Extended social force model with a dynamic navigation field for bidirectional pedestrian flow

Abstract

An extended social force model with a dynamic navigation field is proposed to study bidirectional pedestrian movement. The dynamic navigation field is introduced to describe the desired direction of pedestrian motion resulting from the decision-making processes of pedestrians. The macroscopic funda-mental diagrams obtained using the extended model are validated against camera-based observations. Numerical results show that this extended model can reproduce collective phenomena in pedestrian traffic, such as dynamic multilane flow and stable separate-lane flow. Pedestrians’ path choice behavior significantly affects the probability of congestion and the number of self-organized lanes.

Keywords

bidirectional pedestrian flow / social force model / dynamic navigation field / collective phenomena / complex systems

References

[1] D.Helbing and P.Molnár, Social force model for pedestrian dynamics, Phys. Rev. E51(5), 4282 (1995)

[2] V. J.Blueand J. L.Adler, Cellular automata microsimulation for modeling bidirectional pedestrian walkways, Trans. Res. Part B35(3), 293(2001)

[3] W. H. K.Lam, J. Y. S.Lee, and C. Y.Cheung, A study of the bidirectional pedestrian flow characteristics at Hong Kong signalized crosswalk facilities, Transpor. 29(2), 169(2002)

[4] R. L.Hughes, A continuum theory for the flow of pedestrians, Trans. Res. Part B36(6), 507(2002)

[5] M.Isobe, T.Adachi, and T.Nagatani, Experiment and simulation of pedestrian counter flow, Physica A336(3–4), 638(2004)

[6] T. I.Lakoba, D. J.Kaup, and N. M.Finkelstein, Modifications of the Helbing–Molnár–Farkas–Vicsek social force model for pedestrian evolution, Simulation81(5),339(2005)

[7] S. C.Wong, W. L.Leung, S. H.Chan, W. H. K.Lam, N. H. C.Yung, C. Y.Liu, and P.Zhang, bidirectional pedestrian stream model with oblique intersecting angle, J. Transp. Eng.136(3), 234(2010)

[8] D.Helbing, L.Buzna, A.Johansson, and T.Werner, Selforganized pedestrian crowd dynamics: Experi-ments, simulations, and design solutions, Transport. Sci.39(1), 1 (2005)

[9] T.Kretz, A.Grunebohm, M.Kaufman, F.Mazur, and M.Schreckenberg, Experimental study of pedestrian counter flow in a corridor, J. Stat. Mech.2006(10), P10001(2006)

[10] J.Zhang, W.Klingsch, A.Schadschneider, and A.Seyfried, Ordering in bidirectional pedestrian flows and its influence on the fundamental diagram, J. Stat. Mech. P02002(2012)

[11] J.Zhangand A.Seyfried, Comparison of intersecting pedestrian flows based on experiments, Physica A405, 316(2014)

[12] M.Saberi, K.Aghabayk, and A.Sobhani, Spatial fluctuations of pedestrian velocities in bidirectional streams: exploring the e ects of selforganization, Physica A434, 120(2015)

[13] D.Helbingand T.Vicsek, Optimal selforganization, New J. Phys.13, 1 (1999)

[14] T.Morbiato, R.Vitaliani, and A.Saetta, Numerical analysis of a synchronization phenomenon: Pedestrian-structure interaction, Computers & Structures89(17–18), 1649(2011)

[15] C. Q.Wang, A.Pumir, N. B.Garnier, and Z. H.Liu, Explosive synchronization enhances selectivity: Example of the cochlea, Front. Phys.12(5), 128901(2017)

[16] S. F.Ma, H. J.Bi, Y.Zou, Z. H.Liu, and S. G.Guan, Shuttle-run synchronization in mobile ad hoc networks, Front. Phys.10(3), 100505(2015)

[17] F.Zanlungo, T.Ikeda, and T.Kanda, Social force model with explicit collision prediction, Europhys. Lett.93(6), 68005(2011)

[18] G.Flötterödand G.Lámmel, bidirectional pedestrian fundamental diagram, Trans. Res. Part B71, 194(2015)

[19] T.Xiong, P.Zhang, S. C.Wong, C. W.Shu, and M. P.Zhang, A macroscopic approach to the lane forma-tion phenomenon in pedestrian counterflow, Chin. Phys. Lett.28(10), 108901(2011)

[20] Y. Q.Jiang, S. C.Wong, P.Zhang, R. X.Liu, Y. L.Duan, and K.Choi, Numerical simulation of a con-tinuum model for bidirectional pedestrian flow, Appl. Math. Comput.218, 6135(2012)

[21] S. P.Hoogendoorn, F. L. M.van Wageningen-Kessels, W.Daamen, and D. C.Duives, Continuum modelling of pedestrian flows: From microscopic principles to self-organised macroscopic phenomena, Physica A416, 684(2014)

[22] Y. Q.Jiang, S. G.Zhou, and F. B.Tian, A higher-order macroscopic model forbi-directionpedestrian flow, Physica A425, 69(2015)

[23] Y. Q.Jiang, S. G.Zhou, and F. B.Tian, Macroscopic pedestrian flow model with degrading spatial informa-tion, J. Comput. Sci.10, 36(2015)

