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Modeling crowd dynamics through coarsegrained data analysis
1.  School of Mathematical and Statistical Sciences, Arizona State University, Tempe, USA 
2.  Adaptive Behavior and Cognition Group, Max Planck Institut for Human Development, Berlin, Germany 
3.  Centre de Recherches sur la Cognition Animale, Centre de Biologie Intégrative (CBI), Centre National de la Recherche Scientifique (CNRS) & Université de Toulouse 3 Paul Sabatier, 31062 Toulouse, France 
4.  INRIA RennesBretagne Atlantique, Campus de Beaulieu, Rennes, France 
5.  CNRS, Laboratoire de Physique Théorique, Orsay, France 
6.  Department of Mathematics, Imperial College London, London SW7 2AZ, UK 
Understanding and predicting the collective behaviour of crowds is essential to improve the efficiency of pedestrian flows in urban areas and minimize the risks of accidents at mass events. We advocate for the development of crowd traffic management systems, whereby observations of crowds can be coupled to fast and reliable models to produce rapid predictions of the crowd movement and eventually help crowd managers choose between tailored optimization strategies. Here, we propose a Bidirectional Macroscopic (BM) model as the core of such a system. Its key input is the fundamental diagram for bidirectional flows, i.e. the relation between the pedestrian fluxes and densities. We design and run a laboratory experiments involving a total of 119 participants walking in opposite directions in a circular corridor and show that the model is able to accurately capture the experimental data in a typical crowd forecasting situation. Finally, we propose a simple segregation strategy for enhancing the traffic efficiency, and use the BM model to determine the conditions under which this strategy would be beneficial. The BM model, therefore, could serve as a building block to develop on the fly prediction of crowd movements and help deploying realtime crowd optimization strategies.
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[2] 
S. Ali and M. Shah, Floor fields for tracking in high density crowd scenes, Computer Vision – ECCV 2008: 10th European Conference on Computer Vision, 2008, 1–14; Netw Heterog Media., 6 (2008), 401–423. 
[3] 
C. AppertRolland, P. Degond and S. Motsch, Twoway multilane traffic model for pedestrians in corridors, Netw Heterog Media, 6 (2011), 351381. doi: 10.3934/nhm.2011.6.351. 
[4] 
A. Aw and M. Rascle, Resurrection of "second order" models of traffic flow, SIAM J Appl Math., 60 (2000), 916938. doi: 10.1137/S0036139997332099. 
[5] 
N. Bellomo and L. Gibelli, Behavioral crowds: Modeling and Monte Carlo simulations toward validation, Comp. & Fluids, 141 (2016), 1321. doi: 10.1016/j.compfluid.2016.04.022. 
[6] 
N. Bellomo, B. Piccoli and A. Tosin, Modeling crowd dynamics from a complex system viewpoint Math Mod Meth Appl S., 22 (2012), 1230004, 29pp. doi: 10.1142/S0218202512300049. 
[7] 
B. Benfold and I. Reid, 2011 Stable multitarget tracking in realtime surveillance video, Computer Vision and Pattern Recognition (CVPR), 2011 IEEE Conference on, 3457–3464. 
[8] 
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[9] 
C. K. Birdsall and A. B. Langdon, Plasma physics via computer simulation, CRC Press, 2014. 
[10] 
V. J. Blue and J. L. Adler, Cellular automata microsimulation of bidirectional pedestrian flows, Trans Res B., 1678 (1999), 135141. 
[11] 
W. Daamen and S. P. Hoogendoorn, Controlled experiments to derive walking behaviour, Eur J of Trans Infrastruct Res., 3 (2003), 3959. 
[12] 
H. Fehske, R. Schneider and A. Weisse, Computational ManyParticle Physics, Springer, 2007. 
[13] 
C. Feliciani and K. Nishinari, Empirical analysis of the lane formation process in bidirectional pedestrian flow, Physical Review E., 94 (2016), 032304. 
[14] 
G. Fltterd and G. Lmmel, Bidirectional pedestrian fundamental diagram, Transportation Research Part B: Methodological, 71 (2015), 194212. 
[15] 
P. Goatin and M. Mimault, A mixed system modeling twodirectional pedestrian flows, Math Biosci Eng., 12 (2015), 375392. 
[16] 
D. Helbing, Selforganized pedestrian crowd dynamics: Experiments, simulations, and design solutions, Transport Sci., 39 (2005), 124. 
