A Mean-Field Game of Evacuation in Multilevel Building

Boualem Djehiche, Alain Tcheukam, Tembine Hamidou

Research output: Contribution to journalArticle

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 languageEnglish (US)
Article number7874135
Pages (from-to)5154-5169
Number of pages16
JournalIEEE Transactions on Automatic Control
Volume62
Issue number10
DOIs
StatePublished - Oct 1 2017

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Stairs
Maximum principle
Dynamic programming
Costs
Dynamical systems
Boundary conditions

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 journalArticle

Djehiche, Boualem ; Tcheukam, Alain ; Hamidou, Tembine. / A Mean-Field Game of Evacuation in Multilevel Building. In: IEEE Transactions on Automatic Control. 2017 ; Vol. 62, No. 10. pp. 5154-5169.
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