A Hierarchy of Heuristic-Based Models of Crowd Dynamics

Journal of Statistical Physics

Volumn 152, Issue 6, 2013, Pages 1033-1068

  Degond, P ^a   Appert Rolland, C ^b   Moussaid M ^c   Pettre J ^d   Theraulaz, G ^e  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^b UNIVERSITÉ PARIS SUD   (France)

^c MAX PLANCK INSTITUTE FOR HUMAN DEVELOPMENT   (Germany)

^d INRIA   (France)

^e Université Paul Sabatier   (France)

Author keywords

Behavioral heuristics; Closure relation; Fluid model; Game theory; Individual based models; Kinetic model; Monokinetic; Nash equilibrium; Pedestrian dynamics; Rational agents; von Mises Fisher distribution

Indexed keywords

EID: 84883769030     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-013-0805-x     Document Type: Article

References (68)

1. Al-nasur, S., Kashroo, P.: A microscopic-to-macroscopic crowd dynamic model. In: Proceedings of the IEEE Intelligent Transportation Systems Conference, pp. 606-611 (2006).
2. Aoki, I.: A simulation study on the schooling mechanism in fish. Bull. Jpn. Soc. Sci. Fish. 48, 1081-1088 (1982).
3. Appert-Rolland, C., Degond, P., Motsch, S.: Two-way multi-lane traffic model for pedestrians in corridors. Netw. Heterog. Media 6, 351-381 (2011).
4. Aumann, R.: Existence of competitive equilibria in markets with a continuum of traders. Econometrica 32, 39-50 (1964).
5. Aw, A., Rascle, M.: Resurrection of second order models of traffic flow. SIAM J. Appl. Math. 60, 916-938 (2000).
6. Ballerini, M., Cabibbo, N., Candelier, R., Cavagna, A., Cisbani, E., Giardina, I., Lecomte, V., Orlandi, A., Parisi, G., Procaccini, A., Viale, M., Zdravkovic, V.: Interaction ruling animal collective behavior depends on topological rather than metric distance: evidence from a field study. Proc. Natl. Acad. Sci. USA 105, 1232-1237 (2008).
7. Barbaro, A., Degond, P.: Phase transition and diffusion among socially interacting self-propelled agent. Discrete Contin. Dyn. Syst., Ser. B (to appear). arXiv: 1207. 1926.
8. Bellomo, N., Bellouquid, A.: On the modeling of crowd dynamics: looking at the beautiful shapes of swarms. Netw. Heterog. Media 6, 383-399 (2011).
9. Bellomo, N., Dogbé, C.: On the modelling crowd dynamics from scaling to hyperbolic macroscopic models. Math. Models Methods Appl. Sci. 18 Suppl, 1317-1345 (2008).
10. Bellomo, N., Dogbé, C.: On the modeling of traffic and crowds: a survey of models, speculations and perspectives. SIAM Rev. 53, 409-463 (2011).
11. Berres, S., Ruiz-Baier, R., Schwandt, H., Tory, E. M.: An adaptive finite-volume method for a model of two-phase pedestrian flow. Netw. Heterog. Media 6, 401-423 (2011).
12. Blanchet, A.: Variational methods applied to biology and economics. Dissertation for the Habilitation, University Toulouse 1 Capitole (December 2012).
13. Bolley, F., Cañizo, J. A., Carrillo, J. A.: Mean-field limit for the stochastic Vicsek model. Appl. Math. Lett. 25, 339-343 (2012).
14. Bouchut, F.: On zero pressure gas dynamics. In: Perthame, B. (ed.) Advances in Kinetic Theory and Computing, pp. 171-190. World Scientific, Singapore (1994).
15. Bouchut, F., James, F.: Duality solutions for pressureless gases, monotone scalar conservation laws, and uniqueness. Commun. Partial Differ. Equ. 24, 2173-2189 (1999).
16. Burger, M., Markowich, P., Pietschmann, J.-F.: Continuous limit of a crowd motion and herding model: analysis and numerical simulations. Kinet. Relat. Models 4, 1025-1047 (2011).
17. Carlen, E., Degond, P., Wennberg, B.: Kinetic limits for pair-interaction driven master equations and biological swarm models. Math. Models Methods Appl. Sci. 23, 1339-1376 (2013).
18. Chertock, A., Kurganov, A., Polizzi, A., Timofeyev, I.: Pedestrian flow models with slowdown interactions. Math. Models Methods Appl. Sci. (to appear).
