outline objectives related work modeling framework model application: tawaf in makkah experimental...
TRANSCRIPT
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Outline
• Objectives
• Related Work
• Modeling Framework
• Model Application: Tawaf in Makkah
• Experimental Design
• Results
• Demo
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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.
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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
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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.
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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
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Entering
Shopping
Shopping
Exiting
Activity-Chaining in Pedestrians Facility
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Cell j
Cell i
Cell c
Pedestrian P
Cell n
Cell m
Cell o
Initially Later
Real-time destination choice and changing movement direction.
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Willing to move into congestion
(congestion seeking)
Congestion Perception
Not willing to move into congestion
(congestion aversion)
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density
Probability of accepting cell
1.0
0.0
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density
Probability of accepting cell
1.0
0.0
Crowd aversion
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density
Probability of accepting cell
1.0
0.0
Crowd aversionCrowd seeking
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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
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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
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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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return
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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.
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Tawaf Start line
Moving Directions
The cellular automata system used in modeling the Mataf system.
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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.
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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.
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0
10
20
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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
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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
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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
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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
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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
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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
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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
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0
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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
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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
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0
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90
100
0
520
1040
1560
2080
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3120
3640
4160
4680
5200
5720
6240
6760
time (seconds)
%th
roug
hput
/dem
and
congestion aversion
medium congestion perception
congestion seeking
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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
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Demo