Systematic Crowd Mobility Management to Avoid Catastrophic Disasters

of Human Stampedes: The Case of Mina Hajj

Nisrine Ibadah

1 a

, C

esar Benavente-Peces

2 b

, Khalid Minaoui

, Mohammed Rziza

and Mohammed Oumsis

1,3

LRIT Laboratory, Associated Unit to CNRST (URAC 29), IT Rabat Center, Faculty of Sciences,

Mohammed V University in Rabat, Morocco

ETS de Ingenier

ıa y Sistemas de Telecomunicaci

on, Universidad Polit

ecnica de Madrid,

Calle de Nikola Tesla sn, 28031 Madrid, Spain

High School of Technology, Mohammed V University in Rabat, Sal

e, Morocco

Keywords:

Mobility, Trafﬁc Management, Human Crowd, Stoning, Hajj, Mina, Tent City.

Abstract:

Every year, the Holy city of Makkah hosts more than two million Muslims for the pilgrimage ’Hajj’. During

this event, a set of activities should be done by pilgrims. One of the rituals performed is throwing stones in

al-Jamarat area of Mina at pillars target. The throwing Jamarat is a paradigm of stoning the devil, as done by

the prophet Abraham. All pilgrims must reach the site at different times in speciﬁc hours of particular days.

However, this stoning ritual represents the most bottleneck ceremony where the area becomes packed at routes

and around pillars structure. The problem is that, unfortunately, humans cannot be controlled while they are

in a crowd. That takes this place a high safety hazard by increasing accidents’ probably which cause death

of many Muslims last few years. Inspired from this event, this paper presents a new human mobility models

which simulates stoning in Hajj by adopting a new design to solve the safety problems. This suggests control

huge crowds by conducting the relationship between the Jamarat basin, pilgrims, stoning performance, and

the impact of organizing the pilgrims in three rows around the Jamarat basin. This experiment estimate the

throwing time at each pillar in order to manage the temporal and spatial human movement inside the Jamarat

area. The simulation outcomes encourage adopting the new design to prevent crowd panic and disasters.

1 INTRODUCTION

Up to now, mobility modeling ﬁeld cognizes a lot of

interests and research advancements. That especially

ever knows an important expanding of human or so-

ciability based mobility models. From the beginning

of 1990, biologists, physicists, and other groups of

researchers looked into human and animal movement

patterns. Their research detected that their motions

are heavily inﬂuenced by various factors like food

location, foraging, habitat, and tendency to create

groups as herds or communities, for instance, group

of soldiers or rescue workers. That can be applied

to diverse applications of Pocket Switched Networks

(PSN) (Trifunovic et al., 2017). Numerous mobility

patterns have also been suggested inspired by sociol-

ogy and social network. Therefore, There are based

https://orcid.org/0000-0002-3079-3115

https://orcid.org/0000-0002-2734-890X

on the argument that Humans have tendency to so-

cialize where they are governed by social aspects and

the nature of social structure of the belonging commu-

nity. Moreover, people are conﬁned to their own so-

cial group and seldom move outside it. For example;

during their days, people are in ofﬁce, the evening in

a pub or coffee shop and return home at night. Hence,

human mobility is more complex than animals that

stills till now under research.

The pilgrimage to Makkah at Saudi Arabia is one

of the ﬁve needed pillars of Islam. Muslims are

charged for this duty at least one time in their lifetime,

if they can ﬁnancially and physically afford it. Over a

ﬁxed ﬁve days, the holy Makkah hosts around 2 mil-

lion people. A population of international Muslims

that annually comes from more than 150 countries

from all the world. This event represents the largest

mass gathering of all the globe. Recently, the number

of pilgrims has exponentially multiplied, as shown in

Figure 1. That makes the Hajj a huge logistic issue

Ibadah, N., Benavente-Peces, C., Minaoui, K., Rziza, M. and Oumsis, M.

Systematic Crowd Mobility Management to Avoid Catastrophic Disasters of Human Stampedes: The Case of Mina Hajj.

DOI: 10.5220/0010147700660073

In Proceedings of the 10th International Conference on Pervasive and Parallel Computing, Communication and Sensors (PECCS 2020), pages 66-73

ISBN: 978-989-758-477-0

repeated each year at the same time, at the same place

with more and more of hosted pilgrims.

Figure 1: Nationality of pilgrims at the Hajj by millions.