[24] N.Bellomoand C.Dogbé, On the modeling of traffic and crowds: A survey of models, speculations, and per-spectives, SIAM Rev.53(3), 409(2011)

[25] N.Bellomoand L.Gibelli, Toward a mathematical the-ory of behavioral social dynamics for pedestrian crowds, Math. Models Methods Appl. Sci.25(13), 2417(2015)

[26] D.Helbing,I.Farkas, and T.Vicsek, Simulating dy-namical features of escape panic, Nature407(6803), 487(2000)

[27] X. X.Yang, W.Daamen, S. P.Hoogendoorn, Y.Chen, and H. R.Dong, Breakdown phenomenon study in the bidirectional pedestrian flow, Transpor. Res. Proc.2, 456(2014)

[28] R. Y.Guo, Simulation of spatial and temporal separation of pedestrian counter flow through a bottleneck, Physica A415, 428(2014)

[29] L.Hou, J. G.Liu, X.Pan, and B. H.Wang, A social force evacuation model with the leadership e ect, Physica A400, 93(2014)

[30] T.Korecki, D.Palka, and J.Was, Adaptation of social force model for simulation of downhill skiing,J. Com-put. Sci.16, 29(2016)

[31] W. G.Weng, T.Chen, H. Y.Yuan, and W. C.Fan, Cellular automaton simulation of pedestrian counter flow with di erent walk velocities, Phys. Rev. E74(3), 036102(2006)

[32] X. X.Jian, S. C.Wong, P.Zhang, K.Choi, H.Li, and X. N.Zhang, Perceived cost potential field cellular au-tomata model with an aggregated force field for pedes-trian dynamics, Trans. Res. Part C.42, 200(2014)

[33] Y.Tajima, K.Takimoto, and T.Nagatani, Pattern for-mation and jamming transition in pedestrian counter flow, Physica A313(3–4), 709(2002)

[34] R.Nagaiand T.Nagatani, Jamming transition in counter flow of slender particles on square lattice, Physica A366, 503(2006)

[35] L. B.Fu, W. G.Song, W.Lv, X. D.Liu, and S. M.Lo, Multi-grid simulation of counter flow pedestrian dy-namics with emotion propagation, Simul. Model. Pract. Theory60, 1 (2016)

[36] D. R.Parisiand C. O.Dorso, Morphological and dynamical aspects of the room evacuation process, Physica A385(1), 343(2007)

[37] D. R.Parisi, M.Gilman, and H.Moldovan, A modification of the social force model can reproduce experimental data of pedestrian flows in normal conditions, Physica A388(17), 3600(2009)

[38] J.Kwak, H. H.Jo, T.Luttinen, and I.Kosonen, Collective dynamics of pedestrians interacting with attractions, Phys. Rev. E88(6), 062810(2013)

[39] T.Kretz, A.Grosse, S.Hengst, L.Kautzsch, A.Pohlmann, and P.Vortisch, Quickest paths in simu-lations of pedestrians, Advances in Complex Systems14(5), 733(2011)

[40] I.Karamouzas, B.Skinner, and S. J.Guy, Universal power law governing pedestrian interactions, Phys. Rev. Lett.113(23), 238701(2014)

[41] J.Wahle, A. L. C.Bazzan, F.Klügl, and M.Schreck-enberg, Decision dynamics in a traffic scenario, Physica A287(3–4), 669(2000)

[42] W. X.Wang, B. H.Wang, W. C.Zheng, C. Y.Yin, and T.Zhou, Advanced information feedback in intelligent traffic systems, Phys. Rev. E72(6), 066702(2005)

[43] B. K.Chen, X. Y.Sun, H.Wei, C. F.Dong, and B. H.Wang, Piecewise function feedback strategy in intelligent traffic systems with a speed limit bottleneck, IntJ. Mod. Phys. C22(08), 849(2011)

[44] B. K.Chen, C. F.Dong, Y. K.Liu, W.Tong, W. Y.Zhang, J.Liu, and B. H.Wang, Real-time informa-tion feedback based on a sharp decay weighted function, Comput. Phys. Commun. 183(10), 2081(2012)

[45] B. K.Chen, W.Tong, W. Y.Zhang, X. Y.Sun, and B. H.Wang, Flux information feedback strategy in intelli-gent traffic systems, Europhys. Lett. 97(1), 14001(2012)

[46] B. K.Chen, Y. B.Xie, W.Tong, C. F.Dong, D. M.Shi, and B. H.Wang, A comprehensive study of advanced information feedbacks in real-time intelligent traffic systems, Physica A391(8), 2730(2012)

[47] B. K.Chen, D. Z. W.Wang, Y. C.Gao, K.Zhang, L.X.Miao, and B. H.Wang, Effects of traffic lights for Manhattan-like urban traffic network in intelligent transportation systems, Transportmetrica B,

[48] Y. T.Zhang, H. K.Zhao, and J.Qian, High order fast sweeping methods for static Hamilton Jacobi equations, J.Sci. Comput.29(1), 25(2006)

RIGHTS & PERMISSIONS

2017 Higher Education Press and Springer-Verlag Berlin Heidelberg