a multidisciplinary approach to crowd studies
DESCRIPTION
AACIMP 2009 Summer School lecture by Sara Manzoni. "Mathematical Modelling of Social Systems" course. 3rd hour.TRANSCRIPT
A multidisciplinary approach to crowd studies
Dr. Sara ManzoniComplex Systems and Artificial Intelligence research center
Department of Computer Science, Systems and Communication
University of Milano-Bicocca
4th Summer School AACIMP-2009Achievements and Applications of Contemporary Informatics,
Mathematics and Physics
Lecture 1 – 11.08.2009
What is a Crowd? Contributions from social sciences, social psychology on Human behavior and social
collectivities
Some definitions
• “Too many people in too little space” (Kruse, 1996)
• “A gathering of individuals that influence one another and share a purpose, intent or emotional state in a limited space” [Blumer]
• A crowd is a form of collective action: “two or more persons engaged in one or more actions (e.g. locomotion, orientation, vocalization, verbalization, gesticulation, and or manipulation), judged common or concerted on one or more dimensions (e.g. direction, velocity, time, or substantive content” (McPhail, 1991)
What is a Crowd? Contributions from social sciences, social psychology on Human behavior and social
collectivitiesTheories
• Contagion/Transformation Theory (Tarde; Le Bon; Blumer, Canetti)
• Convergence Theory (Berk, Floyd Allport, Neal Miller, John Dollard)
• Emergent Norm Theory (Turner, Killian)
• Value Added Theory (Smelser)
Gabriel Tarde
Gustave LeBon
Robert Ezra Park
Herbert Blumer
Elias Canetti
Neil Smelser
Traditional Theories of Crowd Behavior
Contagion Theory Crowd behaviour is irrational
The crowd • exert an effect on its members • forces individuals to action thanks to anonymity that
encourages people to abandon rationality and responsibility
• helps emotion propagation that can drive to irrational and suitably violent action
Traditional Theories of Crowd Behavior
Convergence theory Crowd behavior is rational
Crowd behavior is • not the result of the crowd itself• carried inside the crowd by specific individuals
• People that would like to behave and act in a certain way come together in order to form and constitute a crowd
• Crowd behavior expresses values and beliefs that are already present in the population (i.e. racist feelings)
• The mob is a rational product of rational values
Traditional Theories of Crowd Behavior
• E mergent/ norm theory Crowd behavior is not fully predictable but it is not irrational
• People in a crowd assume different roles (e.g. some participants become leaders, other lieutenants, followers, inactive bystanders or even opponents)
• Common interests can bring people together in a crowd, but different patterns (of behavior) can emerge inside the crowd itself
• Norms inside a crowd can be vague and changing in the process of aggregation (people state their own rules while participating at the crowd)
• Decision-making has a preponderant role in the behavior of the crowd although external observers may find it difficult to realize
“ the reason why good data on crowd and collective behavior are so scarce is that data are function of theorethical guidance and existing theories provide no guidance; but, useful theories cannot be built in the absence of empirical data ...”
Freely taken from:Clark McPhail, Blumer’s theory of collective behavior: The development of a Non-symbolic interaction explanation, The Sociological Quaterly, Volume 30, Number 3, JAI press 1989
Herbert Blumer 1900-1987
Crowd study: Contributions/Open issues from computer
scienceBetter comprehension of crowd phenomena (crowd study) and development of tools (for crowd study and crowd management)– Data acquisition techniques and technologies
• Direct observation (Stalking, Questionnaires)• Scene analysis • Proximity detection (RF-ID)• Localization systems (GPS, sensor networks)
– Crowd modeling and simulation• Modeling, computational, analysis tools• Simulation and visualization tools
– Knowledge representation• Data representation and analysis • Experts’ knowledge• Available theory/results from social sciences
M ultidisciplinary F ield of
Study
Data acquisition techniques and technologies
Crowd modeling and simulation
Data Acquisition
HOW CAN CROWDS AND INDIVIDUALS BE MEASURED? WHAT CAN BE MEASURED?HOW CAN AVAILABLE TECHNOLOGIES MEASURE CROWDS?
