Simulation of the Pedestrian Flow in the Tawaf Area Using the Social Force Model

In today-s modern world, the number of vehicles is increasing on the road. This causes more people to choose walking instead of traveling using vehicles. Thus, proper planning of pedestrians- paths is important to ensure the safety of pedestrians in a walking area. Crowd dynamics study the pedestrians- behavior and modeling pedestrians- movement to ensure safety in their walking paths. To date, many models have been designed to ease pedestrians- movement. The Social Force Model is widely used among researchers as it is simpler and provides better simulation results. We will discuss the problem regarding the ritual of circumambulating the Ka-aba (Tawaf) where the entrances to this area are usually congested which worsens during the Hajj season. We will use the computer simulation model SimWalk which is based on the Social Force Model to simulate the movement of pilgrims in the Tawaf area. We will first discuss the effect of uni and bi-directional flows at the gates. We will then restrict certain gates to the area as the entrances only and others as exits only. From the simulations, we will study the effect of the distance of other entrances from the beginning line and their effects on the duration of pilgrims circumambulate Ka-aba. We will distribute the pilgrims at the different entrances evenly so that the congestion at the entrances can be reduced. We would also discuss the various locations and designs of barriers at the exits and its effect on the time taken for the pilgrims to exit the Tawaf area.

Authors:

• Zarita Zainuddin
• Kumatha Thinakaran
• Mohammed Shuaib

Keywords:

• circumambulation
• Ka'aba
• pedestrian flow
• SFM
• Tawaf
• entrance
• exit

References:

[1] D. Helbing, I.J. Farkas, P. Molnar, T. Vicsek. Simulation of Pedestrian
Crowds in Normal and Evacuation Situations Pedestrian and evacuation
dynamics, edited by M. Schreckenberg and S. Deo Sarma, 21-58. Berlin:
Springer-Verlag. (2002)
[2] Stucki, Pascal, Christian Gloor, and Prof. Kai Nagel. Obstacles in
Pedestrian Simulations. Department of Computer Sciences, ETH Zurich,
[September 2003]
[3] Y.T. Matbouli, M.A. Alzahrani, Pedestrian Movement Analysis at Tawaf,
King AbdulAziz University.
[4] M.H. AlHaboubi, S.Z. Selim, A Design To Minimize Congestion Around
The Ka'aba, Pergamom-Elsevier Science LTD, Computers Industrial
Engineering; pp: 419-428; Vol: 32 (1997)
[5] D. Helbing, L. Bunza, A. Johansson, T. Werner, Self-Organized Pedestrian
Crowd Dynamics: Experiments, Simulations, and Design
SolutionsTransport Science, pp. 1-24; Vol 39(1) (2005)
[6] Armin Seyfried, Bernhard Steffen, Wolfram Klingschand ,Maik Boltes, The
fundamental diagram of pedestrian movement revisited Journal of Statistical
Mechanics:Theory and Experiment, Oct 2005
[7] Armin Seyfried, Tobias Rupprecht, Oliver Passon, Bernhard Steffen,
Wolfram Klingsch and Maik Boltes, New insights into pedestrian flow
through bottlenecks, http://arxiv.org/abs/physics/0702004v2
[8] U. Weidmann. Transporttechnik der Fußg┬¿anger. Schriftenreihe des IVT 90,
ETH Z¨urich, 1993.
[9] Helbing, D. & MulnaÂr, P. Social force model for pedestrian dynamics.
Phys. Rev. E 51, 4282┬▒4286 (1995).
[10] D. Helbing, I. J. Farkás, P. Molnár, and T. Vicsek (2002) Simulation of
pedestrian crowds in normal and evacuation situations. Pages 21-58 in: M.
Schreckenberg and S. D. Sharma (eds.) Pedestrian and Evacuation
Dynamics (Springer, Berlin).
[11] D. Helbing, P. Molnár, I. Farkas, and K. Bolay (2001) Self-organizing
pedestrian movement. Environment and Planning B 28, 361-383.
[12] Zarita Zainuddin, Kumatha Thinakaran, Ibtesam M Abu-Sulyman(2009)
Simulating the Circumambulation of the Ka'aba using SimWalk, European
Journal of Scientific Research, Volume 38 Issue 3, December 2009.