19. Colombo, R. M., Rosini, M. D.: Pedestrian flows and nonclassical shocks. Math. Methods Appl. Sci. 28, 1553-1567 (2005).
20. Coscia, V., Canavesio, C.: First-order macroscopic modelling of human crowd dynamics. Math. Models Methods Appl. Sci. 18 Suppl, 1217-1247 (2008).
21. Couzin, I. D., Krause, J., James, R., Ruxton, G. D., Franks, N. R.: Collective memory and spatial sorting in animal groups. J. Theor. Biol. 218, 1-11 (2002).
22. Cristiani, E., Piccoli, B., Tosin, A.: Multiscale modeling of granular flows with application to crowd dynamics. Multiscale Model. Simul. 9, 155-182 (2011).
23. Cutting, J. E., Vishton, P. M., Braren, P. A.: How we avoid collisions with stationary and moving objects. Psychol. Rev. 102, 627-651 (1995).
24. Degond, P.: Macroscopic limits of the Boltzmann equation: a review. In: Degond, P., et al. (eds.) Modeling and Computational Methods for Kinetic Equations, pp. 3-57. Birkhaüser, Basel (2003).
25. Degond, P., Appert-Rolland, C., Pettré, J., Theraulaz, G.: Macroscopic pedestrian models based on synthetic vision (submitted).
26. Degond, P., Frouvelle, A., Liu, J.-G.: Macroscopic limits and phase transition in a system of self-propelled particles. J. Nonlinear Sci. 23, 427-456 (2013).
27. Degond, P., Hua, J.: Self-organized hydrodynamics with congestion and path formation in crowds. J. Comput. Phys. 237, 299-319 (2013).
28. Degond, P., Hua, J., Navoret, L.: Numerical simulations of the Euler system with congestion constraint. J. Comput. Phys. 230, 8057-8088 (2011).
29. Degond, P., Liu, J.-G., Ringhofer, C.: A Nash equilibrium macroscopic closure for kinetic models coupled with mean-field games. arXiv: 1212. 6130.
30. Degond, P., Motsch, S.: Continuum limit of self-driven particles with orientation interaction. Math. Models Methods Appl. Sci. 18 Suppl, 1193-1215 (2008).
31. Di Francesco, M., Markowich, P. A., Pietschmann, J.-F., Wolfram, M.-T.: On the Hughes' model for pedestrian flow: the one-dimensional case. J. Differ. Equ. 250, 1334-1362 (2011).
32. Gautrais, J., Ginelli, F., Fournier, R., Blanco, S., Soria, M., Chaté, H., Theraulaz, G.: Deciphering interactions in moving animal groups. PLoS Comput. Biol. 8, e1002678 (2012).
33. Green, E. J., Porter, R. H.: Noncooperative collusion under imperfect price information. Econometrica 52, 87-100 (1984).
34. Grégoire, G., Chaté, H.: Onset of collective and cohesive motion. Phys. Rev. Lett. 92, 025702 (2004).
35. Guy, S. J., Chhugani, J., Kim, C., Satish, N., Lin, M. C., Manocha, D., Dubey, P.: Clearpath: highly parallel collision avoidance for multi-agent simulation. In: ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 177-187 (2009).
36. Helbing, D.: A mathematical model for the behavior of pedestrians. Behav. Sci. 36, 298-310 (1991).
37. Helbing, D.: A fluid dynamic model for the movement of pedestrians. Complex Syst. 6, 391-415 (1992).
38. Helbing, D., Molnàr, P.: Social force model for pedestrian dynamics. Phys. Rev. E 51, 4282-4286 (1995).
39. Helbing, D., Molnàr, P.: Self-organization phenomena in pedestrian crowds. In: Schweitzer, F. (ed.) Self-Organization of Complex Structures: From Individual to Collective Dynamics, pp. 569-577. Gordon and Breach, London (1997).
40. Henderson, L. F.: On the fluid mechanics of human crowd motion. Transp. Res. 8, 509-515 (1974).
41. Hoogendoorn, S., Bovy, P. H. L.: Simulation of pedestrian flows by optimal control and differential games. Optim. Control Appl. Methods 24, 153-172 (2003).
42. Huang, W. H., Fajen, B. R., Fink, J. R., Warren, W. H.: Visual navigation and obstacle avoidance using a steering potential function. Robot. Auton. Syst. 54, 288-299 (2006).
43. Huang, L., Wong, S. C., Zhang, M., Shu, C.-W., Lam, W. H. K.: Revisiting Hughes' dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm. Transp. Res., Part B, Methodol. 43, 127-141 (2009).