S. Bandini, M.L. Federici, S. Manzoni“A qualitative evaluation of Technologies and Techniques for Data Acquisition on Pedestrians and Crowded”Proc. of Special session “At man’s step”@SCSC07, San Diego, CA
What are we interested in Measuring: Data on the crowd
• Number of people (static or inside a march)
• Density of the crowd• Flow, Pressure and
times of ingress/egress from a place
• Groups movement inside a crowd
• …
What are we interested in Measuring: Data on individuals
• Trajectories in a specific environment
• Walking speed in different situations
• Physical Behavior:– Queuing– Streaming– Group formation– Separation– Cohesion– Imitation– …
Measuring Crowds: HOW?Mature and emergent technologies for data
acquisition
• Direct Observation, interviews, questionnaires, stalking
• Technologies for people positioning and counting– Scene analysis: TV Camera – Global Positioning System (GPS)– Proximity technologies (Radio
Frequency IDentification – RFID)– Sensor Networks– PDAs, SmartPhones (GPRS, Wi-
Fi)– Dead reckoning (portable inertial
platform)
Stalking (following people without being seen!)
Data acquisition: an example (2005)
Application of GIS/GPS to track pedestrian movements– Position, velocity,
trajectories – Critical areas
identification
N. Koshaak (Makkah - Saudi Arabia)
0
1
2
3
4
5Scalability
Single Individual Monitoring
Entire Crowd/groups Monitoring
Indoor
Large Scale
Small Scale
Cheap
Outdoor
Precise Localization Data
Continuous Localization
Absolute Position System (GPS) Proximity Tech. (Passive RFiD) Scene Analysis (Video Analysis)
0: null quality1: insufficient2: just sufficient3: discrete4: good5: best Available
Comparing Data Acquisition Technologies and Techniques (1)
0
1
2
3
4
5Scalability
Single Individual Monitoring
Entire Crowd/groups Monitoring
Indoor
Large Scale
Small Scale
Cheap
Outdoor
Precise Localization Data
Continuous Localization
Dead Reckoning (Portable Inertial Platform) Sensor Network (ZigBee) Direct Observation (People Counting)
0: null quality1: insufficient2: just sufficient3: discrete4: good5: best Available
Comparing Data Acquisition Technologies and Techniques (2)
San Diego (CA)At man’s Step special track at Summer Computer Simulation Conference 2007Jul, 13-14 2007
S. Bandini, M.L. Federici, S. Manzoni, “A qualitative comparison of technologies for Data Acquisition on Pedestrians and Crowded Situations”
Crowd modeling and simulation HOW DO PEOPLE BEHAVE IN CROWDED SPACES AND
SITUATIONS?
SIMULATIONS ARE EXPERIMENTAL LABORATORIES FOR HUMAN SCIENCES
Crowd modeling and application directions
• Support the study of pedestrians/crowds behavior
– Envisioning of different behavioral models in realistic environments
– Possibility to perform ‘in-machina’ experiments
• Decision makers might not be experts neither on crowd dynamics nor on software and math tools
– Need of effective ways to edit, execute, visualize and analyze simulations (what-if scenarios)
• Indoor (Buildings, Shopping Centers, Stadiums) vs Outdoor (Urban spaces for public events/transport, Parades, Marches, Fairs, Sport Events, Concerts)
Examples of Crowd Dynamics
• Evacuation dynamics – normal vs panic– open/structured spaces
• Lane formation and other self-organization phenomena
• Crowd formation/dispersion• Crowd movement and behavior (e.g. in
shopping center)
TSTarget System
SWSoftware
MASComp.Model
MAbstractModel
1) Phase 1: Observation
1
22) Phase 2: Model / Theory Construction
3 3) Phase 3: Computational modeling
44) Phase 4: Software implementation
Reality0
1
2
3
4
AbstractionLevels
Schema of the abstract levels involved in a simulation
If we look at the different passages implied in the construction of a simulation model using a Mas we can see that implicitly we are working with many models. Each model represents a level of abstraction. How many levels of abstraction are involved in a simulation process?
The target system is the object of study (Physical model). It is a specific point of view on a portion of reality that we consider “isolated” from the context. The target system is determined by our observation perspective on reality, and by the aspects of reality that we want to capture (i.e. atom level; molecular; macro-level)
The abstract model of the target system can be expressed in natural language, mathematical formulas etc. but usually it is not computational. It can be, at first, also an intuitive set of rules.
The computational model is what we use to represent the abstract model. The computational model is always a formal model. It can be a model Agent Based or Cellular Automata based etc.