[17] 
D. Helbing, Saving human lives: What complexity science and information systems can contribute, J. Stat Phys., 158 (2015), 735781. doi: 10.1007/s1095501410249. 
[18] 
D. Helbing and P. Mukerji, Crowd disasters as systemic failures: Analysis of the Love Parade disaster, EPJ Data Science, 1 (2012), 140. 
[19] 
D. Helbing and P. Molnar, Social force model for pedestrian dynamics, Physical Review E., 51 (1995), 42824286. 
[20] 
D. Helbing, Traffic and related selfdriven manyparticle systems, Rev Mod Phys., 73 (2001), 1067. 
[21] 
D. Helbing, A. Johansson and H. Z. AlAbideen, Dynamics of crowd disasters: An empirical study, Phys Rev E., 75 (2007), 046109. 
[22] 
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[23] 
S. P. Hoogendoorn and P. H. Bovy, Pedestrian routechoice and activity scheduling theory and models, Transport Res BMeth., 38 (2004), 169190. 
[24] 
R. L. Hughes, A continuum theory for the flow of pedestrians, Transport Res BMeth., 36 (2002), 507535. 
[25] 
L. Jian, Y. Lizhong and Z. Daoliang, Simulation of bidirection pedestrian movement in corridor, Physica A., 354 (2005), 619628. 
[26] 
A. Johansson, From crowd dynamics to crowd safety: A videobased analysis, Adv Complex Syst., 11 (2008), 497527. 
[27] 
B. S. Kerner, The physics of traffic: Empirical freeway pattern features, engineering applications, and theory, Springer Verlag, 2004. 
[28] 
A. Kirchner, K. Nishinari and A. Schadschneider, Friction effects and clogging in a cellular automaton model for pedestrian dynamics, Phys Rev E., 67 (2003), 056122. 
[29] 
A. Klar, Multivalued fundamental diagrams and stop and go waves for continuum traffic flow equations, SIAM J Appl Math., 64 (2004), 468483. doi: 10.1137/S0036139902404700. 
[30] 
L. Kratz and K. Nishino, Tracking pedestrians using local spatiotemporal motion patterns in extremely crowded scenes, IEEE Trans. on Pattern Analysis and Machine Intelligence, 34 (2012), 9871002. 
[31] 
T. Kretz, et. al., Experimental study of pedestrian counterflow in a corridor, J Stat MechTheory E., 2006 (2006), P10001. 
[32] 
A. Kurganov and E. Tadmor, New highresolution central schemes for nonlinear conservation laws and convectiondiffusion equations, J Comput Phys., 160 (2000), 241282. doi: 10.1006/jcph.2000.6459. 
[33] 
W. H. Lam, A generalised function for modeling bidirectional flow effects on indoor walkways in Hong Kong, Transport Res APol, 37 (2003), 789810. 
[34] 
S. Lemercier, Reconstructing motion capture data for human crowd study, Motion in Games, (2011), 365376. 
[35] 
S. Lemercier, Realistic following behaviors for crowd simulation, Comput Graph Forum, 31 (2012), 489498. 
[36] 
R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, Cambridge, 2002. doi: 10.1017/CBO9780511791253. 
[37] 
R. J. LeVeque, Numerical Methods for Conservation Laws, Birkhäuser, 1992. doi: 10.1007/9783034886291. 
[38] 
M. J. Lighthill and G. B. Whitham, On kinematic waves. Ⅱ. A theory of traffic flow on long crowded roads, P Roy Soc Lond A Mat., 229 (1955), 317345. doi: 10.1098/rspa.1955.0089. 
[39] 
A. N. Marana, Realtime crowd density estimation using images, Lect Notes Comput Sc., (2005), 355362. 
[40] 
G. Martine and A. Marshall, State of world population 2007: Unleashing the potential of urban growth, UNFPA, 2007. 
[41] 
M. Moussaid, How simple rules determine pedestrian behavior and crowd disasters, Proc Natl Acad Sci., 108 (2011), 68846888. 
[42] 
M. Moussaid, et al., Traffic instabilities in selforganized pedestrian crowds, Plos Comput Biol., 8 (2012), e1002442. 
[43] 
J. Ondrej, et al., A syntheticvision based steering approach for crowd simulation, ACM Transactions on Graphics, 29 2010. 
[44] 
M. Papageorgiou, C. Diakaki, V. Dinopoulou, A. Kotsialos and Y. Wang, Review of road traffic control strategies, Proceedings of the IEEE, 91 (2003), 20432067. 