One of the focal points of pilgrimage is ’Stoning

of the Devil’ at the Jamaraat Bridge in Mina. That

comes few miles of Makkah and known as the ’Tent

City’, as depicted in Figure 2.

Figure 2: The tent city (Mina) location.

This area is a pedestrian zone that covers about

20 km

and from which pilgrims throw small stones

at the three Jamaraat pillars. During three successive

days, pilgrims throw at a target and hit it seven times

in sequence, starting with the smallest and ﬁnish with

the largest. However, the stoning ritual is conceived

the most bottleneck dangerous and unsafe process by

dint of cramped spaces, tight scheduling, and large

crowds.

Figure 3: Pedestrians’ ﬂow in Jamarat plaza at Hajj.

Therefore, the pilgrimage has previously wit-

nessed several tragic stampedes and catastrophic

crowd disasters in the past. Basing on the civil

defense statement, the last scamper was happened

Thursday 24 September 2015 nearly at 09:00 am

(Mecca time) towards the Jamraat Bridge at the in-

tersection between 223 and 204 streets, as presented

in Figure 2. This disastrous accident is looked as

the deadliest stampede of the 21st century with 2110

deaths and about 863 were injured, as dramatically

shown in Figure 4.

Indeed, disasters are far from rare in Mecca, as

displayed in Table 1. There occur trampled of deaths

and suffocated people which are usually killed in

squeeze crushes. This large crowd necessitates de-

cisive control with the notably increase in the number

of pilgrims. The need for more researches that sug-

gests an efﬁcient and new perfections for Hajj rituals

primarily in stoning. Inspired from all previous tragic

stampedes, this current paper proposes a new human

mobility model which manage and control movement

ﬂows of pedestrians during the three consecutive days

Table 1: Tragic stampedes during Hajj.

Date What happened where Deaths

24 September 2015 Stampede at junction of streets 204 & 223 in Mina 2110

12 January 2006 Stampede at Jamarat Bridge in Mina 364

1 February 2004 27-minutes stampede during Jamarat stoning 251

11 February 2003 Stampede at Jamarat in Mina 14

5 March 2001 Stampede at Jamarat in Mina 35

9 April 1998 Stampede/overpass fall-off at Jamarat Mina 118

15 April 1997 Fire fuelled by high winds in tent city, Mina 343

23 May 1994 Stampede at Jamarat in Mina 270

2 July 1990 Stampede/suffocation in tunnel leading to Haram 1426

31 July 1987 Security forces break up anti-US demo by Iranian Hajis 402

Systematic Crowd Mobility Management to Avoid Catastrophic Disasters of Human Stampedes: The Case of Mina Hajj

Figure 4: Tragic human stampedes.

at Mina. This pattern prevents crows and panic stam-

ples while stoning the devil by taking into considera-

tion number of predistians within a speciﬁc time pe-

riod and limited space location of the tent city.

The remaining part of the paper is organized as

follows. Section 2 tackles some related works of some

human mobility models previously suggested for dif-

ferent and under diverse constraints. Section 3 high-

lights the mobility features, the main motivation, the

detailed process and properties of the proposed hu-

man mobility model. Section 4 discusses the obtained

pattern, and ﬁnally the conclusion.

2 RELATED WORKS

Human motion management research ﬁeld knows

many human mobility models that have been pro-

posed till now. These patterns are primary applied to

extract and recognize human whereabouts for mobile

networks. Among these patterns, we propose a brief

description of the most used at network simulations:

In (Jeon et al., 2017), the authors present the

Community-based mobility model (CMM) where the

motion of mobile nodes are based on socialization be-

havior and human decision. These devices are carried

by Humans which by nature they tend to gather and

establish communities. All movements are in groups

and between groups. This mobility heavily depends

on the social relationships among devices. An Inter-

action matrix is used to model structure of connex-

ions between people carrying devices. The strength

of interaction between any two nodes i and j are rep-

resented by an element m(i,j). A connectivity ma-

trix (C) is picked up where if and only if m(i,j) is

bigger than a speciﬁc threshold (often 0.25) leads to

C(i,j)=1 and if it is less than 0.25, the c(i,j)=0. From

this matrix, we can detect structures of relationships

into a community via algorithms which already pro-

posed Girvan and Newman (Girvan and Newman,

2001). Communities are initially located within a def-

inite place or a square inside a grid. Moreover, a

given device may change its current position after a

time-interval t. And, the next waypoint (destination)

mainly relies on the location of other nodes with a

strong social connectivity. Furthermore, every node is

found in various communities at different times. That

reﬂects real-life activity where a person is at differ-

ent locations within a day. For instance, a person is

mostly at the ofﬁce from morning till afternoon, at the

coffee shop in the evening with friends, and at home

at night with family. So, a person changes communi-

ties belonging within a day at different locations and

at different times.

