A Mean-Field Game of Evacuation in Multilevel Building

  title={A Mean-Field Game of Evacuation in Multilevel Building},
  author={Boualem Djehiche and Alain Tcheukam Siwe and Hamidou Tembine},
  journal={IEEE Transactions on Automatic Control},
This paper puts forward a simple mean-field game that captures some of the key dynamic features of crowd and pedestrian flows in multilevel building evacuations. It considers both microscopic and macroscopic route choice by strategic agents. To achieve this, we use mean-field differential game with local congestion measure based on the location of the agent in the building. Including the local mean-field term and its evolution along the path causes a sort of dispersion of the flow: the agents… 

Evolutionary Game Dynamics for Crowd Behavior in Emergency Evacuations

This paper proposes a novel game formulation of the model as a discrete-state continuous-time game, where the players update their strategies to reach the exit within a defined time horizon, whilst avoiding undesirable situations such as congestion and being trampled.

A Tractable Mean Field Game Model for the Analysis of Crowd Evacuation Dynamics

An existence theory for the infinite population mean field game based equilibrium dynamics is developed, and its Nash property for a large but finite population of agents is established.

Crowd Management Services in Hajj: A Mean-Field Game Theory Approach

This paper modeled the problem as a Mean-Field-Game (MFG) where the solution is a system composed of a Backward Hamilton-Jacobi-Bellman equation and a Forward Transport (Kolmogorov) equation and results show the efficiency of the MFG solution on the total time out of the pilgrims to reach the ritual.

A Mean Field Game Model of Spatial Evolutionary Games

Evolutionary Game Theory (EGT) studies evolving populations of agents that interact through normal form games whose outcome determines each individual’s evolutionary fitness. In many applications,

Modeling tagged pedestrian motion: A mean-field type game approach

Behavior Near Walls in the Mean-Field Approach to Crowd Dynamics

A system of stochastic differential equations (SDE) of mean-field type that by means of sticky boundaries and boundary diffusion accounts for the possibility of pedestrians to spend time at, and to move along, walls and is related to the social cost minimization in an interacting particle system.

Multi-agent interaction and nonlinear Markov games

In this Part I approach players in groups are not independent rational optimizers and are either directly controlled by principals and serve the interests of the latter or resist the actions of the principals by evolving their strategies in an 'evolutionary manner' via interactions with other players subject to certain clear rules, deterministic or stochastic.

The current method for stationary mean-field games on networks

This work addresses the mathematical formulation of first-order stationary mean-field games on networks, including junction conditions for the Hamilton-Jacobi (HJ) equation and transmission Conditions for the transport equation, and shows how to solve this system by linear programming.

COVID-19: A Data-Driven Mean-Field-Type Game Perspective

A data-driven model can capture most of the reported data on COVID-19 on confirmed cases, deaths, recovered, number of testing and number of active cases in 66+ countries and reports non-Gaussianity and non-exponential properties in 15+ countries.



Evacuation of multi-level building: Design, control and strategic flow

This work introduces a simple mean-field network game that captures some of the key dynamic features of crowd and pedestrian flows in multi-level building evacuations. It considers a route choice by

On a mean field game optimal control approach modeling fast exit scenarios in human crowds

This paper presents an optimal control approach modeling fast exit scenarios in pedestrian crowds, formulated in the framework of mean field games and based on a parabolic optimal control problem.

Mean field games with nonlinear mobilities in pedestrian dynamics

This paper discusses the modeling of the macroscopic optimal control approach and shows how the optimal conditions relate to Hughes model for pedestrian flow and results on the existence and uniqueness of minimizers are provided.

Resource pooling for optimal evacuation of a large building

This paper is concerned with modeling, analysis and optimization/control of occupancy evolution in a large building. The main concern is efficient evacuation of a building in the event of threat or

Pedestrian, Crowd and Evacuation Dynamics

Self-organization Spontaneous organization not induced by initial or boundary conditions, by regulations or constraints, and it often causes different kinds of spatio-temporal patterns of motion, which are caused by social interactions rather than by physical interactions or fields.

Finite Difference Methods for Mean Field Games

Mean field type models describing the limiting behavior of stochastic differential game problems as the number of players tends to + ∞, have been recently introduced by J-M. Lasry and P-L. Lions.

Optimal building evacuation time considering evacuation routes

State-of-the-art crowd motion simulation models