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Best Response Model for Evacuees’ Exit
Selection
Simo Heliövaara & Harri Ehtamo
Systems Analysis laboratory, Helsinki University of Technology
[email protected]
Timo Korhonen & Simo Hostikka
VTT, Technical Research Centre of Finland
S ystems Analysis
Laboratory
Helsinki University of Technology
Our Research
• NIST: Fire Dynamics Simulator
(FDS) , state-of-the-art fire
simulation
• Helbing et al: Physical model
for crowd dynamics
• Our research: Agent-based
models for evacuation behavior
• Result: FDS+Evac -module
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Helsinki University of Technology
Exit Selection Background
• The agents need to have ”intelligence” to react to
a changing environment (e.g., congestion on exit
routes, fire, smoke)
• Previous approaches:
– Heuristic adaptive algorithms (Gwynne et. al 1999)
– Centralized allocation of agents to exits (Lo et. al
2006)
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The Exit Selection Game
• The goal of each agent is to
select the exit that minimizes its
individual evacuation time
consisting of walking time and
queuing time.
• Because the agents’ queuing
times depend on the other
agents’ strategies (target exits),
this is a game model.
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Best-Response and Nash Equilibrium
• In Best-Response Dynamics agents choose the
strategy that would give them the highest payoff on the next round:



• The Nash equilibrium s  (s1 ,, sn ) satisfies:

i

i
s  BRi ( s ) i
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Nash Equilibrium of the game
• In the paper we prove that
the exit selection game has a
unique Nash equilibrium (NE)
in pure strategies
• The result is interesting.
General existence theorems
only imply equilibrium in
mixed strategies
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Decentralized Algorithms
• We show that decentralized best-response
algorithms converge to the NE fast
• In the computation, the agents need not know
each others’ payoff functions but only their
current actions
• Note: the NE is not an equilibrium in the sense of
dynamic optimization. Rather, it is equilibrium of
myopic agents.
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Helsinki University of Technology
Comparing Algorithms
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50
PUA
40
RRA
Iterations
• PUA (Parallel Update
Algorithm): All agents
update simultaneously
• RRA (Round Robin
Algorithm): Agents
update in a fixed order
• Theoretical upper
bound for convergence
is N iteration rounds
with both algorithms
30
20
10
0
100
200
300
400
Number of agents
500
Computing the Nash Equilibrium - PUA
• Example. The red exit is three times as wide as
the blue
• 300 agents
• Random initial distribution
• PUA algorithm is used
i=1
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i=2
i=3
i = 10
equilibrium
Computing the Nash equilibrium - RRA
• The same situation with the RRA algorithm
• The convergence is faster
i=1
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i=2
i=3
i=5
equilibrium
Online Updating
• As the evacuation proceeds the NE may change
– Agents are set to update their best responses
frequently
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Further development of the model
• Evacuation time is not the only factor affecting
exit selection:
– Fire conditions (smokiness, temperature, etc.)
– Familiarity of exit routes
– Visibility of exits
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Discussion
• An exit selection game
– A pure Nash equilibrium
– Best response algorithms converge fast
• Future research:
– Interaction between agents, e.g., herding,
leader/follower agents, swarming, etc.
– Spatial interaction and polymorphic population
patterns
– Evolutionary game theory
S ystems Analysis
Laboratory
Helsinki University of Technology
Literature
H. Ehtamo, S. Heliövaara, T. Korhonen, and S. Hostikka, Game Theoretic Best Response
Dynamics for Evacuees' Exit Selection, Accepted for publication in Advances in Complex
Systems
T. Korhonen, S. Hostikka, S. Heliövaara, H. Ehtamo, and K. Matikainen. Integration of an
Agent Based Evacuation Simulation and the State-of-the-Art Fire Simulation. Proceedings of
the 7th Asia-Oceania Symposium on Fire Science & Technology. Hong Kong, 20 - 22 Sept.
2007.
K. McGrattan, B. Klein, S. Hostikka, and J. Floyd. Fire Dynamics Simulator (Version 5)
User's Guide. National Institute of Standards and Technology, 2008.
http://www.sal.hut.fi/Publications
http://www.vtt.fi/proj/fdsevac/
[email protected]
S ystems Analysis
Laboratory
Helsinki University of Technology
Thank You!
S ystems Analysis
Laboratory
Helsinki University of Technology