A Spatial Partitioning Based Crowd Evacuation Model
Pages 5247 - 5252
Abstract
This paper studies a large population evacuation model within the linear quadratic mean field games framework. The evacuation time horizon is fixed, and space is subdivided into regions. Depending on its initial position with respect to the specified regions, each agent has a limited selection of possible exit choices. Agents’ motions are affected by their respective regional cohorts’ positions mean. Regions interact through their shared exits’ flows which creates an inter-regional network effect. A sufficient upper bound on the time horizon is derived to guarantee that finite escape time behavior is avoided. Besides, existence of an infinite population based Nash equilibrium is established. Finally, we illustrate, through simulations, the model’s behavior for given agents’ initial distributions and exits arrangement setups.
References
[1]
A. Lachapelle and M. T. Wolfram, “On a mean field game approach modeling congestion and aversion in pedestrian crowds,” Transportation Research Part B: Methodological, vol. 45, pp. 1572–1589, 12 2011.
[2]
B. Djehiche, A. Tcheukam, and H. Tembine, “A Mean-Field Game of Evacuation in Multilevel Building,” IEEE Transactions on Automatic Control, vol. 62, pp. 5154–5169, 10 2017.
[3]
W. H. Warren, “Collective Motion in Human Crowds,” Current Directions in Psychological Science, vol. 27, pp. 232–240, 8 2018.
[4]
A. Aurell and B. Djehiche, “Modeling tagged pedestrian motion: A mean-field type game approach,” Transportation Research Part B: Methodological, vol. 121, pp. 168–183, 2019.
[5]
M. J. Kinsey, S. M. Gwynne, E. D. Kuligowski, and M. Kinateder, “Cognitive Biases Within Decision Making During Fire Evacuations,” 3 2019.
[6]
A. E. Patla, “Understanding the roles of vision in the control of human locomotion,” Gait and Posture, vol. 5, pp. 54–69, 2 1997.
[7]
M. Burger, M. Di Francesco, P. A. Markowich, and M. T. Wolfram, “Mean field games with nonlinear mobilities in pedestrian dynamics,” in Discrete and Continuous Dynamical Systems - Series B, vol. 19, pp. 1311–1333, Southwest Missouri State University, 2014.
[8]
A. Aurell and B. Djehiche, “Mean-field type modeling of nonlocal crowd aversion in pedestrian crowd dynamics,” SIAM Journal on Control and Optimization, vol. 56, no. 1, pp. 434–455, 2018.
[9]
L. Nurbekyan, “One-dimensional, non-local, first-order stationary mean-field games with congestion: A fourier approach,” Discrete and Continuous Dynamical Systems - Series S, vol. 11, no. 5, pp. 963–990, 2018.
[10]
A. Aurell and B. Djehiche, “Behavior near walls in the mean-field approach to crowd dynamics,” SIAM Journal on Applied Mathematics, vol. 80, pp. 1153–1174, 5 2020.
[11]
L. Nurbekyan and J. Saúde, “Fourier approximation methods for first-order nonlocal mean-field games,” Portugaliae Mathematica, vol. 75, pp. 367–396, 11 2018.
[12]
S. Liu, M. Jacobs, W. Li, L. Nurbekyan, and S. J. Osher, “Computational methods for nonlocal mean field games with applications,” arXiv, 4 2020.
[13]
N. Toumi, R. P. Malhamé, and J. Le Ny, “A Tractable Mean Field Game Model for the Analysis of Crowd Evacuation Dynamics,” in Proceedings of the IEEE Conference on Decision and Control, vol. 2020-Decem, pp. 1020–1025, Institute of Electrical and Electronics Engineers Inc., 12 2020.
[14]
T. Sasagawa, “On the Finite Escape Phenomena for Matrix Riccati Equations,” IEEE Transactions on Automatic Control, vol. 27, no. 4, pp. 977–979, 1982.
[15]
R. Salhab, R. P. Malhamé, and J. Le Ny, “A Dynamic Game Model of Collective Choice in Multiagent Systems,” IEEE Transactions on Automatic Control, vol. 63, pp. 768–782, 3 2018.
[16]
M. Huang, R. P. Malhamé, and P. E. Caines, “Nash certainty equivalence in large population stochastic dynamic games: Connections with the physics of interacting particle systems,” in Proceedings of the IEEE Conference on Decision and Control, pp. 4921–4926, IEEE, 2006.
[17]
J. B. Conway, A course in functional analysis, vol. 96. Springer, 2019.
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Dec 2021
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IEEE Press
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Published: 14 December 2021
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