44. Hughes, R. L.: A continuum theory for the flow of pedestrians. Transp. Res., Part B, Methodol. 36, 507-535 (2002).
45. Hughes, R. L.: The flow of human crowds. Annu. Rev. Fluid Mech. 35, 169-182 (2003).
46. Hsu, E. P.: Stochastic Analysis on Manifolds. Graduate Series in Mathematics, vol. 38. American Mathematical Society, Providence (2002).
47. Jiang, Y.-q., Zhang, P., Wong, S. C., Liu, R.-x.: A higher-order macroscopic model for pedestrian flows. Physica A 389, 4623-4635 (2010).
48. Lasry, J.-M., Lions, P.-L.: Mean field games. Jpn. J. Math. 2, 229-260 (2007).
49. Lemercier, S., Jelic, A., Kulpa, R., Hua, J., Fehrenbach, J., Degond, P., Appert-Rolland, C., Donikian, S., Pettré, J.: Realistic following behaviors for crowd simulation. Comput. Graph. Forum 31, 489-498 (2012).
50. Lighthill, M. J., Whitham, J. B.: On kinematic waves, I: flow movement in long rivers; II: a theory of traffic flow on long crowded roads. Proc. R. Soc. A 229, 1749-1766 (1955).
51. Maury, B., Roudneff-Chupin, A., Santambrogio, F., Venel, J.: Handling congestion in crowd motion models. Netw. Heterog. Media 6, 485-519 (2011).
52. Motsch, S., Moussaïd, M., Guillot, E. G., Lemercier, S., Pettré, J., Theraulaz, G., Appert-Rolland, C., Degond, P.: Dynamics of cluster formation and traffic efficiency in pedestrian crowds (submitted).
53. Moussaïd, M., Guillot, E. G., Moreau, M., Fehrenbach, J., Chabiron, O., Lemercier, S., Pettré, J., Appert-Rolland, C., Degond, P., Theraulaz, G.: Traffic instabilities in self-organized pedestrian crowds. PLoS Comput. Biol. 8, e1002442 (2012).
54. Moussaïd, M., Helbing, D., Theraulaz, G.: How simple rules determine pedestrian behavior and crowd disasters. Proc. Natl. Acad. Sci. USA 108, 6884-6888 (2011).
55. Ngai, K. M., Burkle, F. M. Jr., Hsu, A., Hsu, E. B.: Human stampedes: a systematic review of historical and peer-reviewed sources. Disaster Med. Public Health Prep. 3, 191-195 (2009).
56. Nishinari, K., Kirchner, A., Namazi, A., Schadschneider, A.: Extended floor field CA model for evacuation dynamics. IEICE Transp. Inf. Syst. E 87-D, 726-732 (2004).
57. Ondrej, J., Pettré, J., Olivier, A. H., Donikian, S.: A synthetic-vision based steering approach for crowd simulation. In: SIGGRAPH'10 (2010).
58. Paris, S., Pettré, J., Donikian, S.: Pedestrian reactive navigation for crowd simulation: a predictive approach. Eurographics 26, 665-674 (2007).
59. Payne, H. J.: Models of Freeway Traffic and Control. Simulation Councils Inc., La Jolla (1971).
60. Pettré, J., Ondřej, J., Olivier, A.-H., Cretual, A., Donikian, S.: Experiment-based modeling, simulation and validation of interactions between virtual walkers. In: SCA '09: Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 189-198 (2009).
61. Piccoli, B., Tosin, A.: Pedestrian flows in bounded domains with obstacles. Contin. Mech. Thermodyn. 21, 85-117 (2009).
62. Reynolds, C. W.: Steering behaviors for autonomous characters. In: Proceedings of Game Developers Conference, San Jose, California, pp. 763-782 (1999).
63. Rosenthal, R. W.: A class of games possessing pure-strategy Nash equilibria. Int. J. Game Theory 2, 65-67 (1973).
64. Schmeidler, D.: Equilibrium points of nonatomic games. J. Stat. Phys. 7, 295-300 (1973).
65. van den Berg, J., Overmars, H.: Planning time-minimal safe paths amidst unpredictably moving obstacles. Int. J. Robot. Res. 27, 1274-1294 (2008).
66. Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., Shochet, O.: Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75, 1226-1229 (1995).
67. Warren, W. H., Fajen, B. R.: From optic flow to laws of control. In: Vaina, L. M., Beardsley, S. A., Rushton, S. (eds.) Optic Flow and Beyond, pp. 307-337. Kluwer, Dordrecht (2004).
68. Watson, G. S.: Distributions on the circle and sphere. J. Appl. Probab. 19, 265-280 (1982).