Abstract
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 will try to avoid high density areas in order to reduce their overall walking costs and queuing costs at the stairs and exits. Each agent state is represented by a center of a box that follows a simple first-order dynamical system in an Euclidean space. Each agent will move to one of the closest exits that is safer and with less congested path. First, we formulate the problem and derive optimality equations using maximum principle and dynamic programming with boundary conditions. Second, well posedness and existence results are provided. Numerics and simulations are carried out to illustrate mean-field equilibria of a safer evacuation process. Finally, the methodology is shown to be flexible enough to include movement noises and stochastic structural component of the building.
| Original language | English (US) |
|---|---|
| Article number | 7874135 |
| Pages (from-to) | 5154-5169 |
| Number of pages | 16 |
| Journal | IEEE Transactions on Automatic Control |
| Volume | 62 |
| Issue number | 10 |
| DOIs | |
| State | Published - Oct 1 2017 |
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Keywords
- Congestion management
- crowd strategic flow
- mean-field games
- mean-field-type control
ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering
Cite this
A Mean-Field Game of Evacuation in Multilevel Building. / Djehiche, Boualem; Tcheukam, Alain; Hamidou, Tembine.
In: IEEE Transactions on Automatic Control, Vol. 62, No. 10, 7874135, 01.10.2017, p. 5154-5169.Research output: Contribution to journal › Article
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TY - JOUR
T1 - A Mean-Field Game of Evacuation in Multilevel Building
AU - Djehiche, Boualem
AU - Tcheukam, Alain
AU - Hamidou, Tembine
PY - 2017/10/1
Y1 - 2017/10/1
N2 - 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 will try to avoid high density areas in order to reduce their overall walking costs and queuing costs at the stairs and exits. Each agent state is represented by a center of a box that follows a simple first-order dynamical system in an Euclidean space. Each agent will move to one of the closest exits that is safer and with less congested path. First, we formulate the problem and derive optimality equations using maximum principle and dynamic programming with boundary conditions. Second, well posedness and existence results are provided. Numerics and simulations are carried out to illustrate mean-field equilibria of a safer evacuation process. Finally, the methodology is shown to be flexible enough to include movement noises and stochastic structural component of the building.
AB - 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 will try to avoid high density areas in order to reduce their overall walking costs and queuing costs at the stairs and exits. Each agent state is represented by a center of a box that follows a simple first-order dynamical system in an Euclidean space. Each agent will move to one of the closest exits that is safer and with less congested path. First, we formulate the problem and derive optimality equations using maximum principle and dynamic programming with boundary conditions. Second, well posedness and existence results are provided. Numerics and simulations are carried out to illustrate mean-field equilibria of a safer evacuation process. Finally, the methodology is shown to be flexible enough to include movement noises and stochastic structural component of the building.
KW - Congestion management
KW - crowd strategic flow
KW - mean-field games
KW - mean-field-type control
UR - http://www.scopus.com/inward/record.url?scp=85031011176&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85031011176&partnerID=8YFLogxK
U2 - 10.1109/TAC.2017.2679487
DO - 10.1109/TAC.2017.2679487
M3 - Article
AN - SCOPUS:85031011176
VL - 62
SP - 5154
EP - 5169
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
SN - 0018-9286
IS - 10
M1 - 7874135
ER -