Best Response Model for Evacuees’ Exit Selection

Best Response Model for Evacuees’ Exit Selection Simo Heliövaara & Harri Ehtamo Systems Analysis laboratory, Helsinki University of Technology simo.heliovaara@hut.fi Timo Korhonen & Simo Hostikka VTT, Technical Research Centre of Finland

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

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)

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.

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:

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

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.

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

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

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

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

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

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

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@hut.fi

Thank You!

Best Response Model for Evacuees’ Exit Selection