The Software Model (operational model) of the Computational Model
Phase 1: observation of the Target System The Target System has to be observed and data on it collected (this phase can’t be separated from the next). To observe something a selective attention and an Hypothesis on what is observed must be already present in the observer)
Phase 2: Modelization Formulation of an Hypothesis (Model), that could even be simply intuitive, vague or informal. Phase 3: Computational Modeling Translation of the Abstract Model into the Computational Model (language/entities). This Phase constitutes the point of “no return” to reality (an interpretation key that explains how translate back entities of the computational model in entities of reality is needed)
Phase 4: Software Implementation Translation of the Computational Model in the Software Code
Phases from 1 to 4 can be seen as phases of the simulation Building and are concerned with models and abstraction.
The next phases concern instead the Decoding Levels of the simulation
TS
M
MAS
SW
3
2
1) Observation
4
Target System
Software
Comp.Model
AbstractModel
1
2) Model / Theory Construction 3) Computational modeling4) Software implementation
7
7) Verification of Sim in respect to the Theory
9
9) Prediction
8
8) Validation of Theory in respect to Real Data
Reality
5) Computation (sim running)
56
6) Visualization
0
1
2
3
4
AbstractionLevels
Decoding Levels
O Output
SD SimulationDisplaying
T Theory
R Real Data
Phase 5: Software run (calculus-computation)Output: simple results of the softwareexecution Phase 6: Visualization an appropriate
translation of simulation outputs in observable objects
Simulation Displaying: the envisioning of the outputs that is often the only way to operate with the simulation dynamic data
Phase 7: Verification Simulation is running and it has to be verified in respect to our initial theory
Theory: assumptions and rules that constitute the description of the domain
Phase 8: Validation The theory has then to be checked in relation to reality on the base of indicators chosen in precedent phase
Real Data: collection of meaningful measurements in the target system
Phase 9: prediction If the theory is Validated for available data then it is possible to make predictions for future states of the Target System
1
2
3
4
TS
M
MAS
SW O
SD
T
RTarget System
Software
Comp.Model
AbstractModel
Computational Model ChangeAbstract Model Revision
Software Implementation
Check
Decoding and correcting
• Software Implementation Check: If no suitable results are obtained a deeper check into the software may be needed in order to verify that it translates properly the computational model
• Computational Model Change: After a Campaign of Simulation that gave negative results a check of the assumptions that I made to translate my theory in the model is needed. A change of the computational Model can eventually be necessary.
• Abstract Model Revision: If the Computational Model is judged adequate to capture the theory assumptions, but real data don’t give a positive feedback, the abstract model must undergo a revision that will lie on the construction on new hypothesis and empirical observations
1
2
3
4
TS
M
MAS
SW O
SD
T
RTarget System
Software
Comp.Model
AbstractModel
Analysis
Design
Inference
Interpretation
Mapping of the phases of Design, Inference, Interpretation and Analysis in the Schema
Steps in Physical Scientific Practice
From: Modeling Games in the Newtonian World, by David Hestenes
Observation
PhysicalModel
MathematicalModel
Prediction
Hypothesis/Theory Building
Translation inMathematicalFramework
Inference/Deduction
Experiment/Validation
Target System1
2
3
Software4
TS
M
MAS
SW
reality
Comp.Model
AbstractModel
TS
M
Mat
Abstraction in Mabs Abstractions in Physical Theories
Comparison Between Abstraction Implied in Physic Scientific Practice and MAS Simulation Practice
One Step More of Abstraction
is implied
Mas Model Corresponds to
Mathematical Model
Pedestrian Movement at the Micro-Scale: Social Force Model [Batty, Helbing (2001)]
• Four principles “guide” movement– Agents avoid obstacles present in the environment– Agents consider repulsive the presence of other pedestrians when
space is congestioned– Agents also attract each other (principle of the flocking)– Agents “desire” to follow a direction
• To each of these components it is associated a force that pushes the agent towards a specific direction
DesiredPosition
GeometricRepulsion
SocialRepulsion
SocialAttraction+ + + + += εNew Position Old
Position
Crowd modeling Analytical (physical) approach
• Pedestrians particles subject to forces
• Goals: forces of attraction generated by points/reference point in the space
• Interaction among pedestrians: forces generated by particles
• Social forces– Repulsive tendency to stay
