Noise-Induced Stop-and-Go Dynamics in Pedestrian  Single-file Motion

Andreas Schadschneider; Antoine Tordeux

doi:10.17815/CD.2020.70

Authors

Andreas Schadschneider Institut für Theoretische Physik, Universität zu Köln, Cologne, Germany
Antoine Tordeux Institut für Sicherheitstechnik, Bergische Universität Wuppertal, Wuppertal, Germany

DOI:

https://doi.org/10.17815/CD.2020.70

Keywords:

pedestrian single-file motion, stop-and-go dynamics, first-order microscopic models, coloured noise, simulation

Abstract

Stop-and-go waves are a common feature of vehicular traffic and have also been observed in pedestrian flows. Usually the occurrence of this self-organization phenomenon is related to an inertia mechanism. It requires fine-tuning of the parameters and is described by instability and phase transitions. Here, we present a novel explanation for stop-and-go waves in pedestrian dynamics based on stochastic effects. By introducing coloured noise in a stable microscopic inertia-free (i.e. first order) model, pedestrian stop-and-go behaviour can be described realistically without requirement of instability and phase transition. We compare simulation results to empirical pedestrian trajectories and discuss plausible values for the model’s parameters.

References

Herman, R., Montroll, E., Potts, R., Rothery, R.: Traffic dynamics: analysis of stability in carfollowing. Op. Res. 7(1), 86–106 (1959).

Kerner, B.S., Rehborn, H.: Experimental properties of phase transitions in traffic flow. Phys. Rev. Lett. 79, 4030–4033 (1997).

Orosz, G., Wilson, R.E., Szalai, R., Stépán, G.: Exciting traffic jams: Nonlinear phenomena behind traffic jam formation on highways. Phys. Rev. E 80(4), 046,205 (2009).

Chowdhury, D., Santen, L., Schadschneider, A.: Statistical physics of vehicular traffic and some related systems. Phys. Rep. 329(4-6), 199–329 (2000).

Kerner, B.: The Physics of Traffic. Springer (2004).

Zhang, J., Mehner, W., Holl, S., Boltes, M., Andresen, E., Schadschneider, A., Seyfried, A.: Universal flow-density relation of single-file bicycle, pedestrian and car motion. Phys. Lett. A 378(44), 3274– 3277 (2014).

Sugiyama, Y., Fukui, M., Kikushi, M., Hasebe, K., Nakayama, A., Nishinari, K., Tadaki, S.: Traffic jams without bottlenecks. Experimental evidence for the physical mechanism of the formation of a jam. New J. Phys. 10(3), 033,001 (2008).

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).

Helbing, D., Treiber, M.: Gas-kinetic-based traffic model explaining observed hysteretic phase transition. Phys. Rev. Lett. 81, 3042–3045 (1998).

Colombo, R.: Hyperbolic phase transitions in traffic flow. SIAM J. Appl. Math. 63(2), 708–721 (2003).

Ben-Jacob, E., Schochet, O., Tenenbaum, A., Cohen, I., Czirok, A., Vicsek, T.: Generic modelling of cooperative growth patterns in bacterial colonies. Nature 368, 46–49 (1994).

Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., Shochet, O.: Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75, 1226–1229 (1995).

Bussemaker, H., Deutsch, A., Geigant, E.: Mean-field analysis of a dynamical phase transition in a cellular automaton model for collective motion. Phys. Rev. Lett. 78, 5018–5021 (1997).

Buhl, J., Sumpter, D.J.T., Couzin, I.D., Hale, J.J., Despland, E., Miller, E.R., Simpson, S.J.: From disorder to order in marching locusts. Science 312, 1402–1406 (2006).

Hermann, G., Touboul, J.: Heterogeneous connections induce oscillations in large-scale networks. Phys. Rev. Lett. 109, 018,702 (2012).

Muramatsu, M., Nagatani, T.: Soliton and kink jams in traffic flow with open boundaries. Phys. Rev. E 60, 180–187 (1999).

