic metaphor applied to traffic flow.

This approach reports some analogies of crowds with gasses, fluidsand granular media. Footprints in the snow, for example, look similar tosteamlines of fluids while at border lines between opposite direction ofwalking one can observe viscous fingering. The analogies are also the


emergence of pedestrian streams through standing crowds that seemanalogous to the formation of river beds etc. Helbing underlines thatFluid dynamic analogies work better in normal situations while granu-lar aspects become important in panic situations [HFV00].

Helbing states that for each component (agent position, goal posi-tion, position of obstacles, position of other pedestrians) a force is asso-ciated that pushes the agent towards a specific direction, and the resultof these forces will decide the final direction:NewPosition = OldPosition+ DesiredPosition+ GeometricRepulsion+SocialRepulsion+ SocialAttraction+ a constant.

Comments: This approach is one of the most used for pedestrian sim-ulation, and it has the advantage of being based on well known math-ematical formulas inspired by the world of physics. The method basedon potential fields uses vector representation where any point of spacehas magnitude and direction, and the dynamics of a particle subjectedby this field is well known and computable by the use of appropiate for-mulas. Unfortunately, this approach also does not lack faults. One ofthe problems of this approach is that in order to produce a reasonablebehavior, weights of the forces must be accurately balanced. Sometimesthe field that pushes away from obstructions can prevent the solutionof any path. Local minima make the agent stuck. Another problem isthe solution of limit situations as a pedestrian subjected to two oppositeforces of the same intensity.

Following is a presentation of some representative models based onthis approach.

3.1.1 MAGNETIC FORCE

This model was born in 1979 by Okazaki, Matzushita and Ya-mamoto [OMY79]. The basic idea of this model is to consider each pedes-trian (and each obstacle) as a positive charged particle, while the targetis a negative charged object. It is assumed that about speed each pedes-trian cannot overcome a given threshold to avoid excessive acceleration.The charge to assign to each pedestrian is arbitrary, and the movementis given by Coulombs law:

F =

kq1q2r

r2

where:F = is the magnetic force;k = is the Coulombs constant;


q1 = is the magnetic charge of the pedestrian;q2 = is the magnetic charge of the obstacle/target;r = is the distance vector between the pedestrian and the obsta-

cle/target.Therefore the acceleration vector a , useful to avoid collisions, is cal-

culed as a = V cos() tan()

Figure 3.2: Repulsive force used to manage the collision avoidance

where (see figure 3.2):considering

RV = the relative velocity of the entity A with respects

to B;a = is the acceleration acting on A to modify RV direction into AC;V = is A velocity; = is the agle between

RV and

V ;

= is the agle betweenRV and AC.

Comments: Table 3.1 shows an evaluation of Magnetic force modelaccording to some given charcteristics. As all the other Forcebasedmodels, the Magnetic force one focuses on the representation of the dy-namics of motion of single pedestrians. Pedestrians are considered asparticles (very low heterogeneity). The continuous spatial representa-tion and the well represented collision avoidance due to Coulombs re-pulsive interaction, can manage pedestrian movements through an ir-regular spatial structure (high environmantal complexity). This model


Spatial representation continuousFinality evacuation

towards an universal directionHeterogeneity very low

Environment complexity highLargescale mediumVersatility very low

Collective behavior low

Table 3.1: Magnetic force summarized information

is computationally expensive (medium largescale), in particular inpresence of many pedestrians. Moreover, it presents the problem of as-signing a charge to the objects. The charge must be assigned only asthe result of a study of the environment to be modeled and the globalattractiverepulsive field that the charge distributed in the enviromenthas on every portion of walking space. This characteristic makes themodel extremely dependent on the scenario that it is representing (verylow versatility). At the end the Magnetic force model does not have par-ticular elements to represent pedestrians belonging to a group (low col-lective behaviors). Although some phenomena of crowd dynamics (e.g.queuing, streaming) can be observed by the emergence of the behaviorof the single pedestrians.

3.1.2 SOCIAL FORCE

This model has been developed by Helbing and other researchers since1995 [HM95].

Even in this model each pedestrian is subjected to forces that mo-tivate its movements. The pedestrian is attracted by the target andrepulsed by other pedestrians and obstacles.

