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Behavioral Human Crowds

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Crowd Dynamics, Volume 1

Abstract

This chapter provides an introduction to the contents of Bellomo and Gibelli (Crowd dynamics, volume 1 – theory, models, and safety problems. Modeling and simulation in science, engineering, and technology. Birkhäuser, New York, 2018) and a general critical analysis on crowd modeling. The presentation is organized in three parts: firstly, a general framework and rationale toward the modeling and simulations of human crowds are proposed; subsequently the contents of Chaps. 2, 3, 4 , 5 , 6 , 7 , 8 and 9 are summarized by referring to the existing literature; finally, by taking advantage of the contents of the whole book, some speculations are proposed on possible research perspectives. Five key problems are presented, and hints are given to tackle them within a multiscale vision which appears to be the most looking forward idea to be pursued in research projects.

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References

  1. G. Ajmone Marsan, N. Bellomo, and L. Gibelli, Stochastic evolutionary differential games toward a systems theory of behavioral social dynamics, Math. Models Methods Appl. Sci., 26, 1051–1093, (2016).

    Article  MathSciNet  Google Scholar 

  2. G. Albi, M. Bongini, E. Cristiano, and D. Kalise, Invisible control of self-organizing agents leaving unknown environments, Siam J. Appl. Math., 76(4), 1683–1710, (2016).

    Article  MathSciNet  Google Scholar 

  3. B. Andreianov, C. Donadello, U. Razafison and M. D. Rosini, One-dimensional conservation laws with non-local point constraints on the flux, Chapter 5 in Crowd Dynamics, Volume 1 - Theory, Models, and Safety Problems, Modeling and Simulation in Science, Engineering, and Technology, Birkhäuser, New York, (2018).

    Google Scholar 

  4. R. Bailo, J. A. Carrillo, and P. Degond, Pedestrian models based on rational behaviour, Chapter 9 in Crowd Dynamics, Volume 1 - Theory, Models, and Safety Problems, Modeling and Simulation in Science, Engineering, and Technology, Birkhäuser, New York, (2018).

    Google Scholar 

  5. P. Ball, Why Society is a Complex Matter, Springer-Verlag, Heidelberg, (2012).

    Chapter  Google Scholar 

  6. N. Bellomo and A. Bellouquid, On multiscale models of pedestrian crowds from mesoscopic to macroscopic, Comm. Math. Sciences, 13(7), 1649–1664, (2015).

    Article  MathSciNet  Google Scholar 

  7. N. Bellomo, A. Bellouquid, L. Gibelli, and N. Outada, A Quest Towards a Mathematical Theory of Living Systems, Birkhäuser, New York, (2017).

    Chapter  Google Scholar 

  8. N. Bellomo, A. Bellouquid, and D. Knopoff, From the microscale to collective crowd dynamics, Multiscale Model. Simul., 11(3), 943–963, (2013).

    Article  MathSciNet  Google Scholar 

  9. N. Bellomo, D. Clarke, L. Gibelli, P. Townsend, and B.J. Vreugdenhil, Human behaviours in evacuation crowd dynamics: From modeling to “big data” toward crisis management, Phys. Life Rev., 18, 1–21, (2016).

    Article  Google Scholar 

  10. N. Bellomo, and L. Gibelli, Toward a mathematical theory of behavioral-social dynamics for pedestrian crowds, Math. Models Methods Appl. Sci., 25(13), 2417–2437, (2015).

    Article  MathSciNet  Google Scholar 

  11. N. Bellomo and L. Gibelli, Behavioral crowds: Modeling and Monte Carlo simulations toward validation, Computers & Fluids, 141, 13–21, (2016).

    Article  MathSciNet  Google Scholar 

  12. N. Bellomo and L. Gibelli, Crowd Dynamics, Volume 1 - Theory, Models, and Safety Problems, Modeling and Simulation in Science, Engineering, and Technology, Birkhäuser, New York, (2018).

    Google Scholar 

  13. N. Bellomo, L. Gibelli, and N. Outada, On the interplay between behavioral dynamics and social interactions in human crowds, Kinet. Relat. Mod., 12(2), 397–409, (2019).

