A cellular automata model for circular movements of pedestrians during Tawaf

Masjid Al-Haram in Saudi Arabia is one of the most crowded pilgrimage locations in the world. More than two million pilgrims gather in Saudi Arabia annually during the Hajj sea- son, and it is compulsory for them to perform a series of actions in the mosque. In the court area, pilgrims perform one of the most important rituals of Hajj, called Tawaf, which con- sists of seven laps of circular movement around the Kaabah, which is situated in the centre of the court. After the Tawaf, pilgrims pray in the court and leave from one of several doors. In this paper, we present a cellular automata model for the simulation of the pilgrims' cir- cular Tawaf movement. We also use a discrete-event model to simulate the actions and behaviours of the pilgrims. The proposed models are used in a software platform to simu- late the actions and movements of pilgrims in the area. We then present an example appli- cation of the model in predicting whether specific changes to the architecture could increase the throughput of the system.

[1]  A. Schadschneider,et al.  Simulation of pedestrian dynamics using a two dimensional cellular automaton , 2001 .

[2]  Daniel Thalmann,et al.  Hierarchical Model for Real Time Simulation of Virtual Human Crowds , 2001, IEEE Trans. Vis. Comput. Graph..

[3]  George J. Milne,et al.  Modelling Emergent Crowd Behaviour , 2003 .

[4]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[5]  Kevin O'Brien,et al.  Human Behavior Models for Agents in Simulators and Games: Part I: Enabling Science with PMFserv , 2006, Presence: Teleoperators & Virtual Environments.

[6]  Norman I. Badler,et al.  Improving the realism of agent movement for high density crowd simulation , 2006 .

[7]  N. Badler,et al.  Crowd simulation incorporating agent psychological models, roles and communication , 2005 .

[8]  Harry J. P. Timmermans,et al.  A Multi-Agent Cellular Automata System for Visualising Simulated Pedestrian Activity , 2000, ACRI.

[9]  Shigeyuki Okazaki,et al.  A study of simulation model for pedestrian movement with evacuation and queuing , 1993 .

[10]  Helbing,et al.  Social force model for pedestrian dynamics. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  Shokri Z. Selim,et al.  A design to minimize congestion around the Ka'aba , 1997 .

[12]  Dirk Helbing,et al.  Simulating dynamical features of escape panic , 2000, Nature.

[13]  J L Adler,et al.  Emergent Fundamental Pedestrian Flows from Cellular Automata Microsimulation , 1998 .

[14]  John J. Fruin,et al.  Pedestrian planning and design , 1971 .

[15]  Abdullah Zawawi Talib,et al.  Modeling Groups of Pedestrians in Least Effort Crowd Movements Using Cellular Automata , 2009, 2009 Third Asia International Conference on Modelling & Simulation.

[16]  Michael J. Quinn,et al.  PARALLEL IMPLEMENTATION OF THE SOCIAL FORCES MODEL , 2003 .

[17]  Martin T. Pietrucha,et al.  FIELD STUDIES OF PEDESTRIAN WALKING SPEED AND START-UP TIME , 1996 .

[18]  Abdullah Zawawi Talib,et al.  Multi-Agent Simulation of Circular Pedestrian Movements Using Cellular Automata , 2008, 2008 Second Asia International Conference on Modelling & Simulation (AMS).

[19]  Standort Duisburg,et al.  A Cellular Automaton Model for Crowd Movement and Egress Simulation , 2003 .

[20]  Norman I. Badler,et al.  Modeling Crowd and Trained Leader Behavior during Building Evacuation , 2006, IEEE Computer Graphics and Applications.

[21]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[22]  W ReynoldsCraig.  Flocks, herds and schools: A distributed behavioral model , 1987 .

[23]  Dirk Helbing,et al.  Self-Organizing Pedestrian Movement , 2001 .

[24]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[25]  Norman I. Badler,et al.  Being a part of the crowd: towards validating VR crowds using presence , 2008, AAMAS.

[26]  M. Overmars,et al.  Tactical Path Finding in Urban Environments , 2005 .

[27]  Andreas Schadschneider,et al.  CA Approach to Collective Phenomena in Pedestrian Dynamics , 2002, ACRI.

[28]  Khaled Abdelghany,et al.  Microsimulation assignment model for multidirectional pedestrian movement in congested facilities , 2005 .

[29]  Hubert Ludwig Kluepfel,et al.  A Cellular automaton model for crowd movement and egress simulation , 2003 .

[30]  Victor J. Blue,et al.  Modeling Four-Directional Pedestrian Flows , 2000 .

[31]  A. Schadschneider.  Cellular Automaton Approach to Pedestrian Dynamics - Theory , 2001, cond-mat/0112117.

[32]  Michael Schreckenberg,et al.  Pedestrian and evacuation dynamics , 2002 .

[33]  Mikel D. Petty.  Crowd Behavior Cognitive Model Architecture Design , 2005 .

[34]  Andreas Schadschneider,et al.  Friction effects and clogging in a cellular automaton model for pedestrian dynamics. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Wael Saleh Halabi.  Overcrowding and the Holy Mosque, Makkah, Saudi Arabia , 2006 .

[36]  Peter Fritzson,et al.  Modeling and Applications , 2004 .

[37]  George Kingsley Zipf,et al.  Human behavior and the principle of least effort , 1949 .

[38]  Dirk Helbing.  A Fluid-Dynamic Model for the Movement of Pedestrians , 1992, Complex Syst..

[39]  Craig W. Reynolds.  Steering Behaviors For Autonomous Characters , 1999 .

[40]  Jan Dijkstra,et al.  Towards a multi-agent model for visualizing simulated user behavior to support the assessment of design performance , 2002 .