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On the Analysis of Human Mobility Model for

Content Broadcasting in 5G Networks

Chun Pong Lau∗, Abdulrahman Alabbasi†, and Basem Shihada∗

∗Computer, Electrical and Mathematical Sciences and Engineering

King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia

{lau.pong, basem.shihada}@kaust.edu.sa

†School of Information and Communication Technology

Royal Institute of Technology (KTH), SE-100 44, Stockholm, Sweden

alabbasi@kth.se

Abstract—Today’s mobile service providers aim at ensur-

ing end-to-end performance guarantees. Hence, ensuring an

efﬁcient content delivery to end users is highly required.

Currently, transmitting popular contents in modern mobile

networks rely on unicast transmission. This result into a

huge underutilization of the wireless bandwidth. The urban

scale mobility of users is beneﬁcial for mobile networks

to allocate radio resources spatially and temporally for

broadcasting contents. In this paper, we conduct a compre-

hensive analysis on a human activity/mobility model and

the content broadcasting system in 5G mobile networks.

The objective of this work is to describe how human daily

activities could improve the content broadcasting efﬁciency.

We achieve the objective by analyzing the transition prob-

abilities of a user traveling over several places according to

the change of states of daily human activities. Using a real-

life simulation, we demonstrate the relationship between

the human mobility and the optimization objective of the

content broadcasting system.

I. INTRODUCTION

In the convention, random walk and random way-

point models are used in mobility modeling [1]. These

models follow the stochastic approach in moving direc-

tion, velocity, and independent with the previous status.

However, human mobility is far from being considered

random. It is known that people exhibit a high degree

of spatial and temporal regularity, following a simple

and reproducible pattern such as traveling between home

and work locations [2]. Xu et al. empirically studied

human mobility from the big data of a mobile network

in a metropolitan city with over 9600 cellular towers.

The results reveal that the human mobility has strong

correlations with the mobile trafﬁc. Furthermore, the

mobility and the mobile trafﬁc have regular patterns

and can be linked with social ecology [3]. Therefore,

studying of human mobility models become crucial in

data dissemination in various types of communication

networks. For example, in opportunistic networks, there

is no ﬁx end-to-end path for transmitting data from a

source to the destination. Instead, the data are relayed

by the mobile nodes in a hop-by-hop fashion [4].

In order to reproduce synthetic realistic mobility

patterns close to reality, daily activities of the human

schedule are considered in the mobility models. Ekman

et al. proposed the working day movement model in

[5] by presenting the everyday life of average people,

such as sleeping at home, working in the ofﬁce, and

evening activities. Issacman et al. proposed WHERE

which model large populations move with different

metropolitan areas from real-world probability distribu-

tions [6]. This model primarily generates synthetic traces

for the people moving between two places. It is scalable

to more locations but with introducing extra complexity.

Zheng et al. proposed the agenda driven mobility model

in [7] emphasizing the social role of a human for making

movement decisions.

The number of mobile subscribers has dramatically

grown during the recent years. The bandwidth demand

for popular media contents such as movies, TV shows,

games, and software updates continue to increase. It

poses a severe network congestion problem for content

delivery in the mobile networks [8]. In the future ﬁfth-

generation (5G) networks, content providers would be

able to deploy their distribution algorithms through the

functionalities of software deﬁned network (SDN) and

network function visualization (NFV) onto the core

network (CN) and the radio access network (RAN) [9].

In the SDN approach, a cloud-based software deﬁned

controller (SDC) receives high-level services policies

from content providers and implements control signal in

the CN and RAN for radio resources allocation, content

distribution schedule, and cooperated broadcasting and

multicasting, such as researches in [10]–[12].