at a distance– Attractive imitative
mechanisms
Lane formation
‘Freezing by heating’
D. Helbing, I. J. Farkas, T. Vicsek: Freezing by Heating in a Driven Mesoscopic System, PHYSICAL REVIEW LETTERS, VOLUME 84, NUMBER 6, 2000
Crowd modelling: Cellular Automata
• Environment bidimensional lattice of cells
• Pedestrian specific state of a cell (e.g. occupied, empty)
• Movement generated thanks to the transition rule
– an occupied cell becomes empty and an adjacent one, which was previously vacant, becomes occupied
• Choice of destination cell in a transition generally includes information on– Benefit-Cost/Gradient: information
about “cell desirability”– Magnetic Force: models the effect of
presence of other agents in the environment (attraction/repulsion of crowds)
Crowd modelling: From CA to Situated MAS
• Individuals are separated from the environment– Agents, not just cell occupancy states– may have different behaviors: several
action deliberation models can be integrated
– heterogeneous system
• Agents interact by means of mechanisms not necessarily related to underlying cell’s adjacency– Action at a distance is allowed
Situated MAS action and interaction
• Agents are situated– they perceive their context and
situation– their behaviour is based on their
local point of view– their possibility to interact is
influenced by the environment• Situated Agents Interaction models
– Often inspired by biological systems (e.g. pheromones, computational fields)
– Generally provide a modification of the environment, which can be perceived by other entities
– May also provide a direct communication (as for CAs interaction among neighbouring cells)
Situated Cellular Agents (SCA)
Multi Agent model providing• Explicit representation of
agents’ environment• Interaction model strongly
related to agents’ positions in the environment– Among adjacent agents
(reaction)– Among distant agents,
through field emission-diffusion-perception mechanism
• Possibility to model heterogeneous agents, with different perceptive capabilities and behaviour
CompareT(f×c,t) = true
emit(f)
react(s,ab,s’) react(s,ac,s’)
Situated Cellular Agents (SCA)• Formal and computational framework to
represent and study of dynamics in pedestrian systems
– autonomous interacting entities – situated in an environment whose spatial
structure represents a key factor in their behaviors (i.e. actions and interactions)
• Based on MMASS (Multilayered Multi-Agent Situated Systems)[S. Bandini, S. Manzoni, C. Simone, Dealing with Space in Multi-Agent System: a model for Situated MAS, in Proc. of AAMAS 2002, ACM Press, New York, 2002]
• MMASS relaxes constraints on uniformity, locality and closure of CA[S. Bandini, S. Manzoni, C. Simone: Enhancing Cellular Spaces by Multilayered Multi Agent Situated Systems, Proc. of ACRI 2002: 156-167]
– Open systems can be modeled– Not homogeneous agent environment – Heterogeneous agents– Interaction involving spatially not adjacent agents
SCA model
Agents andbehaviours At-a-distance
interaction
Spatialstructure
SCA Space
• Space: set P of sites arranged in a network
• Each site p∈P is defined by <ap, Fp, Pp> where– ap∈A ∪{⊥}: agent situated in p
– Fp⊂F: set of fields active in p
– Pp⊂P: set of sites adjacent to p
SCA Fields
• <Wf, Diffusionf, Comparef, Composef>
– Wf: set of field values
– Diffusionf: P X Wf X P Wf X…X Wf
field diffusion function
– Composef: Wf X …X Wf Wf
field composition function
– Comparef: Wf X Wf {True, False}
field comparison function• Fields are generated by agents to interact at-a-distance and
asynchronously
SCA Agents
• a∈A : <s,p,T>• T < ∑T, PerceptionT, ActionT>
– ∑T: set of states that agents can assume
– ActionT: set of allowed actions for agents of type T
– PerceptionT:
∑T [N X Wf1] … [N X Wf|F|]
• PerceptionT(s) = (cT(s), tT(s))
• cT(s): perception modulation
• tT(s): sensibility threshold
• An agent a = <s,p,T> perceives the field value wfi
of a field fi = <Wf, Diffusionf, >i, *i>when ciT(s)*fi
wfi,>fi tiT(s)) and
SCA Agent Actions
• ActionsT: set of actions that agents of type T can perform
• Agent behavior: perception-deliberation-action cycle– Perception of local environment (e.g. free sites, fields)– Action selection based on agent state, position and type– Action execution
• Four basic actions– intra-agent actions: triggerT(), transportT()
– inter-agent actions: emitT(), reactionT()
action: trigger(s,fi,s’)condit: state(s), perceive(fi)effect: state(s’)action: transport(p,fi,q)condit: position(p), empty(q), near(p,q), perceive(fi)effect: position(q), empty(p)
action: emit(s,f,p)condit: state(s)effect: present(f, p)
action: reaction(s, ap1, ap2, …, apn,s’)condit: state(s), agreed(ap1, ap2,…, apn)effect: state(s’)
Situated MAS and crowd modeling
• Pedestrians agents
• Environment graph, as an abstraction of the actual environmental structure
