Simulation of complex systems: the case of crowds (Phd course - lesson 1/7)

Simulation of complex systems: the case of crowds

Giuseppe Vizzari

Complex Systems and Artificial Intelligence Research Center (CSAI)University of Milano-Bicocca, Italy

Outline

• Complex Systems?

• Pedestrian and crowd simulation, a brief introduction and motivations

• Levels of analysis of pedestrian/crowd behaviour

• Approaches to pedestrian modelling (macro vs. micro)

• Macroscopic modelling rationale

• Microscopic modelling alternatives and styles

• A reflection on the specificities of crowd simulation simulation projects

• Conclusions and discussion

Complex Systems?

• Several (more ore less formal) definitions:• A complex system is a highly structured

system, which shows structure with variations

• A complex system is one whose evolution is very sensitive to initial conditions or to small perturbations, one in which the number of independent interacting components is large, or one in which there are multiple pathways by which the system can evolve

• A complex system is one that by design or function or both is difficult to understand and verify

• A complex system is one in which there are multiple interactions between many different components

• Complex systems are systems in process that constantly evolve and unfold over time

• …

• Features of complex systems:• Composed by several interacting elements

• Nonlinearity

• Networked or hierarchical structure

• Positive and negative feedbacks

• Possibility to evolve and adapt

• Robustness and plasticity

• …

• Complex systems research is a hot topic for scientists… but also for engineers!

• One of their main features is their internal structure and the interaction among their composing parts… that very often is studied by means of simulations

Non linearity?

Simple vs Complicated vs Complex

• Simple system• Cause and effect relationships known, stable,

repeatable and predictable• Known system• Example: bicycle

• Complicated system• No fundamental difference with respect to cause and

effect relationships, but on a much larger scale and with increased requirements around coordination or specialised expertise

• “Knowable" system• Examples: car, bus, airplane, rocket

• Complex system• Cause and effect relationships often understandable in

retrospect, but not necessarily easily reproduced and predictable

• Systems that can (to a certain extent) be analysed by means of simulation

• Examples: living organism (even simple as yeast), human organisation (not just an organisational chart, a real organisation, e.g. a Department)… a CA model (the Game of Life)!

Outline









Motivations of crowd modeling and simulation

• Designer’s decision support• Normal and evacuation situations• Positioning of signs• Malls and shopping centres

• Support crowd management by means of the elaboration of what-if scenarios• Situations where large crowds are

frequent (sport events, festivals, religious events)

• Public transport systems, in particular stations

• Support the study of pedestrian behaviour• Envisioning of different behavioural

models in realistic environments• Possibility to perform ‘in-machina’

experiments

Crowds of pedestrians as complex systems

• Overall system behaviour depends on individuals’ decisions and actions…• … that are generally influenced by a

large number of factors• … intertwined in an often

unpredictable way• Mixed and conflicting mechanisms

• Competition for the shared space…• … but also cooperation (non written

social norms) to prevent stall situations

• Imitation...• ... but also natural tendency to stay

at a distance (proxemics)• Emergent phenomena • …but also rules, norms

• …

Considerations About Elder Pedestrians

• Elder pedestrians are frequent• Their impact on the transportation

infrastructures can be significant• Structures should be ready to host

them properly• Service points should be organised

and managed taking them into consideration

• Simulation can support the evaluation of designs and highlight potential issues

• New models for supporting the should be able to deal with• Heterogeneity in pedestrian speed• Systematic differences in reaction

times• Presence of groups, potentially

structured, some of which with strong cohesion

Impact of groups in pedestrian and crowd dynamics

• Current approaches generally consider every pedestrian as a individual with no relationships• Considering only his/her own

goals• Considering other pedestrians

as moving obstacles • Nonetheless, in several situations

pedestrians are bound by relationships influencing their movement• Generally speaking, a crowd is

made up of groups of pedestrians...

• What do we miss by neglecting this aspect of pedestrian behaviour?