In (Ibadah et al., 2018), Self-Similar Least Ac-

tion Walk (SLAW) has been introduced which com-

bines the main features of human motion, as: least-

action trip planning (LATP), truncated power-law

inter-contact times, heavy-tail ﬂight and pause-time

distribution, self-similar dispersal of destinations, and

heterogeneously bounded mobility areas of individu-

als.

The authors analyze major parts of Dartmouth

WLAN traces to suggest Time-Variant Community

Model (TVCM). They recognize two main mobility

features. They differentiated skewed location visit-

ing preferences and periodical re-appearance at the

same position. Skewed location visiting preferences

demonstrates how one node can spend its time at di-

verse places. However, periodical re-appearance at

the same position displays the period in which a de-

vice appears at the same place again. According to

traces, a node spends at a speciﬁc AP an average of

65% of its online time and more than 95% at few than

5 APs (Batabyal and Bhaumik, 2015).

In (Wang et al., 2015), Sociological Orbit aware

Location Approximation and Routing (SOLAR) con-

siders repeated visits of a given node to a set of lo-

cations. It is noticed that people routinely located

at a speciﬁc place for an appointed period of their

daily lives. The authors call these locations as ”hubs”.

Thus, the ”mobility proﬁle” of a person is the repeti-

tion of inter-hub motion which is in generally periodic

or orbital. In SOLAR, the whole experimental area is

divided into several hubs. Every individual randomly

selects a set of hubs which it can visit, as a hub-list.

Based on the ”hub-stay time”, each node remains or

travel inside the hub. And then, it moves to the next

hub. The intra-hub motion can adopt random walk or

random waypoint and the inter-hub is linear.

In (Mei and Stefa, 2009), Small World in Motion

(SWIM) is presented where its concept is based on

two human mobility facts; 1. Human tend to mostly

visit some popular places and frequently near to their

home. And, they seldom visit far places and less pop-

ular. And, 2. Human spend less time at less popular

places and most time at the most popular. However,

PECCS 2020 - 10th International Conference on Pervasive and Parallel Computing, Communication and Sensors

Table 2: Qualitative features of the human mobility models,

Y: Yes, N: No, A: Ambiguous.

Human mobility Realistic Scalable Possibility of a Uses Possibility

models mathematical geographic of

representation map simulation

MhMM Y Y Y Y Y

CMM Y Y Y Y Y

SLAW Y Y N Y Y

TVCM N Y N N Y

SOLAR N Y A N Y

SWIM N Y N N Y

a home location is assigned to each node. And also,

the whole area is partitioned to a number of destina-

tion landmarks which deﬁne a weight inversely pro-

portional to the distance between the home location

and the destination and proportional to destination’s

popularity. When a new waypoint is selected by a

node, it moves with a constant speed towards this des-

tination. Once a node visits a landmark, its popularity

is continuously updated according to present nodes at

the same time. When a speciﬁc node reaches the tar-

geted location, it waits there for some time and then it

selects a new destination.

The Table 2 shows the qualitative features of the

previous discussed models. All the proposed human

mobility models are often inspired from sociological

movements as for social networks. There are based

on the supposition of depending on their nature of so-

cial communities. In this paper, we present a human

mobility model which is related to Jamarat bridge

to manage movement crowds of pilgrims during the

stoning the devil at the Hajj. The main features and

motivation is presented and analyzed in the next sec-

tion.

3 PROPOSED PATTERN: MINA

HUMAN MOBILITY MODEL

(MhMM)

3.1 Problem Deﬁnition and Analysis

Panic stampede is one of the most dramatic collec-

tive attitudes that often causes to the death of peo-

ple who are trampled down or crushed by others.

The diverse collective incident observed in pedestrian

crowds have currently catched the interest of a huge

number of scientists. The real-life implementation

revealed that mostly of the years, some pilgrims die

due to the congestion on throwing the stones (rami al-

jamrat). Some communicated statistics are as follow:

• More than two million of pilgrims per year;

• 20% of pilgrims delegate other pilgrims to do

”rami” instead of them;

• Bridge length is about 600 m;

• Bridge width is about 40 m;

• Number of jamrat is three;

• The distances between the three jamrat are respec-

tively 150 m and 190 m;

• According to religion ﬁxed instructions, the loca-

tions of the three jamrats cannot be shifted.