Tomer, E., Safonov, L., Havlin, S.: Presence of many stable nonhomogeneous states in an inertial car-following model. Phys. Rev. Lett. 84, 382–385 (2000).

Treiber, M., Kesting, A., Helbing, D.: Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts. Transport. Res. B: Meth. 44(89), 983– 1000 (2010).

Portz, A., Seyfried, A.: Modeling Stop-and-Go Waves in Pedestrian Dynamics. . In: Lect. Notes Comp. Sci., vol. 6068, pp. 561–568 (2010).

Moussaïd, M., Helbing, D., Theraulaz, G.: How simple rules determine pedestrian behavior and crowd disasters. Proc. Nat. Acad. Sci. 108(17), 6884–6888 (2011).

Kuang, H., Fan, Y., Li, X., Kong, L.: Asymmetric effect and stop-and-go waves on single-file pedestrian dynamics. Procedia Eng. 31, 1060 – 1065 (2012).

Lemercier, S., Jelic, A., Kulpa, R., Hua, J., Fehrenbach, J., Degond, P., Appert-Rolland, C., Donikian, S., Pettr, J.: Realistic following behaviors for crowd simulation. Comput. Graph. Forum 31(2pt2), 489–498 (2012).

Seyfried, A., Portz, A., Schadschneider, A.: Phase coexistence in congested states of pedestrian dynamics. In: Lect. Notes Comp. Sci., vol. 6350, pp. 496–505 (2010).

Hänggi, P., Jung, P.: Colored Noise in Dynamical Systems, pp. 239–326. John Wiley & Sons, Inc. (2007).

Helbing, D., Farkas, I., Vicsek, T.: Freezing by heating in a driven mesoscopic system. Phys. Rev. Lett. 84(6), 1240–1243 (2000).

Arnold, L., Horsthemke, W., Lefever, R.: White and coloured external noise and transition phenomena in nonlinear systems. Z. Phys. B 29(4), 367–373 (1978).

Castro, F., Sánchez, A.D., Wio, H.S.: Reentrance phenomena in noise induced transitions. Phys. Rev. Lett. 75, 1691–1694 (1995).

Gilden, D., Thornton, T., Mallon, M.: 1/f noise in human cognition. Science 267(5205), 1837–1839 (1995).

Zgonnikov, A., Lubashevsky, I., Kanemoto, S., Miyazawa, T., Suzuki, T.: To react or not to react? Intrinsic stochasticity of human control in virtual stick balancing. J. R. Soc. Interface 11(99) (2014).

Williams, R., Herrup, K.: The control of neuron number. Annu. Rev. Neurosci. 11(1), 423–453 (1988).

Helbing, D., Molnár, P.: Social force model for pedestrian dynamics. Phys. Rev. E 51(5), 4282–4286 (1995).

Takayasu, M., Takayasu, H.: 1/f noise in a traffic model. Fractals 01(04), 860–866 (1993).

Wagner, P.: How human drivers control their vehicle. Eur. Phys. J. B 52(3), 427–431 (2006).

Treiber, M., Kesting, A., Helbing, D.: Delays, inaccuracies and anticipation in microscopic traffic models. Phys. A 360(1), 71–88 (2006).

Hamdar, S., Mahmassani, H., Treiber, M.: From behavioral psychology to acceleration modeling: Calibration, validation, and exploration of drivers cognitive and safety parameters in a risk-taking environment. Transp. Res. B-Meth. 78, 32 – 53 (2015).

Tordeux, A., Schadschneider, A.: White and relaxed noises in optimal velocity models for pedestrian flow with stop-and-go waves. J. Phys. A 49(18), 185,101 (2016).

Lindgren, G., Rootzen, H., Sandsten, M.: Stationary Stochastic Processes for Scientists and Engineers. Taylor & Francis (2013).

Jiang, R., Wu, Q., Zhu, Z.: Full velocity difference model for a car-following theory. Phys. Rev. E 64, 017,101 (2001).

Tordeux, A., Seyfried, A.: Collision-free nonuniform dynamics within continuous optimal velocity models. Phys. Rev. E 90, 042,812 (2014).