The force is expressed by:

mvi(t)

t= m

v0ei Vi(t) + (t)

+

j( 6=i)fij(xi(t), xj(t)) + fb(xi(t))

where:xi(t) = the position of the pedestrian i at the time istant t;vi(t) = the velocity of the pedestrian i at the time istant t;


m = the mass of the pedestrian (m/ can be considered as a frictionconstant);

v0 = the ideal pedestrian velocity without external interactions;ei = direction of the pedestrian; it can be calculed by the followingexpression:

ei =xi

0 xi(t)xi0 xi(t)

i(t) = individual velocity variation;fij = repulsive force between the pedestrian i and j; it can be cal-

culed by the following expression:

fij(xi(t), xj(t)) = OA(dij D)B

where:B = a constant;dij = the distance between the pedestrian i and j;D = the diameter of the space occupied by the pedestrian j;A = a decreasing monotonic function.fb = the interaction forces between pedestrians and obstacles, given

by:

fb(xi) = OA(di D/2)B

where: di = the distance from the nearer wall.Some extensions of this model introduce specific formulas to repre-

sent the trail formation phenomenon (see [HSKM97]). The trail for-mation mechanism is inspired by the pheromone communication usedby ants for their selforganization movement through the environ-ment1. Therefore, according to this extension a moving agent contiu-ously changes its environment by leaving markings while moving.These markings can, for example, be imagined as damaged vegetationon the ground. The spatiotemporal distribution of the existing markingswill be described by a ground potential Gk(r, t), where k can distinguishdifferent kinds of markings, and t is the time. Each marking has a dura-bility whose mechanism is inspired by the chemical decay of the antspheromone trace. Large values of Gk(r, t) represent the formation of atrail.

1The pheromone mechanism has inspired a lot of scientific works whose aim is themodeling of the movement of swarms and the study of their selforganization. See forexample [BDT99].


Spatial representation continuousFinality general pedestrian movement

Heterogeneity very lowEnvironment complexity high

Largescale mediumVersatility very low

Collective behavior medium

Table 3.2: Social force summarized information

Comments: This model reproduces a behavior similar to the magneticforce model, but it does not need any arbitrary value. It suffers fromthe limits typical of the forcebased models, but it is one of the bestand most used models for the microsimulation of pedestrian dynamics.The values shown in table 3.2 are almost the same as in table 3.1 ofthe Magnetic force model because of the similarity of the approach. Theonly different value is related to the Collective behavior. The mediumvalue for this entry is due to the presence of the extensions for the use ofpotential force fields to define the trail formation phenomenon. This el-ement of the model is very interesting and can represent some phenom-ena of crowd dynamics (e.g. the selforganization of people in lanes),but it is not appliable to many others (e.g. the aggregation and disper-sion of people into dense groups and their compact movement towardsa common target).

3.2 CABASED APPROACH

Cellular Automata (CA), introduced by John Von Neumann in 1966, area class of spatially and temporally discrete mathematical systems char-acterized by local interactions [Wol86]. Even if the interaction is basedon simple local rules, the resulting structures from the CA evolutionmay be extremely complex [Wol94] [.Wo84]. In fact CA have been usedsuccessfully to model spatial dynamics across the spectrum of appliedscience and vast literature has been devoted to the area including ap-plications to physics (fluid dynamics, reaction-diffusion, solidification ofcrystals, interfacial diffusion fronts), environmental processes (popula-tion genetics, interrelationships between prey and predators in ecosys-tems, plant growth, propagation of infectious diseases, the effects of fireand dispersal on spatial patterns in forests) or engineering (geographi-cal information systems, routing traffic in an urban area, image process-

3.2 CABASED APPROACH 43

ing, cryptography, generating random numbers) [BX94] [WE92].A cellular automaton consists of a regular array of identically pro-

grammed units called cells which interact with their neighbors, subjectto a finite set of prescribed rules for local transitions. All cells form aregular spatial lattice. Time progresses in discrete steps. The state of acell at time t + 1 is a function only of its own state and of the states ofits neighbors at time t. All cell states are updated synchronously. In or-der to establish a rigorous mathematical definition, we need some basicnotions.