[45] 
H J. Payne, FREFLO: A macroscopic simulation model of freeway traffic, Transp Res Record, 1979. 
[46] 
M. Plaue, M. Chen, G. Brwolff and H. Schwandt, Trajectory extraction and density analysis of intersecting pedestrian flows from video recordings, Photogrammetric Image Analysis, Springer, (2011), 285296. 
[47] 
C. W. Reynolds, Flocks, herds and schools: A distributed behavioral model, ACM SIGGRAPH Computer Graphics, 21 (1987), 2534. 
[48] 
P. Rietveld, Nonmotorised modes in transport systems: A multimodal chain perspective for The Netherlands, Transportation Research Part D: Transport and Environment, 5 (2000), 3136. 
[49] 
E. Ronchi, F. N. Uriz, X. Criel and P. Reilly, Modelling largescale evacuation of music festivals, Case Studies in Fire Safety, 5 (2016), 1119. 
[50] 
M. Rosini, Macroscopic Models for Vehicular Flows and Crowd Dynamics: Theory and Applications, Springer, 2013. doi: 10.1007/9783319001555. 
[51] 
M. Saberi, K. Aghabayk and A. Sobhani, Spatial fluctuations of pedestrian velocities in bidirectional streams: Exploring the effects of selforganization, Physica A: Statistical Mechanics and its Applications, 434 (2016), 120128. 
[52] 
N. Shiwakoti and M. Sarvi, Enhancing the panic escape of crowd through architectural design, Transportation Research Part C: Emerging Technologies, 37 (2013), 260267. 
[53] 
G. K. Still, Crowd Dynamics, PhD Thesis, University of Warwick, 2000. 
[54] 
E. Tory, et. al., An adaptive finitevolume method for a model of twophase pedestrian flow, 2011. 
[55] 
W. G. Weng, A behaviorbased model for pedestrian counter flow, Physica A, 375 (2007), 668678. 
[56] 
N. Wijermans, C. Conrado, M. van Steen, C. Martella and J. Li, A landscape of crowdmanagement support: An integrative approach, Safety Science, 86 (2016), 142164. 
[57] 
M. Wirz, Probing crowd density through smartphones in cityscale mass gatherings, EPJ Data Science, 2 (2013), 124. 
[58] 
S. Yaseen, Realtime crowd density mapping using a novel sensory fusion model of infrared and visual systems, Safety Sci, 57 (2013), 313325. 
[59] 
J. Zhang, W. Klingsch, A. Schadschneider and A. Seyfried, Ordering in bidirectional pedestrian flows and its influence on the fundamental diagram, J. Stat. Mech. Theory Exp., 2 (2012), P02002. 
[60] 
B. Zhou, F. Zhang and L. Peng, Higherorder SVD analysis for crowd density estimation, Comput Vis Image Und., 116 (2012), 10141021. 
show all references
References:
[1] 
S. A. AlGadhi, H. S. Mahmassani and R. Herman, A speedconcentration relation for bidirectional crowd movements with strong interaction, Pedestrian and Evacuation Dynamics, (2002), 320. 
[2] 
S. Ali and M. Shah, Floor fields for tracking in high density crowd scenes, Computer Vision – ECCV 2008: 10th European Conference on Computer Vision, 2008, 1–14; Netw Heterog Media., 6 (2008), 401–423. 
[3] 
C. AppertRolland, P. Degond and S. Motsch, Twoway multilane traffic model for pedestrians in corridors, Netw Heterog Media, 6 (2011), 351381. doi: 10.3934/nhm.2011.6.351. 
[4] 
A. Aw and M. Rascle, Resurrection of "second order" models of traffic flow, SIAM J Appl Math., 60 (2000), 916938. doi: 10.1137/S0036139997332099. 
[5] 
N. Bellomo and L. Gibelli, Behavioral crowds: Modeling and Monte Carlo simulations toward validation, Comp. & Fluids, 141 (2016), 1321. doi: 10.1016/j.compfluid.2016.04.022. 
[6] 
N. Bellomo, B. Piccoli and A. Tosin, Modeling crowd dynamics from a complex system viewpoint Math Mod Meth Appl S., 22 (2012), 1230004, 29pp. doi: 10.1142/S0218202512300049. 
[7] 
B. Benfold and I. Reid, 2011 Stable multitarget tracking in realtime surveillance video, Computer Vision and Pattern Recognition (CVPR), 2011 IEEE Conference on, 3457–3464. 
