adaptive pedestrian behaviour for the preservation of group cohesion: observations and simulations

Adaptive pedestrian behaviour for the preservation of group cohesion: observations and simulations

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

TRB 2014 - Washington DC - Jan. 12, 2014

Outline

• Pedestrian and crowd simulation: why groups?

• Some observations and empirical data

• An adaptive pedestrian model for preserving group cohesion

• The model in a benchmark scenarios

• Conclusions and discussion


Impact of groups in pedestrian and crowd dynamics

• Most modelling 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?

TRB 2014 - Washington DC - Jan. 12, 2014TRB 2014 - Washington DC - Jan. 12, 2014

Groups in the literature - Observations

• At least two studies report observations about groups• Willis A, Gjersoe N, Havard C,

Kerridge J, Kukla R, 2004, "Human movement behaviour in urban spaces: implications for the design and modelling of effective pedestrian environments" Environment and Planning B: Planning and Design 31(6) 805 – 828

• Michael Schultz, Christian Schulz, and Hartmut Fricke. “Passenger Dynamics at Airport Terminal Environment”, Pedestrian and Evacuation Dynamics 2008, Springer-Verlag, 2010

• Observations carried out in low density conditions

• Groups of small size were most frequently observed

TRB 2014 - Washington DC - Jan. 12, 2014TRB 2014 - Washington DC - Jan. 12, 2014

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)


Admission test University of Milano-Bicocca

• Admission test of the Faculty of Psychology at the University of Milano-Bicocca - September 1, 2011

• Counting activity supported by video footages of the event

• About two thousand students attended the test• About 34% individuals, 50%

couples, 13% triples and 3% groups of 4 members (!)

• Statistically validated relationship between group size and velocity• Additional quantitative analyses about

the arrival and entrance process, LOS• Qualitative analysis of group shapes and

related phenomena• More details in an ACRI 2012 (C&CA) and

upcoming PED 2012 paper


Vittorio Emanuele II Gallery, Milan

• Popular commercial-touristic walkway in Milan’s city centre

• Goals of the survey:• level of density and walkway

level of service (A and B);• presence of groups (over 84%);• group size and proxemics

spatial patterns, trajectories and walking speed (groups are slower but their trajectories are shorter);

• group proxemics dispersion (they preserve cohesion, even if large ones occupy more space)

• still hard to evaluate spatial arrangement of group members

Group dispersion

Couples Triples 4 Members

Distance Centroid

0.58 m (sd 0,22)

0.76 m (sd 0,11)

0.67 (sd 0.12)


A model considering groups

• Based on the floor-field CA approach, with significant difference on movement choice

• Employing traditional factors for movement destination choice• Goal orientation• Presence of obstacles• Presence of other pedestrians

(basic proxemics)• A notion of group has been introduced

• To generate a generalised effect of cohesion among members of groups

• ... able to overcome goal orientation for certain types of groups (e.g. families, close friends)

• Speed heterogeneity also introduced (poster on Monday afternoon)

Considered factors:+ cell is closer to pedestrian's goal (voided by high group dispersion) + presence of group members nearby- presence of other pedestrians nearby- presence of obstacles nearby

Movement blocking factors:- cell is occupied by another pedestrian (but in very high densities the cell can be shared by two pedestrians)- cell is occupied by an obstacle


A few formal details

• Stochastic choice of destination cell; for each cell c, the probability of choosing an action a leading to it is

• The “utility” value of the cell is defines as follows:where• Goal is associated to the static floor field and Obs to the wall potential• Sep is associated to the proxemic repulsion• D is an inertia factor• Over regulates the possibility of having two pedestrians sharing the same cell in

case of high density• Coh and Inter represent group cohesion factors respectively for small simple

groups and large potentially structured groups


Overlapping

• Overlapping is a transient situation in which pedestrians share the same cell• ... it can sometimes be

observed in counterflow situations in which there is not enough space for avoidance

• It can only happen if local density exceeds a given threshold

• The choice is still penalised (Over ≤ 0)

• No more than two pedestrians can share a single cell

[Kretz et al., 2006]


Ordering in bidirectional pedestrian flows and its influence on the fundamental diagram 5

Figure 3. Schematic illustration of the bidirectional pedestrian experiment in a corridor.

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Figure 4. Snapshots from the experiments (left) and actual trajectories of pedestrians (right).In the plots, red solid lines represent the paths of left moving pedestrians, while the blackdashed lines represent the paths of right moving pedestrians.

Simple and structured groups

• Simple groups are made up of family members, friends, people that know each other

• They often adapt their behaviour to preserve the cohesion of the group

• Large groups can include perfect strangers that share for some time a common goal

• Members of this group have a tendency to stay close to each other...

• ... but this tendency is not so strong to prevent group fragmentation

• And generally they are actually structured (they can include other - often simple - groups), so we call them structured


• Multipliers of the different components of movement “utility” are adjusted according to the state of the group

!