User mobility has been considered for caching and

content delivery system. Poularakis et al. proposed a

distributed approximation algorithm in [13] for deliver-

ing content in a femto-caching architecture. The femto-

caching architecture was proposed in [14] for ofﬂoading

the popular large size video contents onto femtocell-like

base station (BS). Lee et al. analyze human mobility

from traces of location-based social networks to develop978-1-5386-3531-5/17/$31.00 c

2017 IEEE

a method to deliver video data by moving people to

static kiosks [15]. Authors in [16] exploit the human

mobility patterns and social tie for caching contents in

the mobile devices for distribution through device-to-

device communication. To summarize, mobile networks

utilize these large-scale universal mobility patterns to

schedule broadcasting to deliver popular contents in the

crowded area for reducing the trafﬁc congestion, radio

resources usage as well as the energy consumption.

Although the mobility models are widely adopted in the

content delivery systems, there is a lack of statistical

analysis in this area.

In this paper, we focus on analyzing the synthetic

human activity-based mobility models and demonstrate

how the future 5G mobile network could utilize this

information for massive content delivery. We describe

a typical model of human activity and mobility model

and the optimization objective function for a content

broadcasting system. The contribution of this work is

ﬁrst to statistically evaluate the human activity mobility

model. We begin by deriving the probability of a user

starting an activity. Followed by the probability of a user

to end an activity. Then, connecting the probability of a

user being in a location at a given time to derived proba-

bilities. It followed by deriving the total expected number

of users within a location. Then, the content delivery

system exploits this information for the decision making

to achieve the optimization goal which is disseminating

a content to all of the subscribers with the least amount

of radio resources in an optimal timing. We support our

study by conducting a real-life simulation incorporated

with a real geographical location and realistic schedules

to demonstrate the human movement and the proper

timing for content distribution.

The rest of this paper is organized as follows. Sec-

tion II presents human mobility model and the content

broadcasting system in 5G mobile networks. The statis-

tical modeling is explained in Section III. Section IV

describes the details of the simulation setup and result.

Finally, the paper is concluded in Section V.

II. SY ST EM MO DE LS

In this section, the human mobility model is described

followed by the efﬁcient content broadcasting system.

A. Human Activity Mobility Model

The mobile users are categorized into different sets

of user groups G={g1, ..., gG}according to their

occupation, living habit, and behavior for generating

individual mobility traces with a degree of randomness,

while representing the realistic environment. The human

states mobility model makes use of the human daily life

routine for each user group which is composed of a set

of states V={v1, ..., vV}.The users within the same

user group have similar daily routines from the same

TABLE I

MOD EL PARAMETERS

Symbols Descriptions

G={g1,..., gG}A set of user groups

V={v1,..., vV}A set of mobility states

uIndex of a user

viIndex of an activity state

Au

viActivity of user uat state vi

Lu

viLocation of user uat state vi

Du

viStaying Duration of user uat state vi

tDu

viUpper bound of the duration Dvi

tDl

viLower bound of the duration Dvi

Su

viStarting time of user ubeing at state vi

tSu

viUpper bound of state starting range of vi

tSl

viLower bound of state starting range of vi

Eu

viEnding time of user uﬁnishing at state vi

mu

vi,vj(t)Transition probability from vito vjat time t

B={b1,..., bB}A set of base stations

C={c1,..., cC}A set of contents

Nc,b,t Number of subscribers of content cin BS bat time t

ac

tNumber of active cells of content cat time t

set of states with same activity stages and state starting

range, but different staying locations and durations.

Each state viconsists of the following components

for each user u, an activity stage Au

vi, a staying location

Lu

vi, a staying duration Du

vi, a state starting range and a

set of transition probabilities.

1) Activity Stage: An activity stage Au

viis the name of

a daily activity such as ‘Sleeping’ and ‘Working’. A se-

ries of activity stage forms a life routine for a user group.

Each user group has different sets of activity stages in

their corresponded mobility model. For example, a group

of ofﬁce staff has a ‘Working in ofﬁce’ stage while a

group of students has a stage ‘At school’.

2) Staying Location: A staying location Lu

viis ran-

domly chosen from a various set of places, depends

on the activity and the user group. There is static

and dynamic spatial information for a mobile user in

different states. For instance, home and work locations

are static. These places remained unchanged for a mobile

user in this model. On the other hand, the dining and

recreation locations are dynamic. The mobile user may

visit different places for dining and leisure on various

days. These locations are randomly chosen from a set

Lu

viof related locations within a reasonable distance.