    Article  Google Scholar 

  14. A. Bellouquid and N. Chouhad, Kinetic models of chemotaxis towards the diffusive limit: asymptotic analysis, Math. Models Methods Appl. Sci., 39, 3136–3151, (2016).

    Article  MathSciNet  Google Scholar 

  15. A.L. Bertozzi, J. Rosado, M.B. Short, and L. Wang, Contagion shocks in one dimension, J. Stat. Phys., 158, 647–664, (2015).

    Article  MathSciNet  Google Scholar 

  16. G.A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford University Press, (1994).

    Google Scholar 

  17. R. Borsche, A. Klar, and F. Schneider, Numerical methods for mean-field and moment models for pedestrian flow, Chapter 7 in Crowd Dynamics, Volume 1 - Theory, Models, and Safety Problems, Modeling and Simulation in Science, Engineering, and Technology, Birkhäuser, New York, (2018).

    Google Scholar 

  18. M. Burger, P. Markowich, J.F. Pietschmann, Continuous limit of a crowd motion and herding Model: analysis and numerical simulations, Kinet. Rel. Models, 4(4), 1025–1047, (2011).

    Article  MathSciNet  Google Scholar 

  19. D. Burini and N. Chouhad, Hilbert method toward a multiscale analysis from kinetic to macroscopic models for active particles, Math. Models Methods Appl. Sci., 27, 1327–1353, (2017).

    Article  MathSciNet  Google Scholar 

  20. D. Burini, S. De Lillo, and L. Gibelli, Stochastic differential “nonlinear” games modeling collective learning dynamics, Phys. Life Rev., 16, 123–139, (2016).

    Article  Google Scholar 

  21. J.-A. Carrillo, S. Martin, and M.-T. Wolfram An improved version of the Hughes model for pedestrian flow Math. Model. Methods Appl. Sci., 26(04), 671–697, (2016).

    Article  MathSciNet  Google Scholar 

  22. C. Cercignani, R. Illner, and M. Pulvirenti, The Kinetic Theory of a Diluted Gas, Springer, Heidelberg, New York, (1993).

    Google Scholar 

  23. M. Colangeli, A. Muntean, O. Richardson and T. Thieu, Modelling interactions between active and passive agents moving through heterogeneous environments, Chapter 8 in Crowd Dynamics, Volume 1 - Theory, Models, and Safety Problems, Modeling and Simulation in Science, Engineering, and Technology, Birkhäuser, New York, (2018).

    Google Scholar 

  24. E. Cristiani, B. Piccoli, and A. Tosin, Multiscale Modeling of Pedestrian Dynamics, Springer, (2014).

    Google Scholar 

  25. E. Cristiani, F.S. Priuli, and A. Tosin, Modeling rationality to control self-organization of crowds: an environmental approach, SIAM J. Appl. Math., 75(2), 605–629, (2015).

    Article  MathSciNet  Google Scholar 

  26. A. Corbetta, A. Mountean, and K. Vafayi, Parameter estimation of social forces in pedestrian dynamics models via probabilistic method, Math. Biosci. Eng., 12, 337–356, (2015).

    MathSciNet  MATH  Google Scholar 

  27. P. Degond, C. Appert-Rolland, M. Moussaid, J. Pettré, and G. Theraulaz, A hierarchy of heuristic-based models of crowd dynamics, J. Stat. Phys., 152, 1033–1068, (2013).

    Article  MathSciNet  Google Scholar 

  28. P. Degond, C. Appert-Rolland, J. Pettré, and G. Theraulaz, Vision based macroscopic pedestrian models, Kinetic Related Models, 6, 809–839, (2013).

    Article  MathSciNet  Google Scholar 

  29. J.-M. Epstein J.M., Modeling civil violence: An agent based computational approach, Proc. Nat. Acad. Sci., 99, 7243–7250, (2002).

