Post on 18-Dec-2014
description
Optimization in crowd movement models via anticipation
Dmitry Krushinsky, Alexander MakarenkoInstitute for Applied System Analysis,
NTUU “KPI”, UkraineBoris Goldengorin
University of Groningen, the Netherlands
Contents
• Motivation• Brief description of the basic model• Anticipating pedestrians• One-step anticipation and space “de-
localization”• Multi-step anticipation and time “de-
localization”• Conclusions
Why it is important?• The movement of large–scale human crowds potentially can result in a variety of unpredictable
phenomena: loss of control, loss of correct route and panics, that make groups of pedestrians block, compete and hurt each other.
Terrorism
Technological
Natural cataclysms
Mass events
• So, it is evident that special management during such accidents is necessary. Moreover, well-founded plans of evacuation based on realistic scenarios and risk evaluation must be designed. This will either prevent harmful consequences or, at least, alleviate them.
disaster s
Why it is important?
simulation optimizationregulations, direction signs,…
assessmentoptimized infrastructure
Chaotic behavior
- hard to control & predict- undesired phenomena: high “pressure”, shock waves, etc.- poor performance (in emergency)
Determined behavior
- easy to control & predict- evenly distributed pedestrians- good performance (in emergency)
Overview of the modelsSimple
(physically inspired)
Complex(with mentality
accounting)
mic
rosc
opic
mac
rosc
opic
- lattice gas
- billiards
- fluid dynamics
- anticipation
- decision making
- etc.
?
P4
Basic modelData Layer
P1P3P2
Routing Layer
3 states per cell:
•Empty
•Obstacle
•Pedestrian
Cells contain directions that make up shortest exit path
Pk – probability of shift in k-th direction (k=1..4)
Simplest model of anticipating pedestrian
Supposition: the pedestrians avoid blocking each other. I.e. a person tries not to move into a particular cell if, as he predicts, it will be occupied by other person at the next step.
P1P3
P2P4
kP )1( ,occkk PP ⋅−× α
Pk – probability of shift in direction k (k=1..4)Pk,occ – probability of k-th cell in the neighborhood being occupied (predicted)α – free parameter, expressing influence of anticipation
P2
P1
P4
P3
Simplest model of anticipating pedestrian
P3
P2P4
Model-based prediction:
∑+∑−∑=
≠≠≠=kjji
kjijjii
iiocck PPPPPPP
,
3
1,
Cells beyond elementary neighborhood are involved. Thus, the actual (extended) neighborhood has radius R=2.
Spatial de-localizationGrowth of the neighbourhood …
… and impact on performance
Multi-step prediction and temporal de-localization
Example scenarios tree…
… and corresponding graph G(T) (T=4, R=4)
X X XX
X
X
X
X
X
X XX
X
XX
1 1 11
1
1
1
1
1
1 11
1
11
22
2 2
2
2
2
2
2
22 2
2
22
3 33 3
3
3
3
3
3
3 33
3
33
4 4 4 4
4
4
4
4
4
4 4 4
4
445
5 5 5 5
5
5
5
5
5 5 5
5
55
Multi-step prediction and temporal de-localization
Bipartite matching “Greedy” tree
Sparse tree
...
P0P1P2P3P4
...
pede
stria
ns cells13
4 25X 13
42
5X
Finding optimal trajectories: network flow approach
)()()( ijij vqvqec −=edgetheofcapacity)(
functionquality"")(
V,,E),(edgesG(T)EverticesG(T)V
G(T)
−−
∈∈=−∈−∈
ij
i
jijiij
ecvq
vvvve
s t
G3(T)
s t
G1(T)
s t
G2(T)
auxi
liary
gra
phs
Gk(
T)
kP ))T(G()1( kk FP ⋅−+⋅ αα)T(Ginflow.max))T(G( kkF −
Finding optimal trajectories: neural network approach
Example scenarios tree… ... and corresponding perceptron
]1;0[
1
∈
= −∑ji
jk
kki
ji
P
PpP
= ∑ −
k
jkki
ji XwX 1σ
)x(σx
1
1p 01
p02
p03
p1 4
p15
p 25
p26p27
p 36p37p38
24P
25P26P27P28P
00X
w01
w02
w03
w14
w15
w25
w26w27
w36w37w38
24X
25X26X27X28X
Finding optimal trajectories: network flow vs. neural network
• exact• sequential• …
• iterative• parallel• …
Conclusion:evolution of the model of pedestrian
MP(1,0)
MP(2,1)
MP(R,1)
time0 1 2 3 T
MP(R,T)
MP(R,T) – model of pedestrianR – radius of (extended) neighborhood; T – time horizon of anticipation
Conclusion:performance
absolute global minimum
MP(1,0)
MP(2,1)
MP(R,1)
MP(R,T)
evac
uatio
n tim
e
MP(MP(∞∞, ∞), ∞)
?
… … …
Thank you!
? ?
?
time0 1 2 3 T