S ystems AnalysisLaboratoryHelsinki University of Technology

Best Response Model for Evacuees’ Exit Selection

Simo Heliövaara & Harri EhtamoSystems Analysis laboratory, Helsinki University of Technology

simo.heliovaara@hut.fi

Timo Korhonen & Simo HostikkaVTT, Technical Research Centre of Finland

S ystems AnalysisLaboratoryHelsinki 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

S ystems AnalysisLaboratoryHelsinki 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)

S ystems AnalysisLaboratoryHelsinki University of Technology

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.

S ystems AnalysisLaboratoryHelsinki University of Technology

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:),,( 1 nsss

isBRs iii

)(

S ystems AnalysisLaboratoryHelsinki University of Technology

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

S ystems AnalysisLaboratoryHelsinki University of Technology

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.

S ystems AnalysisLaboratoryHelsinki University of Technology

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

S ystems AnalysisLaboratoryHelsinki University of Technology

Computing the Nash Equilibrium - PUA

i = 1 i = 2 i = 3 i = 10equilibrium

• Example. The red exit is three times as wide as the blue• 300 agents• Random initial distribution• PUA algorithm is used

S ystems AnalysisLaboratoryHelsinki University of Technology

Computing the Nash equilibrium - RRA

i = 1 i = 2 i = 3 i = 5equilibrium

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

S ystems AnalysisLaboratoryHelsinki University of Technology

Online Updating

• As the evacuation proceeds the NE may change– Agents are set to update their best responses

frequently

S ystems AnalysisLaboratoryHelsinki University of Technology

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

S ystems AnalysisLaboratoryHelsinki University of Technology

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 AnalysisLaboratoryHelsinki 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/Publicationshttp://www.vtt.fi/proj/fdsevac/simo.heliovaara@hut.fi

S ystems AnalysisLaboratoryHelsinki University of Technology

Thank You!