Figure 5: The three circles of jamarat.

This paper proposes an improved concept of man-

agement and control the pedestrian ﬂow movements

at the Jamarat area in the regular annual pilgrimage to

Hajj season. More than two million of pilgrims ev-

ery year perform their rituals in the midst of a narrow

space and limited time constraint.

3.2 MhMM Concepts

We usually move in our real life depending on geo-

graphic restrictions. That makes our mobility behav-

iors primarily related to obstacles coordinates. More-

over, with a huge number of pedestrians in the same

location, the motion management becomes trickier.

That necessitates a deeper analysis to overcome unex-

pected tragic stampedes and catastrophic crowd disas-

ters. In this case, we need a ﬂexible mobility manage-

ment which will based on real requirements, as the

area size, number of mobile nodes, speciﬁc coordi-

nates of zones, needful time, and traveled distance.

Systematic Crowd Mobility Management to Avoid Catastrophic Disasters of Human Stampedes: The Case of Mina Hajj

All these mobility features must be related to a realis-

tic conduct of mobile nodes with taking into consid-

eration the historical and spatial dependencies inside

the simulation ﬁeld. That later allows accurate tra-

jectories to travel from one zone to another with the

most convenient parameters. The proposed model can

modulate pilgrims motions within a speciﬁc time pe-

riod and limited space location of the tent city. There-

fore, in this part, we attempt to itemize the various

steps of the new human mobility model entitled Mina

Human Mobility Model (MhMM).

Indeed, each pilgrim is considered as a mobile

node which is identiﬁed by a node number, initial co-

ordinates, a speed from a range of 1.5m/s to 5.5m/s,

is attributed to reﬂect all pedestrians class (fat, tall,

adult, child and old). These nodes are two types: 20%

of total mobile nodes are ﬁxed at zone 1. However,

80% can move to the other zones by selecting a new

position to enter in zone 2 in order to start a move-

ment round. These mobile nodes must travel three

rotations where each one contains ﬁve movement de-

cisions to return to the departure position. The same

process must be repeated three times with a bit differ-

ence; the small jamarrat at ﬁrst tour then the median

at the second afterwards the biggest as the third. Be-

sides that, one day must be between two consecutive

tours namely 86400 seconds is added to the arrival in-

stant of the previous one. The resulted outcomes en-

sue a coherent human mobility model. That owns the

tractability of all nodes which their motion features,

as node identiﬁer, coordinates, speed and time.

3.3 MhMM Implementation Process

Based on previous features, the implementation of

Mina pattern follows ﬁve main steps, as displayed by

the diagram process of Figure 6. The aforementioned

steps are detailed as follows:

Step 1: Mina Field Partition

The creation of Mina area represents the ﬁrst step

to generate Mina human mobility model. This ﬁeld is

spread on approximately 20km

. In this part, we sug-

gest a new design to improve stoning process from the

tent city to Jamarrat bridges, as shaped in Figure 7.

This area is split to several zones:

• Zone 1 represents the lodging region for mobile

node which reﬂect the tent area. They must start

and return to this zone after the stoning process.

• Zone 2 is the passage between zones 1 and 3.

• Zone 3 depicts the stoning region with the three

Jamarat bridges that each mobile pilgrims must

reach one bridge at each full round.

• Zone 4 return path to zone 1 after stoning at zone

Figure 7: Mina ﬁeld partition.

This step is generated once time during all de-

ployment time. The detailed coordinates of the re-

sulted design will be used by all mobile nodes with

the aim to correctly move according to the attributed

geographic restrictions inside this area.

Step 2: Initial Spatial Node Distribution

- Before start moving, we uniformly distribute to-

tal number of pilgrims within the ﬁrst zone. This pro-

cedure allows each mobile node to own a spatial lo-

cation (xi, yi) that represents its lodging position, as

depicted in Figure 8.

Figure 6: Implementation process of Mina human mobility model (MhMM).

PECCS 2020 - 10th International Conference on Pervasive and Parallel Computing, Communication and Sensors

Figure 8: Initial spatial human distribution.