Not just “physical” crowds

Simulation: a definition and motivations

Simulation: a definition and motivations• (Computer) Simulation represents a

way to exploit a computational model


way to exploit a computational model – to evaluate designs and plans

without actually bringing them into existence in the real world




– to evaluate theories and models of complex systems by envisioning the effect of the modelling choices, with the aim of gaining insight of their functioning





• The use of “synthetic environments” is sometimes necessary, because the simulated system cannot actually be observed





• The use of “synthetic environments” is sometimes necessary, because the simulated system cannot actually be observed– Because it is actually being designed





• The use of “synthetic environments” is sometimes necessary, because the simulated system cannot actually be observed– Because it is actually being designed– For ethical or practical reasons

Simulation life-cycle

5


• From the target system to its computational model and a simulator

Modelingand design

of a simulator

Target System

Model and simulator

5


• From the target system to its computational model and a simulator• Execution of a simulation campaign

Simulation execution

Modelingand design

of a simulator

Target System

Model and simulator Data generated by the simulation(s)

5


• From the target system to its computational model and a simulator• Execution of a simulation campaign• Evaluation/validation of the model (and simulator) against collected

data


Dynamics of Target System

Modelingand design

of a simulator

Analysis of results + interpretation

(model evaluation leading to explanation

orprediction)

Target System


Collected Data

5


• From the target system to its computational model and a simulator• Execution of a simulation campaign• Evaluation/validation of the model (and simulator) against collected

data• Possible usage for explanation and/or prediction


Dynamics of Target System

Modelingand design

of a simulator

Analysis of results + interpretation

(model evaluation leading to explanation

orprediction)

Target System


Collected Data

5

A comprehensive framework for integrated synthesis and analysis

Outline









Pedestrians and crowds: levels of analysis

Chapter 5. Identification of processes and elements in a pedestrian flow model 105

The operational level pertains to immediate decisions of the pedestrian concerning hisbehaviour. Interactions with other pedestrians play an important role at this level.

An overview of the mentioned decision levels, related processes at and interactions be-tween different decision levels are given in figure 5.1. Also, inputs and outputs on eachlevel are indicated in this figure.

STRATEGIC

TACTICAL

OPERATIONAL

Activity set choice

Derivedactivity set

Network topology

Timetable

RouteActivity schedule

Activity areas

Route choice

Activity area choice

Activity scheduling

Dynamic networkcharacteristics

Geometry

ObstaclesVehicle characteristics

WalkingWaiting

Performing an activityTrajectory choice

Figure 5.1: Levels in pedestrian behaviour based on Hoogendoorn et al. (2001) and figure 3.1

At the strategic level, travellers decide on the activities to be performed in the station.While some of these activities may be discretionary (e.g. buying a newspaper), othersmay be mandatory (validating a ticket before accessing a train). The activity choice setmay be related to characteristics of the pedestrian as well as of the infrastructure (avail-ability, type and location of shops). At the time of writing, the individual’s activity choiceset, including the fact whether activities are mandatory or not, is assumed exogenous inSimPed, given in the form of a distribution of various pedestrian types over the activities.The activity choice set contains the maximum number of activities each pedestrian willperform. All other choices at the strategic level, such as mode choice and departure timechoice are also exogenous and form input for the simulation tool.

The tactical level pertains to short-term decisions of the pedestrian in the facility, giventhe choices made at the strategic level. On the strategic level, pedestrians determine a listof activities they want to perform in the transfer node or pedestrian facility. The activitieson this list may be performed at different locations. Optimal locations for an individual

[Hoogendoorn et al., 2001]

Outline









Modeling approaches: what to model?

