Abstract
Although various theories have been adopted to develop reliable pedestrian walking models, a limited effort has been made to calibrate them rigorously based on individual trajectories. Most researchers have validated their models by comparing observed and estimated traffic flow parameters such as speed, density, and flow rate, or replaced the validation by visual confirmation of some well-known phenomena such as channelization and platooning. The present study adopted maximum likelihood estimation to calibrate a social-force model based on the observed walking trajectories of pedestrians. The model was assumed to be made up of five components (i.e., inertia, desired direction, leader–follower relationship, collision avoidance, and random error), and their corresponding coefficients represented relative sensitivity. The model also included coefficients for individual-specific characteristics and for a distance-decay relationship between a pedestrian and his/her leaders or colliders. The calibration results varied with the two density levels adopted in the present study. In the case of high density, significant coefficient estimates were found with respect to both the leader–follower relationship and collision avoidance. Collision avoidance did not affect the pedestrian’s walking behavior for the low-density case due to channelization. The distance limit was confirmed, within which a pedestrian is affected by neighbors. At the low-density level, by comparison with women, men were found to more actively follow leaders, and pedestrians walking in a party were found to be less sensitive to the motion of leaders at the high-density level.
Similar content being viewed by others
References
Antonini, G., Mrtinez, S.V., Bierlaire, M., Thiran, J.P.: Behavioral priors for detection and tracking of pedestrians in video sequences. Int. J. Comput. Vision 69, 159–180 (2006)
Ben-Akiva, M., Walker, J., Bernardino, A.T., Gopinath, D., Morikawa, T., Polydoropoulou, A.: Integration of choice and latent variable models. In: Mahmassani, H.S. (ed.) Perpetual Motion: Travel Behaviour Research Opportunities and Application Challenges, pp. 431–470. Elsevier, Amsterdam (2002)
Blue, V.J., Adler, J.L.: Cellular automata microsimulation for modeling bi-directional pedestrian walkways. Transp. Res. B 35, 293–312 (2001)
Burstedde, C., Klauck, K., Schadschneider, A., Zittartz, J.: Simulation of pedestrian dynamics using a two-dimensional cellular automaton. Phys. A 295, 507–525 (2001)
Fang, G., Kwok, N.M., Ha, Q.P.: Swarm interaction-based simulation of occupant evacuation. In: Proceeding of Pacific-Asia Workshop on Computational Intelligence and Industrial Application, pp. 329–333 (2008)
Guo, R.Y., Huang, H.J.: A mobile lattice gas model for simulating pedestrian evacuation. Phys. A 387, 580–586 (2008)
Helbing, D., Molár, P.: Social force model for pedestrian dynamics. Phys. Rev. E 51, 4282–4286 (1995)
Hoogendoorn, S.P.: Walker behaviour modelling by differential games. In: Proceedings of Computational Physics of Transport and Interface Dynamics. Springer, Berlin (2002)
Hoogendoorn, S.P., Daamen, W.: Microscopic parameter identification of pedestrian models and implications for pedestrian flow modeling. Transp. Res. Rec. 1982, 57–64 (2006)
Isobe, M., Adachi, T., Nagatani, T.: Experiment and simulation of pedestrian counter flow. Phys. A 336, 638–650 (2004)
Izquierdo, J., Montalvo, R.P., Fuertes, V.S.: Forecasting pedestrian evacuation times by using swarm intelligence. Phys. A 388, 1213–1220 (2009)
Jian, L., Lizhong, Y., Daoliang, Z.: Simulation of bi-direction pedestrian movement in corridor. Phys. A 354, 619–628 (2005)
Johansson, A., Helbing, D.: Analysis of Empirical Trajectory Data of Pedestrians. Handbook of Pedestrian and Evacuation Dynamics 2008, Part 1, pp. 203–214, (2010)
Klingsch, W.W.F., Rogsch, C., Schadschneider, A., Schreckenberg, M.: Pedestrian and Evacuation Dynamics 2008. Springer, Heidelberg (2010)
Kretz, T., Grünebohm, A., Schreckenberg, M.: Experimental study of pedestrian flow through a bottleneck. J. Stat. Mech. P10014 (2006)
