Abstract
We propose in this paper a minimal speed-based pedestrian model for which particle dynamics are intrinsically collision-free. The speed model is an optimal velocity function depending on the agent length (i.e. particle diameter), maximum speed and time gap parameters. The direction model is a weighted sum of exponential repulsion from the neighbours, calibrated by the repulsion rate and distance. The model’s main features like the reproduction of empirical phenomena are analysed by simulation. We point out that phenomena of self-organisation observable in force-based models and field studies can be reproduced by the collision-free model with low computational effort.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Chowdhury, D., Santen, L., Schadschneider, A.: Statistical physics of vehicular traffic and some related systems. Phys. Rep. 329(4), 199–329 (2000)
Degond, P., Appert-Rolland, C., Moussaid, M., Pettré, J., Theraulaz, G.: A hierarchy of heuristic-based models of crowd dynamics. J. Stat. Phys. 152(6), 1033–1068 (2013)
Schadschneider, A., Chowdhury, D., Nishinari, K.: Stochastic transport in complex systems: from molecules to vehicles. Elsevier (2010)
Helbing, D., Farkas, I.J., Vicsek, T.: Freezing by heating in a driven mesoscopic system. Phys. Rev. Lett. 84(6), 1240 (2000)
Helbing, D., Johansson, A., Mathiesen, J., Jensen, M.H., Hansen, A.: Analytical approach to continuous and intermittent bottleneck flows. Phys. Rev. Lett. 97(16), 168001 (2006)
GmbH, T.H.: Handbuch pedgo 2, pedgo editor 2. http://www.evacuation-simulation.com
Schneider V.K.R.: Simulating evacuation processes with aseri. In: Pedestrian and Evacuation Dynamics, pp. 303–314 (2002)
AG, P.: PTV Vissim 7.0—User Manual. PTV Group, Haid-und-Neu-Str. 15, D-76131 Karlsruhe, Germany (2014)
Berrou, J.L., Beecham, J., Quaglia, P., Kagarlis, M.A., Gerodimos, A.: Calibration and validation of the legion simulation model using empirical data. In: Pedestrian and Evacuation Dynamics, pp. 167–181 (2005)
Helbing, D.: Traffic and related self-driven many-particle systems. Rev. Mod. Phys. 73(4), 1067 (2001)
Chraibi, M., Seyfried, A., Schadschneider, A.: Generalized centrifugal-force model for pedestrian dynamics. Phys. Rev. E 82(4), 046111 (2010)
Helbing, D., Molnár, P.: Social force model for pedestrian dynamics. Phys. Rev. E 51, 4282–4286 (1995)
Chraibi, M., Seyfried, A., Kemloh, U., Schadschneider, A.: Force-based models of pedestrian dynamics. Netw. Heterog. Media 6, 425–442 (2011)
Köster, G., Treml, F., Gödel, M.: Avoiding numerical pitfalls in social force models. Phys. Rev. E 87, 063305 (2013)
Ondřej, J., Pettré, J., Olivier, A.H., Donikian, S.: A synthetic-vision based steering approach for crowd simulation. ACM Trans. Graph. 29, 123 (2010)
Van den Berg, J., Lin, M., Manocha, D.: Reciprocal velocity obstacles for real-time multi-agent navigation. In: IEEE International Conference on Robotics and Automation, 2008. ICRA 2008, pp. 1928–1935. IEEE (2008)
Fiorini, P., Shiller, Z.: Motion planning in dynamic environments using velocity obstacles. Int. J. Robot. Res. 17(7), 760–772 (1998)
Maury, B., Venel, J.: Un modle de mouvement de foule. In: ESSAIM 18, 143–152 (2007)
Venel, J.: Integrating strategies in numerical modelling of crowd motion. In: Pedestrian and Evacuation Dynamics 2008, pp. 641–646. Springer (2010)
Guo, R.Y., Wong, S., Huang, H.J., Zhang, P., Lam, W.H.: A microscopic pedestrian-simulation model and its application to intersecting flows. Physica A 389(3), 515–526 (2010)
Pelechano, N., O’Brien, K., Silverman, B., Badler, N.: Crowd simulation incorporating agent psychological models, roles and communication. Technical Report, DTIC Document (2005)
Dietrich, F., Köster, G.: Gradient navigation model for pedestrian dynamics. Phys. Rev. E 89(6), 062801 (2014)
Bando, M., Hasebe, K., Nakayama, A., Shibata, A., Sugiyama, Y.: Dynamical model of traffic congestion and numerical simulation. Phys. Rev. E 51(2), 1035 (1995)
Nakayama, A., Hasebe, K., Sugiyama, Y.: Instability of pedestrian flow and phase structure in a two-dimensional optimal velocity model. Phys. Rev. E 71(3), 036121 (2005)
Monneau, R., Roussignol, M., Tordeux, A.: Invariance and homogenization of an adaptive time gap car-following model. Nonlinear Differ. Equ. Appl. 21(4), 491–517 (2014)
Zhang, J., Klingsch, W., Schadschneider, A., Seyfried, A.: Ordering in bidirectional pedestrian flows and its influence on the fundamental diagram. J. Stat. Mech. Theory Exp. 2012(02), P02002 (2012)
Corradi, O., Hjorth, P.G., Starke, J.: Equation-free detection and continuation of a hopf bifurcation point in a particle model of pedestrian flow. SIAM J. Appl. Dyn. Syst. 11(3), 1007–1032 (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Tordeux, A., Chraibi, M., Seyfried, A. (2016). Collision-Free Speed Model for Pedestrian Dynamics. In: Knoop, V., Daamen, W. (eds) Traffic and Granular Flow '15. Springer, Cham. https://doi.org/10.1007/978-3-319-33482-0_29
Download citation
DOI: https://doi.org/10.1007/978-3-319-33482-0_29
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-33481-3
Online ISBN: 978-3-319-33482-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)