Pedestrian/Crowdmodels

Macroscopic(continuous fluids)

Microscopic(individual pedestrians)

Overall equations (mass conservation,flow velocity) determining velocity anddensity in the analysed area

Individual state, position, decision aremodelled; aggregate measures derivefrom these decisions

+ lower computational costs for large crowd- limited applicability

+ generally greater applicability- higher computational costs for large crowd

Macroscopic crowd models rationaleMathematical models Numerical tests Conclusion

Macroscopic models

Pedestrians as "thinking fluid"1

Averaged quantities:⇢(t,x) pedestrians density~v(t,x) mean velocity

Mass conservation(@

t

⇢+ divx

(⇢~v) = 0

⇢(0,x) = ⇢

0

(x)

for x 2 ⌦ ⇢ R2, t > 0

Two classes1st order models: velocity given by a phenomenologicalspeed-density relation ~v = V (⇢)~⌫

2nd order models: velocity given by a momentum balance equation

Density must stay non-negative and bounded: 0 ⇢(t,x) ⇢

max

Different from fluid dynamics:preferred directionno conservation of momentum / energyn ⌧ 6 · 1023

1R.L. Hughes, Transp. Res. B, 2002P. Goatin (INRIA) Mathematical modeling of crowds January 12, 2014 5 / 22

Mathematical models Numerical tests Conclusion

Eikonal equation: level set curves for |rx

�| = 1

In an empty space: potential is proportional to distance to destination

P. Goatin (INRIA) Mathematical modeling of crowds January 12, 2014 7 / 22

[Goatin, 2014]

• Global constraints are specified, e.g.• Mass conservation• Velocity function over the analysed area

• Different types models according to the velocity function definition

• 1st order: goal orientation and speed density relation

• 2nd order: momentum balance equation• Considerations

• All pedestrians share the same goals and attitude

• Difficult to consider dynamic aspects in the environment and situation

• Not able to capture all aspects of crowd dynamics (e.g. some emerging phenomena)

• Suitable for optimisation problems in specific contexts

Example application and results of a recent macroscopic approach

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Figure 2: Evacuee assignment using optimal free flow routing.

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Figure 3: Evacuee assignment (iteration 30) for two time stamps.

12

TRB 2014 Annual Meeting Paper revised from original submittal.

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Figure 3: Evacuee assignment (iteration 30) for two time stamps.

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TRB 2014 Annual Meeting Paper revised from original submittal.

[Hoogendoorn et al., 2014]

Agent Based Models for simulation: peculiarities, advantages, risks

7


• The analytical unit is the individual agent, not aggregate variables

7



• This means, on one hand, that additional insight on the modelled system is required

7




• On the other hand such a model should be able to

7





• Generate the same aggregate dynamics as traditional ones

7





• Generate the same aggregate dynamics as traditional ones

• Be able to represent, manage, analyse additional aspects, such as for instance spatial ones

7

Alternative microscopic pedestrian and crowd models

• Particle based

• Mostly, but not exclusively, social force model and derivatives

• Continuous space and time

• Cellular Automata

• Ad-hoc rules (e.g. Blue & Adler, intersections) or floor field approach (e.g. Nishinari, Schadschneider, ...)

• Discrete in time and space

• Multi-Agent Systems

• Several approaches from computer graphics (e.g. Thalmann, Terzopoulos, Donikian, Manocha), some approaches are extensions of CA, ...

• Behavioural models generally more complex that in CA approaches

Particle based approach


• Pedestrians à particles subject to forces



• Goals: forces of attraction generated by points/reference point in the space

Lane formation




Lane formation

‘Freezing by heating’




• Interaction among pedestrians: forces generated by particles

Lane formation






• Social forces

Lane formation






• Social forces• Repulsive à tendency to stay

at a distance

Lane formation






• Social forces• Repulsive à tendency to stay

at a distance• Attractive à imitative

mechanisms

Lane formation


Cellular Automata and crowd modelling


• Environment à bi-dimensional lattice of cells



• Pedestrian à specific state of a cell (e.g. occupied, empty)




• Movement à generated thanks to the transition rule




• Movement à 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 which is not provided by basic CAs






• Choice of destination cell in a transition generally includes information which is not provided by basic CAs– Benefit-Cost/Gradient: predefined

information related to cell desirability






• Choice of destination cell in a transition generally includes information which is not provided by basic CAs– Benefit-Cost/Gradient: predefined

information related to cell desirability– Magnetic Force/Social Force: model

the effect of presence of other agents in the environment (attraction/repulsion of crowds)