[8] 
J. H. Bick and G. F. Newell, A continuum model for twodirectional traffic flow, Q. Appl. Math., 1960. 
[9] 
C. K. Birdsall and A. B. Langdon, Plasma physics via computer simulation, CRC Press, 2014. 
[10] 
V. J. Blue and J. L. Adler, Cellular automata microsimulation of bidirectional pedestrian flows, Trans Res B., 1678 (1999), 135141. 
[11] 
W. Daamen and S. P. Hoogendoorn, Controlled experiments to derive walking behaviour, Eur J of Trans Infrastruct Res., 3 (2003), 3959. 
[12] 
H. Fehske, R. Schneider and A. Weisse, Computational ManyParticle Physics, Springer, 2007. 
[13] 
C. Feliciani and K. Nishinari, Empirical analysis of the lane formation process in bidirectional pedestrian flow, Physical Review E., 94 (2016), 032304. 
[14] 
G. Fltterd and G. Lmmel, Bidirectional pedestrian fundamental diagram, Transportation Research Part B: Methodological, 71 (2015), 194212. 
[15] 
P. Goatin and M. Mimault, A mixed system modeling twodirectional pedestrian flows, Math Biosci Eng., 12 (2015), 375392. 
[16] 
D. Helbing, Selforganized pedestrian crowd dynamics: Experiments, simulations, and design solutions, Transport Sci., 39 (2005), 124. 
[17] 
D. Helbing, Saving human lives: What complexity science and information systems can contribute, J. Stat Phys., 158 (2015), 735781. doi: 10.1007/s1095501410249. 
[18] 
D. Helbing and P. Mukerji, Crowd disasters as systemic failures: Analysis of the Love Parade disaster, EPJ Data Science, 1 (2012), 140. 
[19] 
D. Helbing and P. Molnar, Social force model for pedestrian dynamics, Physical Review E., 51 (1995), 42824286. 
[20] 
D. Helbing, Traffic and related selfdriven manyparticle systems, Rev Mod Phys., 73 (2001), 1067. 
[21] 
D. Helbing, A. Johansson and H. Z. AlAbideen, Dynamics of crowd disasters: An empirical study, Phys Rev E., 75 (2007), 046109. 
[22] 
L. F. Henderson, The statistics of crowd fluids, Nature, 229 (1971), 381383. 
[23] 
S. P. Hoogendoorn and P. H. Bovy, Pedestrian routechoice and activity scheduling theory and models, Transport Res BMeth., 38 (2004), 169190. 
[24] 
R. L. Hughes, A continuum theory for the flow of pedestrians, Transport Res BMeth., 36 (2002), 507535. 
[25] 
L. Jian, Y. Lizhong and Z. Daoliang, Simulation of bidirection pedestrian movement in corridor, Physica A., 354 (2005), 619628. 
[26] 
A. Johansson, From crowd dynamics to crowd safety: A videobased analysis, Adv Complex Syst., 11 (2008), 497527. 
[27] 
B. S. Kerner, The physics of traffic: Empirical freeway pattern features, engineering applications, and theory, Springer Verlag, 2004. 
[28] 
A. Kirchner, K. Nishinari and A. Schadschneider, Friction effects and clogging in a cellular automaton model for pedestrian dynamics, Phys Rev E., 67 (2003), 056122. 
[29] 
A. Klar, Multivalued fundamental diagrams and stop and go waves for continuum traffic flow equations, SIAM J Appl Math., 64 (2004), 468483. doi: 10.1137/S0036139902404700. 
[30] 
L. Kratz and K. Nishino, Tracking pedestrians using local spatiotemporal motion patterns in extremely crowded scenes, IEEE Trans. on Pattern Analysis and Machine Intelligence, 34 (2012), 9871002. 
[31] 
T. Kretz, et. al., Experimental study of pedestrian counterflow in a corridor, J Stat MechTheory E., 2006 (2006), P10001. 
[32] 
A. Kurganov and E. Tadmor, New highresolution central schemes for nonlinear conservation laws and convectiondiffusion equations, J Comput Phys., 160 (2000), 241282. doi: 10.1006/jcph.2000.6459. 
[33] 
W. H. Lam, A generalised function for modeling bidirectional flow effects on indoor walkways in Hong Kong, Transport Res APol, 37 (2003), 789810. 
[34] 
S. Lemercier, Reconstructing motion capture data for human crowd study, Motion in Games, (2011), 365376. 
[35] 
S. Lemercier, Realistic following behaviors for crowd simulation, Comput Graph Forum, 31 (2012), 489498. 
[36] 
R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, Cambridge, 2002. doi: 10.1017/CBO9780511791253. 