• Movement generated thanks to perception-action mechanism– Sources of signals: relevant objects
(gateways, reference points), but also other agents
– Agents are sensitive to these signals and can be attracted/repelled by them (amplification/contrast)
– Possible superposition of different such effects
transport(p,q)
SCA Crowd Modelling Approach
Definition of the MMASSspatial structure
Definition of activeelements of the
environmentand field types
Definition of mobile agents(types, states, perceptive
capabilities and behaviouralspecification)
Definition of monitoredparameters and
specificationof monitoring mechanisms
Specific simulationconfiguration (number, type,position and initial state of
mobile agents, otherparameters)
Abstract scenariospecification
Computational model for the scenario
Experiment-specificparameters
Underground scenario• An underground station (several interesting crowd
behaviors can be studied)
• Passengers' behaviors are difficult to predict: crowd dynamics emerges from single interactions
– between passengers– between single passengers and parts of the
environment (signals, constraints)
• Passengers (actions)– on board may
• have to get off • be looking for a seat or try standing beside a handle• be seated
– on the station platform may • try to reach for the exit door• get on the train
• Passengers have to match their goals with– Environment obstacles – other passengers goals– implicit behavioral rules that govern the social
interaction in underground stations
SCA model of Underground Station Scenario Spatial structure of the environment
Spatial structure discrete abstraction ofsimulation environment
SCA model of Underground Station Scenario Active Elements of the Environment and Field Types
SCA model of Underground Station Scenario Active Elements of the Environment and Field Types
SCA model of Underground Station Scenario Active Elements of the Environment and Field Types
SCA model of Underground Station Scenario Agent types
An agent type t is a triple <∑t , Perceptiont, Actiont> where
• ∑t : set of agent states• Perceptiont : specifies for every agent
state and field type– a sensitivity coefficient c modulating
(amplifies/attenuates) field values– a sensibility threshold t filtering out
fields that are considered too faint– An agent perceives a field fT when
CompareT(f*c,t) = true• Actiont : behavioral specification for
agents of type t
Passengers
Seat
Station Exit
Wagon Exit
Handles
Dynamic Agents
Static Agents (active objects)
Agent
Types
SCA model of Underground Station Scenario Passengers behavior as state-transition diagram and
attitudes towards movement
Example based on designed behaviors for the case study.Should be calibrated SCA platform editor of agents’ behaviors
W
G
P
E
Waiting: passengers on the platformwaiting for a train
Get Off: people on the wagon that have toget off the train
Passenger: agent on the train that has noimmediate necessity to get off
Exit: passenger that has got down the trainand goes away from the station
S Seated: agent seated on a seatof the wagon
State Transition
W
G
E
P
S
SCA model of Underground Station Scenario Mobile Agents – Movement
State E xits D oors Seats H andles P resence E xit press.
W - Attract (2) - - Repel (3) Repel (1)
P - - Attract (1) Attract (2) Repel (3) Repel (2)
G - Attract (1) - - Repel (2) -
S - Attract (1) - - - -
E Attract (1) - - - Repel (2) -
When multiple signals are perceived, agents evaluate next-destination site according to weighted sum of perceived values
transport(p,q)
∑
SCA model of Underground Station Scenario (demo)
1) Pedestrian agent in site P (on the wagon)
Field “Handle”
SCA model of Underground Station Scenario (demo)
1) Pedestrian agent in site P (on the wagon)
1) Available seats (only one) emit a field
that is perceived as attractive by the agent
Emit (s, f, p)Field “Handle”
Field “Seat”
SCA model of Underground Station Scenario (demo)
1) Pedestrian agent in site P (on the wagon)
2) Available seats (only one in site Q) emit a field that is perceived as attractive by the agent if distance(P,Q)<ped_threshold
3) The agent perceives the field and moves (by a transport action) to the adjacent site, e.g. where the field is more intense Trasport (p,q)
Emit (s, f, p)
SCA model of Underground Station Scenario (demo)
1) Pedestrian agent in site P (on the wagon)
2) Available seats (only one in site Q) emit a field that is perceived as attractive by the agent if distance(P,Q)<ped_threshold
3) The agent perceives the field and moves (by a transport action) to the adjacent site, e.g. where the field is more intense
1) Process iterated until the agent reaches the site where the local max of intensity is perceived
Trasport (q,t)
Emit (s, f, p)
SCA model of Underground Station Scenario (demo)
Trasport (t,r)