    Article  Google Scholar 

  30. Z. Fu, L. Luo, Y. Yang, Y. Zhuang, P. Zhang, L. Yang, H. Yang, J. Ma, K. Zhu, and Y. Li, Effect of speed matching on fundamental diagram of pedestrian flow, Physica A, 458, 31–42, (2016).

    Article  Google Scholar 

  31. H. Gintis, Game Theory Evolving, 2nd Ed., Princeton University Press, Princeton NJ, (2009).

    Google Scholar 

  32. M. Haghani, and M. Sarvi, Social dynamics in emergency evacuations: Disentangling crowds attraction and repulsion effects, Physica A, 475, 24–34, (2017).

    Article  Google Scholar 

  33. D. Helbing, Traffic and related self-driven many-particle systems, Rev. Modern Phys., 73, 1067–1141, (2001).

    Article  MathSciNet  Google Scholar 

  34. D. Helbing and P. Molnár, Social force model for pedestrian dynamics Phys. Rev. E, 51, 4282–4286, (1995).

    Article  Google Scholar 

  35. D. Helbing, P. Molnár, I.-J. Farkas, and K. Bolay, Self-organizing pedestrian movement, Environ. Plan. B Plan. Des., 28(3), 361–383, (2001).

    Article  Google Scholar 

  36. D. Helbing D. and A. Johansson, Pedestrian crowd and evacuation dynamics, Enciclopedia of Complexity and System Science, Springer, 6476–6495, (2009).

    Google Scholar 

  37. D. Helbing, A. Johansson, and H.-Z. Al-Abideen, Dynamics of crowd disasters: An empirical study, Phys. Rev. E, 75, paper no. 046109, (2007).

    Google Scholar 

  38. D. Hilbert, Mathematical problems, Bull. Amer. Math. Soc., 8(10) (1902), 437–479.

    Article  MathSciNet  Google Scholar 

  39. S.P. Hoogendoorn, F. van Wageningen-Kessels, W. Daamen, and D.C. Duives, Continuum modelling of pedestrian flows: From microscopic principles to self-organised macroscopic phenomena, Physica A, 416, 684–694, (2014).

    Article  Google Scholar 

  40. R. L. Hughes A continuum theory for the flow of pedestrians, Transp. Research B, 36, 507–536, (2002).

    Article  Google Scholar 

  41. R.L. Hughes, The flow of human crowds, Annu. Rev. Fluid Mech., 35, 169–182, (2003).

    Article  MathSciNet  Google Scholar 

  42. M. Kinateder, T. D. Wirth, and W. H. Warren, Crowd Dynamics in Virtual Reality, Chapter 2 in Crowd Dynamics, Volume 1 - Theory, Models, and Safety Problems, Modeling and Simulation in Science, Engineering, and Technology, Birkhäuser, New York, (2018).

    Google Scholar 

  43. A. Lachapelle, M.T. Wolfram, On a mean field game approach modeling congestion and aversion in pedestrian crowds Transportation Research B, 45, 1572–1589, (2011).

    Google Scholar 

  44. F. Martinez-Gil, M. Lozano, I. Garcia-Fernández and F. Fernández, Modeling, evaluation and scale on artificial pedestrians: A literature review, ACM Computing Surveys, In press (2018).

    Google Scholar 

  45. B. Maury, and J. Venel A discrete contact model for crowd motion, ESAIM: M2AN, 45, 145–168, (2011).

    Article  MathSciNet  Google Scholar 

  46. M. Moussaïd, E.-G. Guillot, M. Moreau, J. Fehrenbach, O. Chabiron, S. Lemercier, J. Pettré, C. Appert-Rolland, P. Degond, and G. Theraulaz, Traffic instabilities in self-organized pedestrian crowds PLoS Comput. Biol., 8(3), (2012).

    Article  Google Scholar 

  47. M. Moussaïd, D. Helbing, S. Garnier, A. Johansson, M. Combe, and G. Theraulaz, Experimental study of the behavioural mechanisms underlying self-organization in human crowds, Proc. Roy. Soc. B, 276, 2755–2762, (2009).