The selection process of the location is independent of

the other state parameters.

3) Staying Duration: The staying duration Du

viof

each state viis a random variable which following a

truncated normal distribution with a lower bound tDl

vi

and an upper bound tDu

vi. Each state has individual mean

µDvi, variance σDvi, and truncation boundary for the

staying duration according to the activity stage and user

group. For example, the staying duration of a ‘Sleeping’

state of an adult may have a mean of 7 hours with a larger

variance whereas 10 hours for a child with a smaller

variance.

4) State Starting Range: The state starting range

consists of a pair of lower bound tSl

viand upper bound

tSu

vifor controlling the start of a state. It is independent

of the staying duration. A state starts if and only if the

starting time Su

viis within this range.

In addition to the components mentioned above, the

starting time and the ending time of a state for a user

are introduced. The ending time of a state is deﬁned as

the sum of the starting time and the staying duration.

Let Eu

viis the ending time of user ustaying at the state

vi, and it is formulated as,

Eu

vi=Su

vi+Du

vi, (1)

where Su

viis the starting time of state viof user u. We

assume, the starting time of initial state Su

v1is a constant

at t=t0.

5) Transition Probability: The transition probability

mu

vi,vj(t)is the probability of transiting from state vi

to vjat time t. It is a function of time depends on the

ending time of the current state i, the starting range of

state j, and a state selection probability ρi,j .

The transition from a state ito a future state jcan be

triggered when the ending time of the current state iis

within the range of the starting time in state j.

Studying the human mobility model is essential for

understanding the daily mobility patterns for content

broadcasting. In the following subsection, the content

broadcasting system is introduced to utilize the user

mobility information for making delivery decisions.

B. Content Broadcasting System in 5G Mobile Networks

We consider a mobile network that has a set of BS B=

{b1, ..., bB}deployed in a certain region. Let tbe the

time segment. A set of contents C={c1, ..., cC}arrive

at the system as a Poisson process. In the region, there is

a set of mobile users U={u1, ..., uU}. A subscriber is

a mobile user who subscribes to content which has not

yet been delivered. Let qu,c be a binary variable where

qu,c = 1 if a mobile user uis a subscriber of a content

c. Let qu,c,b,t be a binary variable where qu,c,b,t = 1 if a

subscriber of a content cis associated with BS bat time

segment t. The total number of subscribers of content c

in BS bat time tis equal to,

Nc,b,t =X

u∈U

qu,c,b,t.(2)

An active cell for a content is deﬁned as a BS that has

at least a single active subscriber. The number of active

cells of content cat time tis denoted as ac

tas,

ac

t=X

b∈B

[Nc,b,t >0],(3)

where the notation [.] is the Iverson bracket. If the

condition in the square bracket is fulﬁlled, the number

is 1, while 0 otherwise.

An active cell ac

timplies that there is at least one

active subscriber of a content cwithin the cell coverage

area at time t. This deﬁnition can be changed as per

the network engineering demands. The constraint can

be relaxed through replacing the 0on the right side

of the inequality in (3) by a threshold. From the BS

point of view, if the radio reception levels of the mobile

users are good, broadcasting content in a cell to all

subscribers yield the most efﬁciency. It requires only a

single radio transmission instead of multiple duplicated

transmission comparing to unicast transmissions. From

the network point of view, perceiving a time with the

minimum number of broadcasting transmissions will be

the most efﬁcient way to deliver a content, i.e., using

the minimum amount of radio resource for transmitting

to all of the subscribers. Therefore, our objective is to

search for a time segment tthat minimizes the number of

active cells ac

tfor delivering the content c. The original

problem is formulated as follows,

min

tac

t(4a)

subject to tc

a< t < tc

e,(4b)

where tis the time segment, which is an integer. The

variables tc

aand tc

eare the arrival and expiry time of

content c. The model parameters are summarized in

Table I. We model this problem by considering the

human activity states as random events; then we used

conditional probability theorems to ﬁnd an expression

for the minimum number of active cells. This analysis

is provided in the next section.

