Outline Objectives Related Work Modeling Framework Model Application: Tawaf in Makkah Experimental Design Results Demo

Objectives To present a modeling framework for pedestrian movement in congested areas. To apply the model to pilgrims’ movement in the main prayer hall of the holy mosque (Al-Haram Al-Sharief) in Makkah, Saudi Arabia.

Related Work Set of pedestrian simulation models: Wolpert and Zillman (1969). Baer (1974). Okazaki (1979). Gipps and Marksjo (1985), which is an early basis for pedestrians’ cellular automata models. Helbing (1991, 1992); Helbing and collaborators (several). Social Force model, and extensive body of contributions. Løvås GG. (1994) Blue and Adler (1998 and 2000). These models produce acceptable fundamental flow patterns for unidirectional and bi-directional pedestrian flows. Jiang (1999) SimPed. Dijkstra et al (2000) developed a multi-agent Cellular Automata system. Teknomo et al (2001) A. Keßel, H. Klüpfel, and M. Schreckenberg (2002) Hoogendoorn and Bovy (2002) Cangelosi and Holden (2003): variation to Blue and Adler’s models with new set of behavioral rules

Model Input Supply Geometries and layout of the area under consideration. Locations at which each of the activities could be performed in the facility. Demand The travel plan h of each individual i is given. This plan includes the entrance location, start time, speed, congestion perception, set of activities, sequence of activities, activity duration.

Cell i The regular Cellular Automata System in which each cell has only one adjacent cell from each side. The proposed Cellular Automata System and Set of adjacent cells for each cell in the considered area. The Cellular Automata System

Entering Shopping Exiting Activity-Chaining in Pedestrians Facility

InitiallyLater Real-time destination choice and changing movement direction.

Willing to move into congestion (congestion seeking) Congestion Perception Not willing to move into congestion (congestion aversion)

density Probability of accepting cell

density Probability of accepting cell Crowd aversion

density Probability of accepting cell Crowd aversion Crowd seeking

Simulation User Behavior Demand Generation Area Configuration Configure the CA System Location of Activities Set of Adjacent Cells Determine Entry Cells Entry Queue Load Pedestrian Set Initial Attributes Goal/Destination Choice Movement Direction Congestion Perception Update Location Hold at Activity Location Check Goal

Generate a pedestrian and add to entry queue Next cell c(i = i+1) More cells? More intervals? t = t+1 Stop No Yes No Yes No Yes No Area Configuration Destination choice Determine movement direction (path finder) Determine a cell c(j) in the movement direction Is movement possible? Congestion perception? Move pedestrian Is at his/her exiting destination? Update attributes of cells c(i) and c(j) Exit pedestrian No Yes Check objective According to speed, determine number of possible steps Step (k = 1) Update attributes of cells c(i) and c(j) More steps? Next step (k = k+1) Yes No Simulation interval t = 0 Cell c(i = 1) Is generation cell? Is generation interval? Load pedestrian from entry queue Is occupied cell? Is pedestrian movement updated in the current interval? Is moving pedestrian? No Yes No Yes No Is entry queue empty? Generate pedestrian

Model Application Modeling the Tawaf (circumambulation) rituals performed by the pilgrims’ in the main prayer hall of the holy mosque in Makkah, Saudi Arabia during the annual pilgrimage event. The mosque consists of the main hall, which is surrounded by a multi-story building and another additional open area, with total capacity of 330,000 worshipers.

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Al-Haboubi and Selim (1997a and 1997b) studied the pilgrims’ movement around the Ka’aba. In attempt to minimize congestion around the Ka'aba, they proposed that pilgrims move in spirals to minimize their waiting time, where the width of the spiral is proportional to the total demand in the area.

Tawaf Start line Moving Directions The cellular automata system used in modeling the Mataf system.

The Tawaf movements include entering, circumambulation (looping seven times) around the Ka’aba, and exiting Set of adjacent cells considered by the pilgrim Current destination Moving direction 1- For entering and looping movements.

1 3 2 Set of adjacent cells considered by a pilgrim exiting in the anti- clockwise direction Set of adjacent cells considered by a pilgrim exiting in the clockwise direction 2- For exiting movements.

Average travel distance and average speed Demand LevelLowMediumHigh Average Travel Distance (meter) Average Travel Speed (meter/Sec)

Average travel distance and average speed % conflicts0%50%100% Average Travel Distance (meter) Average Travel Speed (meter/Sec)

3. Effect of Spatial Distribution of Entering Demand Medium Demand Level 0% conflicts of exiting pilgrims Uniform temporal distribution of demand 100% of demand have initial speed of 0.5 m/sec Medium level of congestion perception

Average travel distance and average speed Spatial Distribution of Entering Demand Uniform4 gates2 gates Average Travel Distance (meter) Average Travel Speed (meter/Sec)

Average travel distance and average speed % travelers with high initial speed 0%25%50% Average Travel Distance (meter) Average Travel Speed (meter/Sec)

Average travel distance and average speed Level of congestion perception High (congestion aversion) Med.Low (congestio n seeking) Average Travel Distance (meter) Average Travel Speed (meter/Sec)

Demo