Best Response Model for Evacuees

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Best Response Model for Evacuees Exit Selection

• Simo Heliövaara Harri Ehtamo
• Systems Analysis laboratory, Helsinki University
  of Technology
• simo.heliovaara_at_hut.fi
• Timo Korhonen Simo Hostikka
• VTT, Technical Research Centre of Finland

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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 FDSEvac -module

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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 pay-off
  on the next round

• The Nash equilibrium
  satisfies

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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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Comparing Algorithms

• 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

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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
i 2
i 3
i 10 equilibrium
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Computing the Nash equilibrium - RRA

• The same situation with the RRA algorithm
• The convergence is faster

i 5 equilibrium
i 1
i 2
i 3
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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

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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/ simo.heliovaara_at_hut.fi
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Thank You!