outline objectives related work modeling framework model application: tawaf in makkah experimental...

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

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

Shopping

Exiting

Activity-Chaining in Pedestrians Facility

Cell j

Cell i

Cell c

Pedestrian P

Cell n

Cell m

Cell o

Initially Later

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

1.0

0.0

density

Probability of accepting cell

1.0

0.0

Crowd aversion

density

Probability of accepting cell

1.0

0.0

Crowd aversionCrowd seeking

Simulation

User Behavior

Demand Generation

Area ConfigurationConfigure the CA System

Location of ActivitiesSet of Adjacent Cells

Determine Entry CellsEntry Queue

Load Pedestrian

Set Initial AttributesGoal/Destination Choice

Movement Direction Congestion Perception

Update LocationHold 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

Yes

No

Yes

Yes

No

No

Yes

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 occupied cell?

Is pedestrian movement updated in the current

interval?

Is moving pedestrian?

No

Yes

Yes

Yes

No

Yes

No

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.

return

• 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.

1

3

2

4

Set of adjacent cells considered by the pilgrim

Current destination Moving direction

1- For entering and looping movements.

13

2

Set of adjacent cells considered by a pilgrim exiting in the anti-clockwise direction

1

2

3

Set of adjacent cells considered by a pilgrim exiting in the clockwise direction

2- For exiting movements.

0

10

20

30

40

50

60

70

80

90

100

0

530

1060

1590

2120

2650

3180

3710

4240

4770

5300

5830

6360

6890

time (seconds)

% t

hro

ug

hp

ut/

dem

and

low demand

medium demand

high demand

Average travel distance and average speed

Demand Level Low Medium High

Average Travel Distance (meter)

838.7 903.1 1028.0

Average Travel

Speed (meter/Sec)

0.177 0.164 0.159

0

10

20

30

40

50

60

70

80

90

100

0

410

820

1230

1640

2050

2460

2870

3280

3690

4100

4510

4920

5330

5740

6150

6560

6970

time (seconds)

%th

roug

hput

/dem

and

0% conflicts

50% conflicts

100% conflicts

Average travel distance and average speed

% conflicts 0% 50% 100%

Average Travel Distance (meter)

903.1 898.5 870.0

Average Travel

Speed (meter/Sec)

0.164 0.154 0.143

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

0

10

20

30

40

50

60

70

80

90

100

0

370

740

1110

1480

1850

2220

2590

2960

3330

3700

4070

4440

4810

5180

5550

5920

6290

6660

7030

time (seconds)

%th

roug

hput

/dem

and

uniform

4 gates

2 gates

Average travel distance and average speed

Spatial Distribution of

Entering Demand

Uniform 4 gates 2 gates

Average Travel Distance (meter)

903.1 895.8 891.2

Average Travel

Speed (meter/Sec)

0.164 0.155 0.152

0

10

20

30

40

50

60

70

80

90

100

0

520

1040

1560

2080

2600

3120

3640

4160

4680

5200

5720

6240

6760

time (seconds)

%th

roug

hput

/dem

and

0% 1 m/sec and 100% 0.5 m/sec

25% 1 m/sec and 75% 0.5 m/sec

50% 1m/sec and 50% 0.5 m/sec

Average travel distance and average speed

% travelers with high initial speed

0% 25% 50%

Average Travel Distance (meter)

903.1 906.9 891.2

Average Travel

Speed (meter/Sec)

0.164 0.173 0.185

0

10

20

30

40

50

60

70

80

90

100

0

520

1040

1560

2080

2600

3120

3640

4160

4680

5200

5720

6240

6760

time (seconds)

%th

roug

hput

/dem

and

congestion aversion

medium congestion perception

congestion seeking

Average travel distance and average speed

Level of congestion perception

High

(congestion aversion)

Med. Low

(congestion seeking)

Average Travel Distance (meter)

853.3 903.1 800.6

Average Travel

Speed (meter/Sec)

0.287 0.164 0.112

Demo