From CA to Situated MAS


– Entities are reified, separated from the environment


– Entities are reified, separated from the environment– Agents, not just cell states



– They may have different behaviours– Possibility to grant agents different

information about the environment– Possibility to integrate several

different action deliberation models





different action deliberation models – Possibly heterogeneous system






– Entities interact by means of mechanisms not necessarily related to underlying cell’s adjacency






– Entities interact by means of mechanisms not necessarily related to underlying cell’s adjacency– Action at a distance is allowed

Situated MAS:action and interaction

Situated MAS:action and interaction– Agents are situated


– they perceive their context and situation


– they perceive their context and situation– their behaviour is based on their local

point of view



point of view– their possibility to act (move) and

interact is influenced by the environment





– Situated Agents Interaction models





– Situated Agents Interaction models– Often inspired by biological systems

(e.g. pheromones, computational fields)






(e.g. pheromones, computational fields)– Generally provide a modification of the

environment, which can be perceived by other entities






(e.g. pheromones, computational fields)– Generally provide a modification of the

environment, which can be perceived by other entities

– But may also provide a direct communication (as for CAs interaction among neighbouring cells)

Groups in the literature - Modeling and Simulation• Extensions to the social force model

• Helbing, Theraulaz et al. 2009, 2010• Small groups (2,3,4), unstructured• Low to moderate densities • Validation based on actual observations

• Xu and Duh, 2010• Only couples (groups of 2 pedestrians)• Low to moderate densities • Shallow validation based on literature

(Daamen, 2004)• CA models

• Sarmady, Haron, Zawawi Hj, 2009• Leaders and followers • Groups of 2 to 6 members experimented• Not validated

• Agent-based models• Qiu and Hu 2010

• Structured groups (intra and inter group matrices)

• Large groups experimented (60 pedestrians)• Not validated

• Group members tend to stay close to other group members (additional behavioural component)

Meso level approaches: the best of both worlds?

Outline









Why not use simple queues?


• One could model such a system with one (or more) simple queues...

Pedestrian in the lecture

hall

Exit (one pedestrian

every t ms)




hall


every t ms)


every t ms)



• ... but the model would not be able to ‘answer’ some of the questions we can pose to the previous models• What if t is unknown?

• Only aggregate quantities are managed

• No heterogeneity


hall


every t ms)


every t ms)






• Moreover, it would be very difficult to manage more complex situations, in terms of:


hall


every t ms)


every t ms)






• Moreover, it would be very difficult to manage more complex situations, in terms of:• Environmental structure


hall


every t ms)


every t ms)






• Moreover, it would be very difficult to manage more complex situations, in terms of:• Environmental structure

• Possible behaviours for the pedestrians


hall


every t ms)


every t ms)

So, no “best” modeling approach?

So, no “best” modeling approach?• The choice of the abstract/

computational model depends on several factors:


computational model depends on several factors:• Available knowledge on the

simulated phenomenon/ situation/reality




• Available data on actual scenarios, for sake of calibration, verification and validation





• Goals of the simulation activity





• Goals of the simulation activity• Possible tension between these

elements!

What about Agent Based Modeling and Simulation methodologies?

What about Agent Based Modeling and Simulation methodologies?• It is very difficult to define a methodology

that is both general and actually useful


that is both general and actually useful• General methodologies tend to define

well understood macro phases, but no useful suggestion on how actually carry them out in a specific context




• For instance, in different domains it is not even clear what is the most proper modelling granularity level




• For instance, in different domains it is not even clear what is the most proper modelling granularity level– In crowd modelling, a pedestrian is

modelled as an agent (at least in microscopic models)…






– But in biological systems, what should be represented as an agent? An organism? An organ? A cell? A molecule?






– But in biological systems, what should be represented as an agent? An organism? An organ? A cell? A molecule?

• Specific useful (more or less) formalised modelling approaches and methodologies only in specific contexts

?

