Abstract
A brief overview of mathematical modeling of pedestrian dynamics is presented. Hereby, we focus on space-continuous models which include interactions between the pedestrian by forces. Conceptual problems of such models are addressed. Side-effects of spatially continuous force-based models, especially oscillations and overlapping which occur for erroneous choices of the forces, are analyzed in a quantitative manner. As a representative example of force-based models the Generalized Centrifugal Force Model (GCFM) is introduced. Key components of the model are presented and discussed. Finally, simulations with the GCFM in corridors and bottlenecks are shown and compared with experimental data.
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References
Chattaraj, U., Chakroborty, P., Seyfried, A.: Empirical studies on pedestrian motion through corridors of different geometries. In: Proceedings of Transportation Research Board 89th Annual Meeting, CD Rom, Washington, D.C (2010)
Chraibi, M., Seyfried, A., Schadschneider, A.: The generalized centrifugal force model for pedestrian dynamics. Phys. Rev. E 82, 046111 (2010)
Daamen, W., Hoogendoorn, S.: Capacity of doors during evacuation conditions. Procedia Eng. 3, 53–66 (2010)
Fruin, J.J.: Pedestrian Planning and Design. Elevator World, New York (1971)
Hankin, B.D., Wright, R.A.: Passenger flow in subways. Oper. Res. Soc. 9(2), 81–88 (1958)
Helbing, D.: Collective phenomena and states in traffic and self-driven many-particle systems. Comput. Mater. Sci. 30, 180–187 (2004)
Helbing, D., Molnár, P.: Social force model for pedestrian dynamics. Phys. Rev. E 51, 4282–4286 (1995)
Hirai, K., Tirui, K.: A simulation of the behavior of a crowd in panic. Syst. Control 21, 409–411 (1977)
Holl, S., Seyfried, A.: Hermes – an evacuation assistant for mass events. inSiDe 7(1), 60–61 (2009)
Hoogendoorn, S., Daamen, W.: Pedestrian behavior at bottlenecks. Transp. Sci. 39(2), 147–159 (2005)
Gipps, P.G., Marksjö, B.: A micro-simulation model for pedestrian flows. Math. Comput. Simul. 27, 95–105 (1985)
Kretz, T., Grünebohm, A., Schreckenberg, M.: Experimental study of pedestrian flow through a bottleneck. J. Stat. Mech. Theory Exp. 2006(10), P10014 (2006)
Lakoba, T.I., Kaup, D.J., Finkelstein, N.M.: Modifications of the Helbing-Molnár-Farkas-Vicsek social force model for pedestrian evolution. Simulation 81(5), 339–352 (2005)
Liddle, J., Seyfried, A., Klingsch, W., Rupprecht, T., Schadschneider, A., Winkens, A.: An experimental study of pedestrian congestions: influence of bottleneck width and length. ArXiv e-prints (2009)
Liddle, J., Seyfried, A., Steffen, B., Klingsch, W., Rupprecht, T., Winkens, A., Boltes, M.: Microscopic insights into pedestrian motion through a bottleneck, resolving spatial and temporal variations. ArXiv e-prints (2011)
Löhner, R.: On the modelling of pedestrian motion. Appl. Math. Model. 34(2), 366–382 (2010)
Moussaïd, M., Helbing, D., Garnier, S., Johansson, A., Combe, M., Theraulaz, G.: Experimental study of the behavioural mechanisms underlying self-organization in human crowds. Proc. R. Soc. B 276(1668), 2755–2762 (2009)
Parisi, D.R., Dorso, C.O.: Morphological and dynamical aspects of the room evacuation process. Physica A 385(1), 343–355 (2007)
Pauls J.L.: Suggestions on evacuation models and research questions. In: Shields, T.J. (ed.) Human Behaviour in Fire. Interscience Communications, London (2004)
Pauls J.L.: Stairways and Ergonomics. ASSE, Des Plaines (2006)
Pipes, L.A.: An operational analysis of traffic dynamics. J. Appl. Phys. 24(3), 274–281 (1953)
Reuschel, A.: Fahrzeugbewegungen in der Kolonne. Z. Öster. Ing. Arch. 4, 193–214 (1950)