Lattice: A ddimensional lattice denoted by L, consists of a periodicpaving of a ddimensional space domain. Every cell of L, denoted byc, will be indexed by a tuple (il, i2, ..., iu) of integers. The definition ofa cellular automaton requires the lattice to be regular, i.e., invariantwith respect to translation in d independent directions. We can con-sider various possibilities for one, two, and three dimensions. In theone-dimensional case (1D), cells are ordered along a chain (or may bewrapped into a torus for periodic boundary conditions). For the two-dimensional case (2D), there are three regular lattices depending onthe cell shape, namely triangular, square, and hexagonal lattices.

Let c and c be two cells in L. We define a path between c and c anddenote it by (c, c), as any polygonal line starting from c and ending atc, composed of segments joining the centers of adjacent cells. Such apath is not unique and we consider the set of all possible paths whichconnect c to c, denoted by C(c, c). We associate its length defined by thenumber of cells to each path, except the cell c, connected by one path(c, c). It will be denoted by l(c, c). The mapping given by

L(c, c) = min{l(c, c)|(c, c) C(c, c)}defines a distance on L L which is equivalent to the metric on L.

Neighborood: Let L be a regular lattice, c L and L0 be a subset ofL. Then L0 is said to be cconnected if

c L0, (c, c) C(c, c)We introduce a cell neighbourhood as a set of cells which affect the

evolution of the central cell. We shall only concentrate on the neigh-bourhoods which form cconnected sets. More general cases may alsobe of interest for specific problems. A neighbourhood is then defined bythe mapping

N : L Ln


which makes a relation between the cell c and n neighbouring cellsc1, c2, ..., cn. The integer n (or the number of neighbours) will charac-terize the size of the neighbourhood. The neighbourhood may be punc-tured, i.e., c / N(c), or may include the central cell, i.e., c N(c). Theradius r of N(c) is the smallest nonnegative integer such that

c N(c), L(c, c) r, i = 1...n

State set: It is a nonempty finite and ordered set of state values whichmay consist, for simplicity, of integer numbers. It will be denoted by Sand its power, respectively, by card(S) = k. The state set is usuallysmall (up to five elements) but a larger number of states can realize abetter approximation of continuous dynamics. The state set S may havean algebraic structure or not. In most cases, it is cyclic and the statevalue is defined modulo k. Cell states are given at discrete times t =0, 1, 2..... The state of cell c at time t is denoted by st(c) and the state of itsneighbourhood by st(N(c)). Then we have for every c L, st(c) S, andst(N(c)) Sn. st(N(c)) represents the neighbourhood configuration attime t and st(L) represents the configuration of the cellular automatonat time t.

Transition function: We examine now one of the most importantpoints in cellular automata modeling, i.e., the transition function. Thetransition function governs the evolution of the system itself. It maybe given by an analytical function, a matrix, or a set of transition rules.The transition function f may be considered as a mapping Sn S givenby

f : Sn Sst(N(c)) st+1(c)

where st(N(c)) is the state of the neighbourhood N(c) at time t andst+l(c) is the state of the cell c at time t + 1. The relation

st+l = f(st(N(c)))

is the state equation of the cellular automaton. It depends on the latticegeometry, the neighbourhood, and the state set, and may be determin-istic or probabilistic.

Global definitions: Giving a formal definition of a global cellular au-tomaton:

A cellular automaton is defined as a tuple A = (L,S,N, f)


A configuration of a cellular automaton, at time t, is the mappingsf : L S which associates to every cell of the lattice L an elementof the state S = {s1, ..., sk}

The dynamics of a cellular automaton is determined by a globalfunction F : SL SL which changes the configuration st at time tinto a new configuration st+1 at time t + 1

The evolution of each cell is determined by the transition functionf : Sn S that brings st(N(c)) st+1(c) where st(N(c)) is thestate of the neighborhood N(c) at time t of the cell c

More recently, with the emergence of powerful massively parallelarchitectures, a lively interest in CA models and their extensions hasbeen observed particularly for inhomogeneous environments and com-plex dynamics. Unforunately one of the more problematic extensions ofCA models is the neighborhood expansion in order to obtain action atadistance among system entities. Discrete models, based on CA, arecommonly used in these areas, mainly for the explicit representation ofspatial structures, but also because they are a very simple and elegantmodel. Nonetheless the management of action atadistance representsa weakness of this model. In fact the interaction between cells is limitedby the definition of cell neighborhood, and the influence determined bydistant entities can be obtained as a consequence of sequential appli-cations of transition rules. The most commonly used solution to obtainthis kind of effect consists in varying the concept of neighborhood be-yond the simple Moore and Von Neumann definition. This and otherkind of modifications (to lattice structure and cell state) are often verydeep and the resulting models can hardly be still considered CellularAutomaton.

