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Traffic and Granular Flow '13 pp 3–12Cite as

Modeling of Pedestrians

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Abstract

Different families of models first developed for fluid mechanics have been extended to road, pedestrian, or intracellular transport. These models allow to describe the systems at different scales and to account for different aspects of dynamics. In this paper, we focus on pedestrians and illustrate the various families of models by giving an example of each type. We discuss the specificities of crowds compared to other transport systems.

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Notes

  1. 1.

    Note that in some communities, random shuffle update is called random sequential update, as done in [42]. We shall stick to the denomination used in physics, for which random sequential update rather refers to an update close to continuous time.

References

  1. D. Chowdhury, L. Santen, A. Schadschneider, Statistical physics of vehicular traffic and some related systems. Phys. Rep. 329, 199 (2000)

    Article  MathSciNet  Google Scholar 

  2. T. Vicsek, A. Zafeiris, Collective motion. Phys. Rep. 517(3–4), 71–140 (2012)

    Article  Google Scholar 

  3. T. Chou, K. Mallick. R.K.P. Zia, Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport. Rep. Prog. Phys. 74, 116601 (2011)

    Google Scholar 

  4. C. Appert-Rolland, M. Ebbinghaus, L. Santen, Intracellular transport driven by cytoskeletal motors: general mechanisms and defects. Phys. Rep. (submitted)

    Google Scholar 

  5. B. Alder, T.E. Wainwright, Studies in molecular dynamics. I. General method. J. Chem. Phys. 31, 459 (1959)

    MathSciNet  Google Scholar 

  6. A. Rahman, Correlations in the motion of atoms in liquid argon. Phys. Rev. 136, A405–A411 (1964)

    Article  Google Scholar 

  7. L. Pipes, An operational analysis of traffic dynamics. J. Appl. Phys. 24, 274–281 (1953)

    Article  MathSciNet  Google Scholar 

  8. R. Chandler, R. Herman, E. Montroll, Traffic dynamics: studies in car following. Oper. Res. 6, 165–184 (1958)

    Article  MathSciNet  Google Scholar 

  9. D. Gazis, R. Herman, R. Potts, Car following theory of steady state traffic flow. Oper. Res. 7, 499–505 (1959)

    Article  MathSciNet  Google Scholar 

  10. U. Frisch, B. Hasslacher, Y. Pomeau, Lattice-gas automata for the Navier-Stokes equation. Phys. Rev. Lett. 56, 1505–1508 (1986)

    Article  Google Scholar 

  11. K. Nagel, M. Schreckenberg, A cellular automaton model for freeway traffic. J. Phys. I 2, 2221–2229 (1992)

    Google Scholar 

  12. C. Burstedde, K. Klauck, A. Schadschneider, J. Zittartz, Simulation of pedestrian dynamics using a 2-dimensional cellular automaton. Physica A 295, 507–525 (2001)

    Article  MATH  Google Scholar 

  13. A. Parmeggiani, T. Franosch, E. Frey, Totally asymmetric simple exclusion process with Langmuir kinetics. Phys. Rev. E 70, 046101 (2004)

    Article  MathSciNet  Google Scholar 

  14. M. Lighthill, G. Whitham, On kinematic waves. II. A theory of traffic flow on long crowded roads. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. A 229, 317–345 (1955)

    Google Scholar 

  15. P. Richards, Shock waves on the highway. Oper. Res. 4, 42–51 (1956)

    Article  MathSciNet  Google Scholar 

  16. H. Payne, Models of freeway traffic and control, in Mathematical Model of Public Systems. Simulation Councils Proceedings Series, La Jolla, vol. 1 (1971), pp. 51–60

    Google Scholar 

  17. M.R.A. Aw, Resurrection of “second order” models of traffic flow and numerical simulation. SIAM J. Appl. Math. 60, 916–938 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  18. PEDIGREE project: website http://www.math.univ-toulouse.fr/pedigree (2009–2011)

  19. S. Hoogendoorn, S. Ossen, M. Schreuder, Empirics of multianticipative car-following behavior. Transp. Res. Rec. 1965, 112–120 (2006)

    Article  Google Scholar 

  20. A. Seyfried, B. Steffen, W. Klingsch, M. Boltes, The fundamental diagram of pedestrian movement revisited. J. Stat. Mech. 2005, P10002 (2005)