Reuschel, A.: Fahrzeugbewegungen in der Kolonne bei gleichförmig beschleunigtem oder verzögertem Leitfahrzeug. Z. Öster. Ing. Arch. 59, 73–77 (1950)
Rissanen, J.: Minimum-description-length principle. In: Encyclopedia of Statistical Sciences. John Wiley & Sons, Inc., Hoboken (2004)
Schadschneider, A.: I’m a football fan ⋯ get me out of here. Phys. World 21, 21–25 (2010)
Schadschneider, A., Klingsch, W., Klüpfel, H., Kretz, T., Rogsch, C., Seyfried, A.: Evacuation Dynamics: Empirical Results, Modeling and Applications. In: Encyclopedia of Complexity and System Science, vol. 5, pp. 3142–3176. Springer, Berlin/Heidelberg (2009)
Schadschneider, A., Chowdhury, D., Nishinari, K.: Stochastic Transport in Complex Systems. From Molecules to Vehicles. Elsevier, Amsterdam (2010)
Seyfried, A., Passon, O., Steffen, B., Boltes, M., Rupprecht, T., Klingsch, W.: New insights into pedestrian flow through bottlenecks. Transp. Sci. 43(3), 395–406 (2009)
Seyfried, A., Schadschneider, A.: Empirical results for pedestrian dynamics at bottlenecks. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds.) Parallel Processing and Applied Mathematics. Volume 6068 of Lecture Notes in Computer Science, pp. 575–584. Springer, Berlin/Heidelberg (2010)
Seyfried, A., Steffen, B., Lippert, T.: Basics of modelling the pedestrian flow. Physica A 368, 232–238 (2006)
Suma, Y., Yanagisawa, D., Nishinari, K.: Anticipation effect in pedestrian dynamics: modelling and experiments. Physica A 391, 248–263 (2012)
Templer, J.A.: The Staircase: Studies of Hazards, Falls, and Safer Design. MIT, Cambridge (1992)
Werner, T., Helbing, D.: The social force pedestrian model applied to real life scenarios. In: Galea, E.R. (ed.) Pedestrian and Evacuation Dynamics, pp. 17–26. CMS, London (2003)
Wolfram, S.: Statistical mechanics of cellular automata. Rev. Mod. Phys. 55, 601–644 (1983)
Yanagisawa, D., Kimura, A., Tomoeda, A., Ryosuke, A., Suma, Y., Ohtsuka, K., Nishinari, K.: Introduction of frictional and turning function for pedestrian outflow with an obstacle. Phys. Rev. E 80(3), 036110 (2009)
Yu, W.J., Chen, L.Y., Dong, R., Dai, S.Q.: Centrifugal force model for pedestrian dynamics. Phys. Rev. E 72(2), 026112 (2005)
Zhang, J., Klingsch, W., Schadschneider, A., Seyfried, A.: Transitions in pedestrian fundamental diagrams of straight corridors and t-junctions. J. Stat. Mech. (2011). doi:10.1088/1742-5468/2011/06/P06004
Zhang, J., Klingsch, W., Seyfried, A.: High precision analysis of unidirectional pedestrian flow within the Hermes project. In: The Fifth Performance-based Fire Protection and Fire Protection Engineering Seminars, Guangzhou, China (2010)
Zhang, J., Klingsch, W., Schadschneider, A., Seyfried, A.: Ordering in bidirectional pedestrian flows and its influence on the fundamental diagram. J. Stat. Mech. 2, P02002 (2012)
Zheng, X., Palffy-Muhoray, P.: Distance of closest approach of two arbitrary hard ellipses in two dimensions. Phys. Rev. E 75(6), 061709 (2007)
Acknowledgements
This work is within the framework of two projects. The authors are grateful to the Deutsche Forschungsgemeinschaft (DFG) for funding the project under Grant-No. SE 1789/1-1 as well as the Federal Ministry of Education and Research (BMBF) for funding the project under Grant-No. 13N9952 and 13N9960.
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Chraibi, M., Schadschneider, A., Seyfried, A. (2013). On Force-Based Modeling of Pedestrian Dynamics. In: Ali, S., Nishino, K., Manocha, D., Shah, M. (eds) Modeling, Simulation and Visual Analysis of Crowds. The International Series in Video Computing, vol 11. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8483-7_2
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