Comments: Peculiarities of CAbased models are the ex-plicit representation as a regular grid of the modeled environ-ment [Sch02] [BKK+02] [SS02], where the size of each cell is theminimal space occuped by a pedestrian (e.g. 40 40cm). The state ofthe cell includes the representation of the presence of individuals, ofenvironmental obstacles and the direction of pedestrians goals throughstatic and dynamic potential fields . The cell local interaction involvedin CA state transition function therefore also represents pedestrianmovement by cell state change (e.g. an occupied cell becomes emptyand synchronously an adjacent empty cell becomes occupied).

In the context of pedestrian and crowd dynamics, approachesbased on Cellular Automata are demonstrated to be particularly ad-


equate [BA01]. The success of CAbased approaches derives mainlyfrom the fact that they are simplier to understand and use by experts ofseveral application contexts.

However, they suffer from the limitation of considering individualsas homogeneous entities and generally do not provide a support to dy-namism and flexibility of represented situations, while sometimes it ispreferred to introduce some behavioral rules on an individual scale. Ithas to be also underlined that movement in CA models is just an ap-parent movement, as it is just an effect of state transitions of cellson a grid. Another problem of this approach is the representation ofheterogeneus goals influencing pedestrian movements; for this reasonthe CAapproach is usually applied to evacuation scenarios, where allpedestrians are heading toward the exits (examples of evacuation dy-namics works from public spaces are: classrooms evacuation [Klu03],metro stations [MS06]).

Following a presentation of some representative models based onthis approach.

3.2.1 BENEFIT COST

This model was proposed for the first time in 1985 by Gipps and Mark-sjo [GM85]. Its basic idea is that human movement is the result of theevaluation between the benefits and damages in approaching or sepa-rating from objects or locations.

In this model the environment consists in a lattice, and the walk-ing surfice is discretized in cells. How much space a cell represents isthe important question to face considering the level of granularity andexpressivity to obtain in the simulation.

Each cell can contain more than a pedestrian, and in the state ofthe cell there is the indication of the number of pedestrians that are inthat portion of space, and the pedestrians in the neighborhood. Thisnumber can be interpreted as a repulsive force representing the sociallaw according to which two unknown people do not approach each other.

Therefore, the cost of a movement can be calculed as:

S =1

( )2 +

where:S = the cost of approaching to other pedestrians (or other repulsive

objects); = the distance between the cell i and the given pedestrian;


= 0, 4, a constant value minor than the pedestrian diameter (=0, 5m);

= 0, 015 an arbitrary constant.the benefit is given by:

P (i) = K cos(i)| cos(i)| = K(Si Xi)(Di Xi)|(Si Xi)(Di Xi)|(Si Xi)2(Di Xi)2

where:P (i) = is the benefit of approaching to the target. (Its value is 0 if

the pedestrian does not move);K = a constant to modify the balance between the benefit P and the

cost S;i = the angle between the line connecting the pedestrian and the

target, and the line connecting the actual position of the pedestrian andthe cell i;

Si = the target position;Xi the current position of the pedestrian;Di the position of the considered destination cell.Therefore for each neighbor cell can be calculed B = S P (i), and

the cell with the higher value B is the best target for the consideredpedestrian. If two or more pedestrians try to move to the same place,one of them is repositioned to the starting point.

Spatial representation discreteFinality general pedestrian movement

Heterogeneity very lowEnvironment complexity very low

Largescale very highVersatility medium

Collective behavior low

Table 3.3: Benefit cost summarized information

Comments: This model is the progenitor of the other pedestrian dy-namic models. It is very simple, and this is one of the advantages ofthe Benefit cos

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