Step 3: Pilgrims Classiﬁcation

- Due to onerous Hajj activities, Islam allows

only at this ritual to delegate another pilgrim which

is physically capable to throw stones of old people,

sick, or pregnant; for instance. This category is es-

timated as nearby 20% which still ﬁxed during all

three stoning days at zone 1. The other 80% nodes

are marked as mobile where they must access respec-

tively to other zones (2,3, and 4).

Step 4: Entrance to Zone 2

- In order to start moving; at this step, the mobile

node must own an entrance point to the second zone

(x2, y2). These coordinates will be selected based on

the Mina ﬁeld partition. According to the ﬁrst step,

the x2 will be randomly selected between [240, 195]

while the y2 will be 300.

- Meanwhile, an assigned speed s(i[n]) must be cho-

sen from a range of [1.5m/s, 5.5 m/s].

- Then; to render this model more realistic, it must

respect motion laws where t = d/s. The distance

D(z1,z2) between the departure point and the entrance

position will be calculated based on the Pythagorean

theorem. That allows to deduce the time needed

t[z1, z2] to travel this calculated distance where T =

D(z1,z2) / s(i[n]).

Step 5: Entrance to Zone 3

- The same process of Step 3 will be done. The

node selects an entrance point to the third zone. The

(x3, y3) will be respectively between [120,180] and

[0,180]. The distance must be calculated to result in

the occupied time t[z2, z3] between (x2, y2) and (x3,

y3). This time will be addition to t[z1, z2] to own the

current T5 with T5 = t[z1, z2] + t[z2, z3].

Step 6: Stoning Target

- This step makes the dissimilarity for the pro-

posed model. Three different stoning targets are avail-

able, the small, the medium and the biggest. Three

cycles must be done for each target at three succes-

sive days.

- For the ﬁrst turn, the targeted point will be the small

bridge Sb(xs, ys). So, we must result the distance

traveled from (x3, y3) to (xs, ys). Then, the recorded

time T6 which will be added to last T5: T6 = (t[z1,

z2] + t[z2, z3]) + t[z3, zS1]

- The same process will be repeated for the two other

targets; medium and biggest with two other indepen-

dent turns.

Step 7: Entrance to Zone 4

- As the Step 5, we must select an entrance posi-

tion to zone 4 before reaching the stoning target. The

(x4, y4) will be respectively between [90,135] and

[180,300]. The distance must be calculated to result

in the occupied time t[z3, z4] between the stoning po-

sition and (x4, y4). This time will be addition to last

T6 to own the current T7 which equals to T6 + t[z3,

zS1]

Step 8: Entrance to Zone 1

- As the Step 5, we must choose an entrance posi-

tion to zone 1 before reaching the departure location.

The (x41, y41) will be respectively between [105,60]

and [180,300]. The distance must be calculated to re-

sult in the occupied time T8[z4, z41] between (x4, y4)

and (x41, y41). This time will be additionned to last

T7 to own the current T8.

T8 = T7 + t[z4, z41]

Step 9: Return to the Departure Location

- That represents the last movement decision for

each cycle. After several travels, each mobile node

must return to its departure location (x1,y1). The dis-

tance must be calculated to result in the occupied time

t[z41, z1] between the (x41, y41) and (x1, y1). This

time will be additionned to last T6 to own the current

T9 where T9 = T8 + t[z41, z1]

From all these steps are recorded to result in a coher-

ent and realistic synthetic mobility model. Mina hu-

man MM saves for each node three different cycles,

with the difference at ”Step 6”. These movement de-

cisions represent all detailed steps of stoning during

three consecutive days.

4 RESULTS AND DISCUSSION

4.1 Mina Human MM Interpretation

The Mina human MM outputs are saved that record

all movement details that contain pertinent informa-

Systematic Crowd Mobility Management to Avoid Catastrophic Disasters of Human Stampedes: The Case of Mina Hajj

tion of mobile nodes at each independent step, as the

departure position, the identiﬁer of pilgrims, motion

duration, speed changing, and so on. This informa-

tion is related each other to result in a coherent mo-

bility pattern from the initial distribution to pilgrims

arrivals. An example of Mina human MM are shown

in Figure 9.

Figure 9: Mina human mobility model generation.

From this capture, we deduce some mobility deci-

sions, as:

• The mobile nodes are stable or mobile, as the real-

life pilgrims classiﬁcation (Step 3).

• For ﬁxed person, assigned coordinates (X, Y) are

selected at the initial spatial distribution (Step 2),

as deﬁned for nodes 5 and 6 (930, 3700), (960,

4200) respectively.