    Article  Google Scholar 

  21. U. Chattaraj, A. Seyfried, P. Chakroborty, Comparison of pedestrian fundamental diagram across cultures. Adv. Complex Syst. 12, 393–405 (2009)

    Article  Google Scholar 

  22. D. Yanagisawa, A. Tomoeda, K. Nishinari, Improvement of pedestrian flow by slow rhythm. Phys. Rev. E 85, 016111 (2012)

    Article  Google Scholar 

  23. S. Lemercier, A. Jelic, R. Kulpa, J. Hua, J. Fehrenbach, P. Degond, C. Appert-Rolland, S. Donikian, J. Pettré, Realistic following behaviors for crowd simulation. Comput. Graph. Forum 31, 489–498 (2012)

    Article  Google Scholar 

  24. Experiments were organized and realized by the PEDIGREE partnership at University Rennes 1, with the help of the laboratory M2S from Rennes 2

    Google Scholar 

  25. C. Appert-Rolland, A. Jelic, P. Degond, J. Fehrenbach, J. Hua, A. Crétual, R. Kulpa, A. Marin, A.-H. Olivier, S. Lemercier, J. Pettré, Experimental study of the following dynamics of pedestrians, in Pedestrian and Evacuation Dynamics 2012, ed. by U. Weidmann, U. Kirsch, M. Schreckenberg (Springer, Heidelberg, 2014), pp. 305–316

    Google Scholar 

  26. A. Jelić, C. Appert-Rolland, S. Lemercier, J. Pettré, Properties of pedestrians walking in line – fundamental diagrams. Phys. Rev. E 85, 036111 (2012)

    Article  Google Scholar 

  27. A. Jelić, C. Appert-Rolland, S. Lemercier, J. Pettré, Properties of pedestrians walking in line. ii. Stepping behavior. Phys. Rev. E 86, 046111 (2012)

    Google Scholar 

  28. C. Appert-Rolland, P. Degond, S. Motsch, Two-way multi-lane traffic model for pedestrians in corridors. Netw. Heterog. Media 6, 351–381 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  29. C. Appert-Rolland, P. Degond, S. Motsch, A macroscopic model for bidirectional pedestrian flow, in Pedestrian and Evacuation Dynamics 2012, ed. by U. Weidmann, U. Kirsch, M. Schreckenberg (Springer, Heidelberg, 2014), pp. 575–584

    Google Scholar 

  30. C. Appert-Rolland, H. Hilhorst, G. Schehr, Spontaneous symmetry breaking in a two-lane model for bidirectional overtaking traffic. J. Stat. Mech. 2010, P08024 (2010)

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  32. P. Degond, C. Appert-Rolland, J. Pettré, G. Theraulaz, Vision-based macroscopic pedestrian models. Kinet. Relat. Models 6, 809–839 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  33. J.-F. Gouyet, C. Appert, Stochastic and hydrodynamic lattice gas models: mean-field kinetic approaches. Int. J. Bifurcat. Chaos 12, 227–259 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  34. A. Schadschneider, A. Kirchner, K. Nishinari, From ant trails to pedestrian dynamics. Appl. Bionics Biomech. 1, 11–19 (2003)

    Article  Google Scholar 

  35. K. Nishinari, K. Sugawara, T. Kazama, A. Schadschneider, D. Chowdhury, Modelling of self-driven particles: foraging ants and pedestrians. Physica A 372, 132–141 (2006)

    Article  Google Scholar 

  36. A. Kirchner, H. Klüpfel, K. Nishinari, A. Schadschneider, M. Schreckenberg, Simulation of competitive egress behaviour: comparison with aircraft evacuation data. Physica A 324, 689–697 (2003)

    Article  MATH  Google Scholar 

  37. A. Kirchner, K. Nishinari, A. Schadschneider, Friction effects and clogging in a cellular automaton model for pedestrian dynamics. Phys. Rev. E 67, 056122 (2003)

    Article  Google Scholar 

  38. M. Wölki, A. Schadschneider, M. Schreckenberg, Asymmetric exclusion processes with shuffled dynamics. J. Phys. A-Math. Gen. 39, 33–44 (2006)