A reflection: from reality, to models, to a simulation system

• The overall simulation project involves several phase, roles, types of knowledge and competences

• The frequent passages (translation, encoding, decoding, interpretation...) between different levels of abstraction can lead to several problems• Non documented assumptions• Unrealistic/unfeasible simplifications

• Simulation projects are difficult • R. Shannon, “Introduction to the Art and

Science of Simulation” (1998)• ... But some even talk of “dark arts” [J.P.

Marney and H. Tarbert, “Why do simulation? Towards a working epistemology for practitioners of the dark arts” (2000)]

Reality

Subsystem

Abstract model

Computational model

Simulator

Conclusions and discussion

• The study of pedestrians and crowd behaviour fruitfully comprises activity of analysis and synthesis

• The behaviour of pedestrians and crowds can be analysed at different levels

• Both macro and microscopic approaches to the modelling of these phenomena are possible…

• … both have merits and limits in their applicability

• Microscopic approaches take a very different perspective on pedestrians and their environment

• The contribution of different disciplines, experts is crucial but the overall simulation project requires particular attention

• Of course, these model, studies and application domain can be a source for different research area…

• … a source of new problems and potential opportunities

• … a source of suggestions, potentially interesting approaches/solutions

Outline









ありがとうございます。 Giuseppe Vizzari

Minimal bibliography

• Stefania Bandini, Andrea Gorrini, Giuseppe Vizzari: Towards an integrated approach to crowd analysis and crowd synthesis: A case study and first results. Pattern Recognition Letters 44: 16-29 (2014).

• Hoogendoorn, S.P., P.H.L. Bovy & W. Daamen (2001), Microscopic pedestrian wayfinding and dynamics modelling, In: M. Schreckenberg & S. Sharma, (eds.), Pedestrian and Evacuation Dynamics, Springer, Berlin, 123–154.

• Andreas Schadschneider, Wolfram Klingsch, Hubert Klüpfel, Tobias Kretz, Christian Rogsch, Armin Seyfried: Evacuation Dynamics: Empirical Results, Modeling and Applications. Encyclopedia of Complexity and Systems Science 2009: 3142-3176.

• Paola Goatin (2014), Mathematical modeling of crowds. Presentation at TRB 2014 Workshop “Crowd Flow Dynamics, Modeling and Management” - available in “TRB Subcommittee on Crowd Flow Dynamics, Modeling, and Management” Facebook group

• Serge Hoogendoorn, Winnie Daamen, Dorine Duives, and Femke van Wageningen-Kessels: Optimal Crowd Evacuation. TRB 2014

• Helbing, D., A. Johansson, and H. Z. Al-Abideen, Dynamics of crowd disasters: An empirical study. Phys. Rev. E, Vol. 75, 2007, p. 046109.

• Colombo, Rinaldo M., Paola Goatin, Giulio Maternini, and Massimiliano D. Rosini. "Macroscopic Models for Pedestrian Flows." In Big events and transport: the transportation requirements for the management of large scale events. 2010.

• Daamen, Winnie, Serge P. Hoogendoorn, and Piet HL Bovy. "First-order pedestrian traffic flow theory." Transportation Research Record: Journal of the Transportation Research Board 1934, no. 1 (2005): 43-52.

• Helbing, Dirk, and Peter Molnar. "Social force model for pedestrian dynamics." Physical review E 51, no. 5 (1995): 4282.• Klüpfel, H., A Cellular Automaton Model for Crowd Movement and Egress Simulation. Ph.D. thesis, University Duisburg-Essen,

2003.• Burstedde, C., K. Klauck, A. Schadschneider, and J. Zittartz, Simulation of pedestrian dynamics using a two-dimensional

cellular automaton. Physica A: Statistical Mechanics and its Applications, Vol. 295, No. 3 - 4, 2001, pp. 507 – 525.• Vizzari, G., L. Manenti, and L. Crociani, Adaptive Pedestrian Behaviour for the Preservation of Group Cohesion. Complex

Adaptive Systems Modeling, Vol. 1, No. 7, 2013.

Simulation of complex systems: the case of crowds (Phd course - lesson 1/7)

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