Abstract
One of the main objectives of crowd modeling is to optimize evacuation and improve the design of pedestrian facilities. In this work, a sensitivity analysis is performed to study the effect of the parameters of a 2D discrete crowd movement model on the nature of pedestrian’s collision and on evacuation times. After presenting the proposed model in its full version (three degrees of freedom for each individual), a pedestrian–pedestrian collision is considered. We identified the parameters that govern this type of collision and studied their effects on it. Then an evacuation experiment of a facility with a bottleneck exit is introduced and its configuration is used for numerical simulations. It is shown that without introducing a social repulsive force, the obtained flow rate values are much higher than the experimental ones. For this reason, we introduced the social force as defined by Helbing and performed a parametric study to find the set of optimized values of this force’s parameters that enables us to achieve simulation results close to the experimental ones. Using the values of the parameters obtained from the parametric study, the evacuation simulations give flow rate values that are closer to the experimental ones. The same optimized model is then used to find the density in front and inside the bottleneck and to reproduce the lane formation phenomenon as was observed in the experiment. Finally, the obtained results are analyzed and discussed.
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References
Antonini G, Bierlaire M, Weber M (2004), Simulation of pedestrian behavior using a discrete choice model calibrated on actual motion data. In: Proceedings of the 4th STRC Swiss transport research conference, Monte Verita, Ascona, Switzerland
Argoul P, Pécol P, Cumunel G, Erlicher S (2013) A discrete crowd movement model for holding hands pedestrians. In: Proceedings of EUROMECH-Colloquium 548, Amboise, France
Bandini S, Manzoni S, Vizzari G (2004) Situated cellular agents: a model to simulate crowding dynamics. In: IEICE transactions on information and systems: special issues on cellular automata E87-D, pp 669–676
Blue V, Adler J (1998) Emergent fundamental pedestrian flows from cellular automata microsimulation. Transp Res Rec J Transp Res Board 1644:29–36
Bruns H (1895) Das Eikonal. Leipzig Abh Sachs Ges Wiss Math Phys 21:321–436
Burstedde C, Klauck K, Schadschneider A, Zittartz J (2001) Simulation of pedestrian dynamics using a two-dimensional cellular automaton. Phys A 295(3):507–525
Caselli F, Frémond M (2008) Collision of three balls on a plane. Comput Mech 43(6):743–754
Cholet C (1999) Collision d’un point et d’un plan. C R Acad Sci 328:455–458
Chraibi M, Seyfried A, Schadschneider A (2010) Generalized centrifugal-force model for pedestrian dynamics. Phys Rev E 82(4):046111
Dimnet E (2002) Mouvement et collisions de solides rigides ou déformables. PhD thesis, Ecole Nationale des Ponts et Chaussées
Dal Pont S, Dimnet E (2008) Theoretical approach to instantaneous collisions and numerical simulation of granular media using the A-CD\(^{2}\) method. Commun Appl Math Comput Sci 3(1):1–24
Frémond M (1995) Rigid bodies collisions. Phys Lett A 204:33–41
Frémond M (2007) Collisions. Edizioni del Dipartimento di Ingegneria Civile dell’ Università di Roma Tor Vergata
Fukui M, Ishibashi Y (1999) Jamming transition in cellular automaton models for pedestrians on passageway. J Phys Soc Jpn 68(11):3738–3739
Gopal S, Smith TR (1990) Human way-finding in an urban environment: a performance analysis of a computational process model. Environ Plan A 22(2):169–191
Helbing D, Molnàr P (1995) Social force model for pedestrian dynamics. Phys Rev E 51(5):4282–4286
Helbing D, Farkas I, Vicsek T (2000) Simulating dynamic features of escape panic. Nature 407:487–490
Henderson L (1971) The statistics of crowd fluids. Nature 229:381–383
Hoogendoorn S, Bovy P, Daamen W (2001) Microscopic pedestrian wayfinding and dynamics modeling. In: Schreckenberg M, Sharma S (eds) Pedestrian and evacuation dynamics. Springer, Berlin, pp 123–154
Hoogendoorn SP, Daamen W (2005) Pedestrian behavior at bottlenecks. Transp Sci 39(2):147–159
Jeong W.K., Whitaker R. (2007), A fast eikonal equation solver for parallel systems. In: SIAM conference on computational science and engineering
Kimmel R, Sethian J (1996) Fast marching methods for computing distance maps and shortest paths. Technical report 669. University of California, Berkeley, CPAM
Kirchner A, Schadschneider A (2002) Simulation of evacuation processes using a bionics-inspired cellular automaton model for pedestrian dynamics. Phys A 312(12):260–276
Kretz T, Grunebohm A, Schreckenberg M (2006) Experimental study of pedestrian flow through a bottleneck. J Stat Mech Theory Exp 10:P10014. doi:10.1088/1742-5468/2006/10/P10014
Lakoba TI, Kaup DJ, Finkelstein NM (2005) Modification of the Helbing–Molnar–Farkas–Vicsek social force model for pedestrian evolution. Simulation 81:339–352
Langston PA, Masling R, Asmar BN (2006) Crowd dynamics discrete element multi-circle model. Saf Sci 44:395–417
Löhner R (2010) On the modeling of pedestrian motion. Appl Math Model 34(2):366–382
Moreau J (1970) Sur les lois du frottement, de la viscosité et de la plasticité. C R Acad Sci 271:608–611
Moussaïd M, Perozo N, Garnier S, Helbing D, Theraulaz G (2010) The walking behaviour of pedestrian social groups and its impact on crowd dynamics. PLoS ONE 5(4):e10047. doi:10.1371/journal.pone.0010047
Pécol P, Dal Pont S, Erlicher S, Argoul P (2010) Modeling crowd-structure interaction. Mec Ind EDP Sci 11(6):495–504
Pécol P (2011) Modélisation 2D discrète du mouvement des piétons—application à l’évacuation des structures du génie civil et à l’interaction foule-passerelle. Dissertation, Université Paris Est
Pécol P, Dal Pont S, Erlicher S, Argoul P (2011) Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Ann Solid Struct Mech 2(2–4):69–85
Pécol P, Argoul P, Dal Pont S, Erlicher S (2013) The non-smooth view for contact dynamics by Michel Frémond extended to the modeling of crowd movements. AIMS’ J Discret Contin Dyn Syst Ser S(2):547–565
Reynolds CW (1994) Evolution of corridor following behavior in a noisy world. From Anim Animat 3:402–410
Seyfried A, Rupprecht T, Passon O, Steffen B, Klingsch W, Boltes M (2009) New insights into pedestrian flow through bottlenecks. Transp Sci 43(3):395–406
Singh H, Arter R, Dodd L, Drury J (2009) Modeling subgroup behavior in crowd dynamics DEM simulation. Appl Math Model 33:4408–4423
Song W, Lv W, Fang Z (2013) Experiment and modeling of microscopic movement characteristic of pedestrians. Proc Eng 62:56–70
Yu WJ, Chen R, Dong LY, Dai SQ (2005) Centrifugal force model for pedestrian dynamics. Phys Rev E 72(2):026112
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Kabalan, B., Argoul, P., Jebrane, A. et al. A crowd movement model for pedestrian flow through bottlenecks. Ann. Solid Struct. Mech. 8, 1–15 (2016). https://doi.org/10.1007/s12356-016-0044-3
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DOI: https://doi.org/10.1007/s12356-016-0044-3