!!

• The dispersion of the group causes an increased impact of simple group cohesion and a reduced effect of goal attraction (static floor field)

Adaptive group cohesion mechanism

Ad-hoc Rules[2, 1]

General Approaches[14]

[5]

3.2 Validating CA Pedestrian Models[16]

4 RECENT DEVELOPMENTS

4.1 Modeling of Groups[12]

Recent works represent a relevant effort towards the modeling of groups,respectively in particle-based [9, 18] and in agent-based approaches [11]: inall these approaches, groups are modeled by means of additional contribu-tions to the overall pedestrian behaviour representing the tendency to stayclose to other group members. However, most of the above approaches onlydeal with small groups in relatively low density conditions or they were notvalidated against real data.

Balance(k) =

8>><

>>:

13 · k + ( 23 · k ·DispBalance) if k = kc13 · k + ( 23 · k · (1�DispBalance)) if k = kg _ k = ki

k otherwise

4.2 Finer Scale of Discretization[8]

[13]

4.3 Different Types of Pedestrians[8]

[17]

4.4 Conclusions and Future DevelopmentsACKNOWLEDGMENTS

REFERENCES

[1] Victor J. Blue and Jeffrey L. Adler. (2000). Modeling four-directional pedestrian flows.Transportation Research Record, 1710:20–27.

10


Modelling groups - some qualitative results

Counterflow of two structured groups including simple groups of various size, in a 2.4 m wide corridor


Aggregate effects of groups

Counterflow of two structured groups including simple groups of various size, in a 2.4 m wide corridor; shuffled sequential update - ongoing tests with parallel update strategy


Aggregate effects of groups analysed

• We can interpret the results making considering two phenomena

1.Wide groups offer a large profile to the counter flow, so they have a higher probability of facing conflicts

2.Once a group has formed a line, instead, the leader has the same conflict probability of an individual, but the follower has often an advantage

• In low density situations phenomenon (1) prevails, leading to a lower average combined flow for groups of pedestrians whose size is larger than 2

• Pairs in fact can easily form a line, turning phenomenon (1) to (2)

• In high density situations the probability of facing conflicts is very high also for individuals, so phenomenon (2) prevails, leading to higher average combined flow for even large groups (size 5)


Effectiveness of simple group cohesion mechanism

Counterflow of two structured groups including simple groups of various size, in a 3.6 m wide corridor (Dispersion measured in terms of area covered by the group)


Additional results in “experimental” scenarios: T junction

4 J Zhang, W Klingsch, A Schadschneider, and A Seyfried

(a) Snapshot

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(b) Pedestrian trajectories

Fig. 2. Trajectories and snapshot from T-junction experiment.

From these trajectories, pedestrian characteristics including flow, density, ve-locity and individual distances at any time and position can be determined.

3 Experiment analysis

In previous studies, different measurement methods were used to limit thecomparability and fluctuation of the data. E.G. Helbing et al. proposed aGaussian, distance-dependent weight function [13] to measure the local den-sity and local velocity. Predtechenskii and Milinskii [14] used a dimensionlessdefinition to consider different body sizes and Fruin introduced the ”Pedes-trian Area Module” [15]. This study focuses on the Voronoi method proposedin [16, 17], where the density distribution can be assigned to each pedestrian.This method permits examination on scales smaller than the pedestrians forits high spatial resolution.

3.1 Measurement methodology

At a given time t, the Voronoi diagram can be generated from the positionsof each pedestrian. It contains a set of Voronoi cells for each pedestrian i.The cell area, Ai, can be thought as the personal space belonging to eachpedestrian i. Then, the density and velocity distribution over space can bedefined as

ρxy = 1/Ai and vxy = vi(t) if (x, y) ∈ Ai (1)

where vi(t) is the instantaneous velocity of each person (see [17]). The Voronoidensity and velocity for the measurement area Am is defined as

Plot of experimentally observed data [Zhang et al., 2012] [Vizzari et al., 2013]


Conclusions and discussion

• Groups are relevant and significant• Results of simulations are partly

validated• Fundamental diagram and spatial

utilisation in tune with results from the literature… without groups

• Group cohesion mechanism generates results about dispersion that are in tune with Vittorio Emanuele Gallery’s observation…

• … but we don’t have data about groups in high density situations (and it’s hard to obtain such data)

• More observations, experiments and simulations are necessary to improve our understanding of the phenomenon

• Closer collaboration between researchers working on synthesis and analysis of crowds is promising and possibly beneficial for both

ありがとうございます。 Giuseppe Vizzari

adaptive pedestrian behaviour for the preservation of group cohesion: observations and simulations

Technology

groups of pedestrians

members of groups

small groups

couples groups

groups willisa

followers groups

impact of groups

group matrices large