Abstract
Stop-and-go waves in single-file movement are a phenomenon that is observed empirically in pedestrian dynamics. It manifests itself by the co-existence of two phases: moving and stopping pedestrians. We show analytically based on a simplified one-dimensional scenario that under some conditions the system can have unstable homogeneous solutions. Hence, oscillations in the trajectories and instabilities emerge during simulations. To our knowledge there exists no force-based model which is collision- and oscillation-free and meanwhile can reproduce phase separation. We develop a new force-based model for pedestrian dynamics able to reproduce qualitatively the phenomenon of phase separation. We investigate analytically the stability condition of the model and define regimes of parameter values where phase separation can be observed. We show by means of simulations that the predefined conditions lead in fact to the expected behaviour and validate our model with respect to empirical findings.
This is a preview of subscription content, log in via an institution to check access.
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(4–6), 199–329 (2000)
Orosz, G., Wilson, R.E., Stepan, G.: Traffic jams: dynamics and control. Philos. Trans. R. Soc. Lond. A: Math. Phys. Eng. Sci. 368(1957), 4455–4479 (2010)
Treiber, M., Kesting, A.: Traffic Flow Dynamics. Springer, Berlin (2013). ISBN 978-3-642-32459-8
Portz, A., Seyfried, A.: Analyzing stop-and-go waves by experiment and modeling. In: Peacock, R., Kuligowski, E., Averill, J. (eds.) Pedestrian and Evacuation Dynamics 2010, pp. 577–586. Springer (2011)
Seyfried, A., Boltes, M., Kähler, J., Klingsch, W., Portz, A., Rupprecht, T., Schadschneider, A., Steffen, B., Winkens, A.: Enhanced empirical data for the fundamental diagram and the flow through bottlenecks. In: Klingsch, W.W.F., Rogsch, C., Schadschneider, A., Schreckenberg, M. (eds.) Pedestrian and Evacuation Dynamics 2008, pp. 145–156. Springer, Heidelberg (2010)
Eilhardt, C., Schadschneider, A.: Stochastic headway dependent velocity model for 1d pedestrian dynamics at high densities. Transp. Res. Procedia 2, 400–405 (2014)
Lemercier, S., Jelic, A., Kulpa, R., Hua, J., Fehrenbach, J., Degond, P., Appert-Rolland, C., Donikian, S., Pettré, J.: Realistic following behaviors for crowd simulation. Comput. Graph. Forum 31, 489–498 (2012)
Portz, A., Seyfried, A.: Modeling stop-and-go waves in pedestrian dynamics. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds.) PPAM 2009, Part II, pp. 561–568. Springer, Berlin, Heidelberg (2010)
Seyfried, A., Portz, A., Schadschneider, A.: Phase coexistence in congested sates of pedestrian dynamics. In: Lecture Notes in Computer Science, vol. 6350, pp. 496–505 (2010)
Chraibi, M., Ezaki, T., Tordeux, A., Nishinari, K., Schadschneider, A., Seyfried, A.: Jamming transitions in force-based models for pedestrian dynamics. Phys. Rev. E 92, 042809 (2015)
Jelić, A., Appert-Rolland, C., Lemercier, S., Pettré, J.: Properties of pedestrians walking in line. ii. stepping behavior. Phys. Rev. E 86, 046111 (2012)
Seitz, M.J., Köster, G.: Natural discretization of pedestrian movement in continuous space. Phys. Rev. E 86, 046108 (2012)
Weidmann, U.: Transporttechnik der Fussgänger. Technical Report Schriftenreihe des IVT Nr. 90, Institut für Verkehrsplanung,Transporttechnik, Strassen- und Eisenbahnbau, ETH Zürich, ETH Zürich, 2nd edn. (1993)
Bando, M., Hasebe, K., Nakayama, A., Shibata, A., Sugiyama, Y.: Dynamical model of traffic congestion and numerical simulation. Phys. Rev. E 51(2), 1035–1042 (1995)
Acknowledgements
In memory of Matthias Craesmeyer. M.C. thanks the Federal Ministry of Education and Research (BMBF) for partly supporting this work under the grant number 13N12045. A.S. thanks the Deutsche Forschungsgemeinschaft (DFG) for support under grant ‘Scha 636/9-1’.
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
Chraibi, M., Tordeux, A., Schadschneider, A. (2016). A Force-Based Model to Reproduce Stop-and-Go Waves in 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_22
Download citation
DOI: https://doi.org/10.1007/978-3-319-33482-0_22
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)