1) Pedestrian agent in site P (on the wagon)
2) Available seats (only one in site Q) emit a field that is perceived as attractive by the agent if distance(P,Q)<ped_threshold
3) The agent perceives the field and moves (by a transport action) to the adjacent site, e.g. where the field is more intense
1) Process iterated until the agent reaches the site where the local max of intensity is perceived
Emit (s, f, p)
SCA model of Underground Station Scenario (demo)
Trasport (r,g)
Emit (s, f, p)
1) Pedestrian agent in site P (on the wagon)
2) Available seats (only one in site Q) emit a field that is perceived as attractive by the agent if distance(P,Q)<ped_threshold
3) The agent perceives the field and moves (by a transport action) to the adjacent site, e.g. where the field is more intense
1) Process iterated until the agent reaches the site where the local max of intensity is perceived
SCA model of Underground Station Scenario (demo)
Trasport (g,k)
1) Pedestrian agent in site P (on the wagon)
2) Available seats (only one in site Q) emit a field that is perceived as attractive by the agent if distance(P,Q)<ped_threshold
3) The agent perceives the field and moves (by a transport action) to the adjacent site, e.g. where the field is more intense
1) Process iterated until the agent reaches the site where the local max of intensity is perceived
Emit (s, f, p)
SCA model of Underground Station Scenario (demo)
React (p,sg,s)
React (a,s s,o)1) Pedestrian agent in site P (on the
wagon)2) Available seats (only one in site Q)
emit a field that is perceived as attractive by the agent if distance(P,Q)<ped_threshold
3) The agent perceives the field and moves (by a transport action) to the adjacent site, e.g. where the field is more intense
4) Process iterated until the agent reaches the site where the local max of intensity is perceived
3) Available_seat agent and pedestrian agent change their state simultaneously (agent seat turns into the occupied state and stops emitting fields while passenger turns into state seated)
Underground Case Study: model execution
• Simulation configuration– 6 agents getting off– 8 agents getting on
Visualization of system dynamics 3D rendering of 2D simulations (offline animation)
• Java based bidimensional simulator • Exported log of the simulation including
– Definition of the spatial structure– System dynamics
• MaxScript that allows 3D Studio Max to generate an animation representing the simulated scenario
Avatar#001#001#001#004#003#000@Avatar#002#002#001#003#005#000@Avatar#001#002#010#003#002#000@Avatar#002#001#001#003#004#000@Space#001#001#001#001#006#000@Space#001#002#001#002#005#000@Space#001#003#001#004#005#000@Space#001#004#001#004#004#000@Space#001#005#001#003#004#000@Space#001#006#001#003#002#000@Space#001#007#001#004#002#000@Space#001#008#001#005#002#000@
Why 3D? • To obtain an effective visualization of simulation dynamics• To obtain a machine-readable spatial abstraction in a semi-
automatic way from existing models of the environment• To exploit the rich information of a 3D model to implement highly
realistic perception
59
Freezing by Heating - Experiments
Helbing
• 3 densities (20-40-60%)• 10 simulations for each densities• After few turns pedestrians-agents get stacked in
front of the exit (80-90% of pedestrian population can’t move for the turn)
Schadschneider
Lane Formation: Experiments
• Simple Behavioural Model: pedestrians are attracted by the desired exit
(Without collision avoidance the phenomenon of freezing by heating is detected also at low densities)
• Introduction of repulsion:
– Each pedestrian at the beginning of the turn emits a presence field that is spread in adjacent sites
– Each pedestrian evaluates negatively the sites where it is perceived the presence of other pedestrians (presence of pedestrians with opposite direction is evaluated more negatively)
• Lane Formation only at low densities
Lane Formation: Experiments• Introduction in the model of the
possibility of an exchange of position between pedestrians that want to occupy one the site of the other
• Introduction of a concept of “irritation” that leads pedestrians to:
– Search for new paths (empty sites become more desirable after some turns of immobility)
– Attempt to exchange position with other agents (less sensitivity to presence field of other pedestrians)
• Experimentations performed with density from 10 to 90%:
4 different configurations of parameters (2 experiments for each density, 500 turns each)
3 different corridor geometries
0
0,2
0,4
0,6
0,8
1
1,2
10 20 30 40 50 60 70 80 90 95 100
Pedestrian Density (Pedestrians / Total Sites)
Pede
stria
n Sp
eed
(Site
s Pe
r Tur
n)
Togawa
Simulation 1
Simulation 2
Simulation 3
Simulation 4
Blue&Adler
Evacuation scenarios
Singola uscita D ue uscite
I Thank You
…… continues ……