• For mobile person as for nodes 7 and 8. A set

of mobility parameters are generated to record all

nodes positions during the stoning the devil.

• Each line displays: the time, node identiﬁer, X-

position, Y-position and the selected human speed

from a range (Step 4).

• Several mobility transitions are accomplished to

reach the intended destination. The last line of

each mobile node displays coordinates of the last

location which must be the same with the ﬁrst po-

sition before moving (Step 2).

• Each mobile pilgrim own 18 mobility decisions

for the three rounds.

4.2 MhMM Features

The human mobility pattern suggested in this paper

owns a set of important features which govern the

whole adopted motion strategy. From all the above-

mentioned steps, we deduce that Mina human MM is

typiﬁed by the following features:

• Mina human MM considers the physical laws of

motion by taking into consideration the relation

between distance, time, and speed (Step 4). That

makes this model more realistic.

• It is a time-dependent mobility model: the current

time mainly relies on previous time instants, i.e.,

basically (t = d/s) (Step 5).

• It can be considered a direction-history based

model. It moves according to the last location. So,

it is a spatially dependent mobility model (Step 4).

• The return time and visiting frequency are prob-

abilistically distributed, mainly in relation to the

resulting trajectory (Steps 2 and 4).

• At the initial stage, it has a spatial distribution

only in zone 1. In the subsequent stages, the

resulting trajectory must be constituted only by

authorized zones without any walls or restricted

ﬁelds, as shown by Figure 7 (Step 1). This fact

leads a realistic movement behavior that seems

like that in daily-life.

The most important movement features of the

Mina human MM compared to other human mobil-

ity models are highlighted in Table 3. The meaning

of the letters is as follows. C: Constant, UD: Uni-

formly Distributed, HB: History Based, PD: Proba-

bilistically Distributed, PL: Truncated Power-law, P:

Periodic, UD: Uniformly Distributed, NA: Not Appli-

cable.

We conclude that the Mina human MM takes into

consideration a set of realistic movement features to

reﬂect a real human mobility model. It abides by

the spatial context with several geographic constraints

(Step 1). Mina human MM permits a ﬂexible motion

even if in a limited ﬁeld, that can be modulated with

diverse constraints. Based on the resulted pattern, pil-

grims can move with the most convient trajectory with

crush preventing (Step 5). That solves the simple ran-

dom process of stoning the devil. It permits an orga-

nized motion which further will be adaptative accord-

ing to pilgrims ﬂow while moving. It exactly reﬂects

a movement with memory which is mainly inspired

from human motion in real-life. It results in a ﬂexible

and adaptative mobility model which operate in nar-

row areas, even when diverse mobility requirements

are considered.

Thanks to its logical process, its conception, the con-

sideration of real-life movements. These parameters

allow the proposed model more efﬁcient and suitable

even when diverse mobility constraints are presence.

PECCS 2020 - 10th International Conference on Pervasive and Parallel Computing, Communication and Sensors

Table 3: Movement features comparison: MhMM vs. other human mobility models.

Mobility Speed Direction Acceleration Pause Flight Return time

models /Deceleration Time Length and Visiting

frequency

MhMM C HB C C/UD C PD

CMM NA PD NA C NA P

SLAW NA PD on set NA TPL TPL P

destinations

TVCM NA PD NA C NA P

SWIM NA UD on set NA C/UD NA P

of locations

5 CONCLUSION

It is important to emulate a real life scenario using a

mobility model. During time, the subject of mobil-

ity modeling have grown where researchers analyze

and suggest new mobility patterns that imitate real

life mobility. The aforementioned factors motivated

us to propose a ﬂexible human mobility model which

is adaptative with the pedestrian’s ﬂow inside the Ja-

marats building. This study suggests multi-solutions

to solve the tragic stampedes and catastrophic crowd

disasters using a simulation program. That uniformly

manage crows by taking into considerations all im-

pacted factors; as the temporal dependencies of previ-

ous movement timing, the spatial dependencies of the

current position foremost depends on the last location.

Meanwhile, geographic restrictions inside the ston-

ing area are considered. Mina human MM acquires

strengths from these realistic combinations. The ben-

eﬁts of this study encourage adopting this solution.

As future works, the Ministry of Municipal and Ru-

ral Affairs in Saudi Arabia must adopt this scheduling

program to register pilgrims to get a timetable and an

assigned route to distribute them uniformly in the dif-

ferent Jamarat building levels. Awareness and guid-

ance for pilgrims are embedded.

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