    Article  MATH  Google Scholar 

  39. M. Wölki, M. Schadschneider, M. Schreckenberg, Fundamental diagram of a one-dimensional cellular automaton model for pedestrian flow – the ASEP with shuffled update, in Pedestrian and Evacuation Dynamics 2005, ed. by N. Waldau, P. Gattermann, H. Knoflacher, M. Schreckenberg (Springer, Berlin, 2007), p. 423

    Google Scholar 

  40. D.A. Smith, R.E. Wilson, Dynamical pair approximation for cellular automata with shuffle update. J. Phys. A: Math. Theor. 40(11), 2651–2664 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  41. H. Klüpfel, The simulation of crowds at very large events, in Traffic and Granular Flow’05, ed. by A. Schadschneider, T. Poschel, R. Kuhne, M. Schreckenberg, D. Wolf (Springer, Berlin/Heidelberg, 2007), pp. 341–346

    Chapter  Google Scholar 

  42. H. Klüpfel, T. Meyer-König, J. Wahle, M. Schreckenberg, Microscopic simulation of evacuation processes on passenger ships, in Proceedings of the 4th International Conference on Cellular Automata for Research and Industry (ACRI00), Karlsruhe, ed. by S. Bandini, T. Worsch (Springer, 2000), pp. 63–71

    Google Scholar 

  43. C. Appert-Rolland, J. Cividini, H. Hilhorst, Frozen shuffle update for an asymmetric exclusion process on a ring. J. Stat. Mech. 2011, P07009 (2011)

    Google Scholar 

  44. C. Appert-Rolland, J. Cividini, H. Hilhorst, Frozen shuffle update for a deterministic totally asymmetric simple exclusion process with open boundaries. J. Stat. Mech. 2011, P10013 (2011)

    Article  Google Scholar 

  45. S.P. Hoogendoorn, W. Daamen, Self-organization in Pedestrian Flow, in Traffic and Granular Flow ’03, ed. by S.P. Hoogendoorn, S. Luding, P.H.L. Bovy, M. Schreckenberg, D.E. Wolf. (Springer-Verlag Berlin, Heidelberg, 2005), pp. 373–382

    Google Scholar 

  46. C. Burstedde, A. Kirchner, K. Klauck, A. Schadschneider, J. Zittartz, Cellular automaton approach to pedestrian dynamics – applications, in Pedestrian and Evacuation Dynamics, ed. by M. Schreckenberg, S.D. Sharma (Springer-Verlag Berlin, Heidelberg, 2001), p. 87

    Google Scholar 

  47. J. Cividini, C. Appert-Rolland, H. Hilhorst, Diagonal patterns and chevron effect in intersecting traffic flows. Europhys. Lett. 102, 20002 (2013)

    Article  Google Scholar 

  48. J. Cividini, Generic instability at the crossing of pedestrian flows, in Traffic and Granular Flow ’13, ed. by M. Chraibi, M. Boltes, A. Schadschneider, A. Seyfried (Springer, Cham, 2014)

    Google Scholar 

  49. S.P. Hoogendoorn, P.H.L. Bovy, Pedestrian route-choice and activity scheduling theory and models. Transp. Res. Part B: Methodol. 38, 169–190 (2004)

    Article  Google Scholar 

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Acknowledgements

The PEDIGREE project has been supported by the French ‘Agence Nationale pour la Recherche (ANR)’ (contract number ANR-08-SYSC-015-01, from 2008 to 2011).

Subsequent data analysis was partially supported by the ‘RTRA Triangle de la physique’ (Project 2011-033T).

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Authors and Affiliations

  1. Laboratory of Theoretical Physics, CNRS UMR 8627, University of Paris-Sud, 91405, Orsay Cedex, France

    Cecile Appert-Rolland

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  1. Cecile Appert-Rolland
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Correspondence to Cecile Appert-Rolland .

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Editors and Affiliations

  1. Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany

    Mohcine Chraibi

  2. Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany

    Maik Boltes

  3. Institut für Theoretische Physik, Universität zu Köln, Köln, Germany

    Andreas Schadschneider

  4. Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany

    Armin Seyfried

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Appert-Rolland, C. (2015). Modeling of Pedestrians. In: Chraibi, M., Boltes, M., Schadschneider, A., Seyfried, A. (eds) Traffic and Granular Flow '13. Springer, Cham. https://doi.org/10.1007/978-3-319-10629-8_1

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