[37] 
R. J. LeVeque, Numerical Methods for Conservation Laws, Birkhäuser, 1992. doi: 10.1007/9783034886291. 
[38] 
M. J. Lighthill and G. B. Whitham, On kinematic waves. Ⅱ. A theory of traffic flow on long crowded roads, P Roy Soc Lond A Mat., 229 (1955), 317345. doi: 10.1098/rspa.1955.0089. 
[39] 
A. N. Marana, Realtime crowd density estimation using images, Lect Notes Comput Sc., (2005), 355362. 
[40] 
G. Martine and A. Marshall, State of world population 2007: Unleashing the potential of urban growth, UNFPA, 2007. 
[41] 
M. Moussaid, How simple rules determine pedestrian behavior and crowd disasters, Proc Natl Acad Sci., 108 (2011), 68846888. 
[42] 
M. Moussaid, et al., Traffic instabilities in selforganized pedestrian crowds, Plos Comput Biol., 8 (2012), e1002442. 
[43] 
J. Ondrej, et al., A syntheticvision based steering approach for crowd simulation, ACM Transactions on Graphics, 29 2010. 
[44] 
M. Papageorgiou, C. Diakaki, V. Dinopoulou, A. Kotsialos and Y. Wang, Review of road traffic control strategies, Proceedings of the IEEE, 91 (2003), 20432067. 
[45] 
H J. Payne, FREFLO: A macroscopic simulation model of freeway traffic, Transp Res Record, 1979. 
[46] 
M. Plaue, M. Chen, G. Brwolff and H. Schwandt, Trajectory extraction and density analysis of intersecting pedestrian flows from video recordings, Photogrammetric Image Analysis, Springer, (2011), 285296. 
[47] 
C. W. Reynolds, Flocks, herds and schools: A distributed behavioral model, ACM SIGGRAPH Computer Graphics, 21 (1987), 2534. 
[48] 
P. Rietveld, Nonmotorised modes in transport systems: A multimodal chain perspective for The Netherlands, Transportation Research Part D: Transport and Environment, 5 (2000), 3136. 
[49] 
E. Ronchi, F. N. Uriz, X. Criel and P. Reilly, Modelling largescale evacuation of music festivals, Case Studies in Fire Safety, 5 (2016), 1119. 
[50] 
M. Rosini, Macroscopic Models for Vehicular Flows and Crowd Dynamics: Theory and Applications, Springer, 2013. doi: 10.1007/9783319001555. 
[51] 
M. Saberi, K. Aghabayk and A. Sobhani, Spatial fluctuations of pedestrian velocities in bidirectional streams: Exploring the effects of selforganization, Physica A: Statistical Mechanics and its Applications, 434 (2016), 120128. 
[52] 
N. Shiwakoti and M. Sarvi, Enhancing the panic escape of crowd through architectural design, Transportation Research Part C: Emerging Technologies, 37 (2013), 260267. 
[53] 
G. K. Still, Crowd Dynamics, PhD Thesis, University of Warwick, 2000. 
[54] 
E. Tory, et. al., An adaptive finitevolume method for a model of twophase pedestrian flow, 2011. 
[55] 
W. G. Weng, A behaviorbased model for pedestrian counter flow, Physica A, 375 (2007), 668678. 
[56] 
N. Wijermans, C. Conrado, M. van Steen, C. Martella and J. Li, A landscape of crowdmanagement support: An integrative approach, Safety Science, 86 (2016), 142164. 
[57] 
M. Wirz, Probing crowd density through smartphones in cityscale mass gatherings, EPJ Data Science, 2 (2013), 124. 
[58] 
S. Yaseen, Realtime crowd density mapping using a novel sensory fusion model of infrared and visual systems, Safety Sci, 57 (2013), 313325. 
[59] 
J. Zhang, W. Klingsch, A. Schadschneider and A. Seyfried, Ordering in bidirectional pedestrian flows and its influence on the fundamental diagram, J. Stat. Mech. Theory Exp., 2 (2012), P02002. 
[60] 
B. Zhou, F. Zhang and L. Peng, Higherorder SVD analysis for crowd density estimation, Comput Vis Image Und., 116 (2012), 10141021. 
Sample set  a  b  c  
0.944  
0.972  
0.982 
Sample set  a  b  c  
0.944  
0.972  
0.982 
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