Abstract
The simulation of pedestrian flow has become an important tool in the fields of planning and operation of public spaces like airports or shopping malls. While evacuation situations have been deeply investigated in numerous publications, the interaction of distinct pedestrian flows still needs more consideration. In this paper, we develop a macroscopic model for the simulation of interacting, more precisely intersecting pedestrian flows by a multiphase convection-diffusion approach. The convection corresponds to a movement towards a strategic direction whereas the diffusion corresponds to a tactical movement that avoids jams. Different populations moving in different directions are represented by different phases. Numerical experiments demonstrate the qualitative behaviour of the simulation model.
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
Preview
Unable to display preview. Download preview PDF.
References
Berres, S., Ruiz-Baier, R., Schwandt, H., Tory, E.M.: An adaptive finite-volume method for a model of two-phase pedestrian flow. Networks and Heterogeneous Media 6, 401–423 (2011)
Bruno, L., Tosin, A., Tricerri, P., Venuti, F.: Non-local first-order modelling of crowd dynamics: A multidimensional framework with applications. Appl. Math. Model. 35, 426–445 (2011)
Burstedde, C., Klauck, K., Schadschneider, A., Zittartz, J.: Simulation of pedestrian dynamics using a two-dimensional cellular automaton. Physica A: Stat. Mech. Appl. 295, 507–525 (2001)
Chen, M., Bärwolff, G., Schwandt, H.: A derived grid-based model for simulation of pedestrian flow. J. Zhejiang Univ.: Science A10, 209–220 (2009)
Cristiani, E., Piccoli, B., Tosin, A.: Multiscale modelling of granular flows with application to crowd dynamics. Multiscale Model. Simul. 9, 155–182 (2011)
Daamen, W., Bovy, P.H.L., Hoogendoorn, S.P.: Modelling pedestrians in transfer stations. In: Schreckenberg, M., Sharma, S.D. (eds.) Pedestrian and Evacuation Dynamics, pp. 59–73. Springer, Heidelberg (2002)
Esser, J., Schreckenberg, M.: Microscopic simulation of urban traffic based on cellular automata. Int. J. Mod. Phys. C 8, 1025–1036 (1997)
Helbing, D., Farkas, I., Vicsek, T.: Simulating dynamical features of escape panic. Nature 407, 487–490 (2000)
Helbing, D., Buzna, L., Johansson, A., Werner, T.: Self-organized pedestrian crowd dynamics: experiments, simulations, and design solutions. Transportation Science 39, 1–24 (2005)
Helbing, D., Farkas, I., Vicsek, T.: Traffic and related self-driven many-particle systems. Reviews of Modern Physics 73, 1067–1141 (2001)
Hoogendoorn, S.P., Daamen, W.: Self-organization in pedestrian flow. Traff. Granul. Flow 3, 373–382 (2005)
Hughes, R.L.: A continuum theory for the flow of pedestrians. Transp. Res. B 36, 507–535 (2002)
Jiang, Y., Zhang, P., Wong, S.C., Liu, R.: A higher-order macroscopic model for pedestrian flows. Physica A 389, 4623–4635 (2010)
Kerner, B.S., Konhäuser, P.: Structure and parameters of clusters in traffic flow. Physical Review E 50, 54–83 (1994)
Lighthill, M.J., Whitham, G.B.: On kinematic waves. II. A theory of traffic flow on long crowded roads. Proc. Roy. Soc. London Ser. A 229, 317–345 (1955)
Piccoli, B., Tosin, A.: Time-evolving measures and macroscopic modelling of pedestrian flow. Arch. Ration. Mech. Anal. 199, 707–738 (2011)
Slawig, T., Bärwolff, G., Schwandt, H.: Simulation of pedestrian flows for traffic control systems. In: Li, E.Y. (ed.) Proc. of the 7th International Conference on Information and Management Sciences (IMS 2008) (Urumtschi, 12. 8. - 19. 8. 08). Series on Information and Management Sciences, vol. 7, pp. 360–374. California Polytechnic State University, California (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schwandt, H., Huth, F., Bärwolff, G., Berres, S. (2013). A Multiphase Convection-Diffusion Model for the Simulation of Interacting Pedestrian Flows. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2013. ICCSA 2013. Lecture Notes in Computer Science, vol 7975. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39640-3_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-39640-3_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39639-7
Online ISBN: 978-3-642-39640-3
eBook Packages: Computer ScienceComputer Science (R0)