Lehmann, E.L., Casella, G.: Theory of Point Estimation, 2nd edn. Springer, Berlin (1998)
Li, Z., Tang, Q.L., Sang, N.: Improved mean shift algorithm for occlusion pedestrian tracking. Electron. Lett. 44, 622–623 (2008)
Liu, Y.H., Mahmassani, H.S.: Global maximum likelihood estimation procedure for multinomial probit (MNP) model parameters. Transp. Res. B 34, 419–449 (2000)
Maerivoet, S., De Moor, B.: Cellular automata models of road traffic. Phys. Rep. 419, 1–64 (2005)
Mehran, R., Oyama, A., Shah, M.: Abnormal crowd behavior detection using social force model. In: Proceeding of IEEE Conference on Computer Vision and Pattern Recognition, pp. 935–942 (2009)
Muramatsu, M., Nagatani, T.: Jamming transition of pedestrian traffic at a crossing with open boundaries. Phys. A 275, 281–291 (2000)
Nagel, K.: From particle hopping models to traffic flow theory. Transp. Res. Rec. 1644, 1–9 (1998)
Nagel, K., Rasmussen, S.: Traffic at the edge of chaos. In: Artificial Life IV: Proceedings of the Fourth International Workshop on the Synthesis and Simulation of Living Systems, pp. 222–225 (1994)
Okazaki, S.: A study of pedestrian movement in architectural space, Part I: pedestrian movement by the application of magnetic models. Trans. A.I.J. 283, 111–119 (1979)
Parisi, D.R., Gilman, M., Moldovan, H.: A modification of the social force model can reproduce experimental data of pedestrian flows in normal conditions. Phys. A 388, 3600–3608 (2009)
Robin, T., Antonini, G., Bierlair, M., Cruz, J.: Specification, estimation and validation of a pedestrian walking behavior model. Transp. Res. B 43, 36–56 (2009)
Shiwakoti, N., Sarvi, M., Rose, G., Burd, M.: Animal dynamics based approach for modeling pedestrian crowd egress under panic conditions. Transp. Res. B Methodol. 45(9), 1433–1449 (2011)
Sohn, K., Kim, D.: Zonal centrality measures and the neighborhood effect. Transp. Res. A 44(9), 733–743 (2010)
Song, W., Xu, X., Wang, B.H., Ni, S.: Simulation of evacuation processes using a multi-grid model for pedestrian dynamics. Phys. A 363, 492–500 (2006)
Szarvas, M., Yoshizawa, A., Yamamoto, M., Ogata, J.: Pedestrian detection with convolutional neural networks. In: IEEE Proceedings on Intelligent Vehicles Symposium, pp. 224–229 (2005)
Takimoto, K., Tajima, Y., Nagatani, T.: Pattern formation and jamming transition in pedestrian counter flow. Phys. A 308, 460–470 (2002)
Teknomo, K.: Microscopic pedestrian flow characteristics: Development of an image processing data collection and simulation model. Ph.D. Dissertation, Tohoku University, Japan (2002)
Thompson, P.A., Marchant, E.W.: A computer model the evacuation of large building population. Fire Saf. J. 24, 138–148 (1995)
Wand, M.P., Jones, M.C.: Kernel Smoothing, Monographs on Statistics and Applied Probability. Chapman & Hall/CRC, New York (1995)
Watts, J.M.: Computer models for evacuation analysis. Fire Saf. J. 12, 237–245 (1987)
Weifeng, F., Lizhong, Y., Weicheng, F.: Simulation of bi-direction pedestrian movement using a cellular automata model. Phys. A 321, 633–640 (2003)
Xiaoping, Z., Wei, L., Chao, G.: Simulation of evacuation process in a square with a partition wall using a cellular automation model for pedestrian dynamics. Phys. A 389, 2177–2188 (2010)
Yamamoto, K., Kokubo, S., Nishinari, K.: Simulation for pedestrian dynamics by real-coded cellular automata (RCA). Phys. A 379, 654–660 (2007)
Yu, W.J., Chen, R., Dong, L.Y., Dai, S.Q.: Centrifugal force model for pedestrian dynamics. Phys. Rev. E 72, 016002 (2005)
Yue, H., Guan, H., Zhang, J., Shao, C.: Study on bi-direction pedestrian flow using cellular automata simulation. Phys. A 389, 527–539 (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ko, M., Kim, T. & Sohn, K. Calibrating a social-force-based pedestrian walking model based on maximum likelihood estimation. Transportation 40, 91–107 (2013). https://doi.org/10.1007/s11116-012-9411-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11116-012-9411-z