    Article  Google Scholar 

  48. M. Moussaïd and G. Theraulaz, Comment les piétons marchent dans la foule. La Recherche, 450, 56–59, (2011).

    Google Scholar 

  49. L. Pareschi and G. Toscani, Interacting Multiagent Systems: Kinetic Equations and Monte Carlo Methods Oxford University Press, Oxford, (2014).

    Google Scholar 

  50. B. Piccoli and F. Rossi, Measure-theoretic models for crowd dynamics, Chapter 6 in Crowd Dynamics, Volume 1 - Theory, Models, and Safety Problems, Modeling and Simulation in Science, Engineering, and Technology, Birkhäuser, New York, (2018).

    Google Scholar 

  51. F. Ronchi, F. Nieto Uriz, X. Criel, and P. Reilly, Modelling large-scale evacuation of music festival. Fire Safety, 5, 11–19, (2016).

    Article  Google Scholar 

  52. E. Ronchi and D. Nilsson Pedestrian Movement in Smoke: Theory, Data and Modelling Approaches, Chapter 3 in Crowd Dynamics, Volume 1 - Theory, Models, and Safety Problems, Modeling and Simulation in Science, Engineering, and Technology, Birkhäuser, New York, (2018).

    Google Scholar 

  53. L. Saint-Raymond, Hydrodynamic limits of the Boltzmann equation, Lecture Notes in Mathematics n.1971, Springer, Berlin, (2009).

    Google Scholar 

  54. A. Schadschneider, M. Chraibi, A. Seyfried, A. Tordeux, and J. Zhang, Pedestrian Dynamics - From Empirical Results to Modeling, Chapter 4 in Crowd Dynamics, Volume 1 - Theory, Models, and Safety Problems, Modeling and Simulation in Science, Engineering, and Technology, Birkhäuser, New York, (2018).

    Google Scholar 

  55. A. Schadschneider, W. Klingsch, H. Kläpfel, T. Kretz, C. Rogsch, and A. Seyfried, Evacuation Dynamics: Empirical Results, Modeling and Applications, Encyclopedia of Complexity and System Scence, 3142–3176, (2009).

    Google Scholar 

  56. A. Schadschneider and A. Seyfried, Empirical results for pedestrian dynamics and their implications for modeling. Netw. Heterog. Media, 6, 545–560, (2011).

    Article  MathSciNet  Google Scholar 

  57. A. Seyfried, B. Steffen, W. Klingsch, and M. Boltes, The fundamental diagram of pedestrian movement revisited, J. Stat. Mech.: Theory and Experiments, 360, 232–238, (2006).

    Google Scholar 

  58. H. Vermuyten, J. Belien, L. De Boeck, G. Reniers, and T. Wauters, A review of optimisation models for pedestrian evacuation and design problems, Safety Science, 87, 167–178, (2016).

    Article  Google Scholar 

  59. L. Wang, M.B. Short, and A.L. Bertozzi, Efficient numerical methods for multiscale crowd dynamics with emotional contagion, Math. Models Methods Appl. Sci., 27, 205–230, (2017).

    Article  MathSciNet  Google Scholar 

  60. N. Wijermans, C. Conrado, M. van Steen, C. Martella, and J.-L. Li, A landscape of crowd management support: An integrative approach, Safety Science, 86, 142–164, (2016).

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematical Sciences, Politecnico of Torino, Torino, Italy

    Nicola Bellomo

  2. School of Engineering, University of Edinburgh, Edinburgh, UK

    Livio Gibelli

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  1. Nicola Bellomo
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  2. Livio Gibelli
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Correspondence to Livio Gibelli .

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Editors and Affiliations

  1. School of Engineering, University of Edinburgh, Edinburgh, UK

    Livio Gibelli

  2. Department of Mathematical Sciences, Politecnico di Torino, Torino, Italy

    Nicola Bellomo

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Bellomo, N., Gibelli, L. (2018). Behavioral Human Crowds. In: Gibelli, L., Bellomo, N. (eds) Crowd Dynamics, Volume 1. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-05129-7_1

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