III. STATISTICAL MODELING

The primary objective of the aforementioned delivery

system is to broadcast the content to all users with the

minimum number of transmissions, i.e., the minimum

number of active cells. For this purpose, we need to ﬁnd

a time and optimal locations that have the maximum

number of subscribers for a content. Therefore, we

calculate the expected number of users at a time tin

location L.

The building blocks of these calculations start with

ﬁnding the probability of a user starting the state jat

time t, which can be calculated based on the staying

duration and starting time of that user at previous states.

We then ﬁnd the probability of ending a state jat time

t. It follows that we incorporate the selection of location

lin the starting and ending time probabilities. Then, we

calculate these probabilities for all users, at all possible

time segments. Followed by ﬁnding the optimal time

which guarantees a minimum number of active cells.

A. Probability of starting a state at a given time segment

In order to calculate the probability of a user ustarting

a state jat time t, we have recognized ﬁve events which

contribute to the starting point, described as follows,

•R: The ending time of previous state iis in between

time tand t−1.

•Z: The ending time Eu

viof previous state imust

be larger than the lower bound of the starting time

tSl

vjof the current state jand lower than the upper

bound of starting time tSu

vj.

•X: For every previous state i, the staying duration

Du

viis lower and upper bounded by tDl

viand tDu

vi,

respectively.

•Y: The current searching time t, must be lower than

the maximum staying duration in previous state i.

•W: There is a positive transition probability from

state ito state j.

Event Rlimits the ending time of previous state iis

within the time segment tas follows,

R:t−1≤Su

vi+Du

vi≤t. (5)

Event Zensures that the ending time of the previous

state iis within the range of starting time of the current

state j. It is formulated as,

Z:tSl

vj≤Su

vi+Du

vi≤tSu

vj.(6)

Event Xdescribes that the staying duration Du

viis a

truncated random variable which is upper bounded by

tDu

viand lower bounded by tDl

vi, which is,

X:tDl

vi≤Du

vi≤tDu

vi.(7)

Event Yindicates the current time t, should be less

than the maximum staying duration of previous state i

in order to have a valid transition from state ito current

state j, which is formulated as,

Y:t≤tSu

vi+tDu

vi.(8)

Finally, event Wis a positive transition probability

from state ito state j. This probability excludes all of

the possibilities for transiting from previous state ito k

other than the current state j.

W:mvi,vj(t)= 1 −X

k>i,k6=j

i,j,k∈{1,...,V }

mvi,vk(t).(9)

The probability of a user ustarting a state jat time

tis a combination of the aforementioned events, and it

is formulated as follows,

Pr{Su

vj=t}= Pr{R, Z, X, Y, W }.(10)

The probability Pr{Su

vj=t}is the probability of

intersection between all events, X, Y, Z, W. Hence, we

can reformulated using conditional probability facts to

the following expression,

Pr{Su

vj=t}=X

i<j

j∈{1,...,V }

Pr{R, Z|X, Y }Pr{X}I{Y}mvi,vj(t).

(11)

Note that event Y does not contain any random variable.

Hence, we express the intersection with event Y as

an indicator function, I(Y) = 1 when Y is true and

I(Y)=0when Y is false. It follows that using (6)-(9),

expression (11) is expanded as in (12).1

1Note that we convert the event Z from its original deﬁnition in (6)

to Z:tSl

vj≤t≤tSu

vj.because we already bound Su

vi+Du

viby t−1

and t.

B. Probability of ending a state at a given time segment

We calculate the probability of the ending time of

state vjat time tsince it is necessary to obtain the next

state probabilities. The ending probability of state vjis

formulated as follows,

Pr{Eu

vj=t}= Pr nSu

vj+Du

vj=to

=X

du

vj∈Dvj

Pr nSu

vj+du

vj=t

Du

vj=du

vjoPr nDu

vj=du

vjo

=X

du

vj∈Dvj

Pr nSu

vj=t−du

vj

Du

vj=du

vjoPr nDu

vj=du

vjo.

(13)

Then, we let nvj=t−du

vjand δvj= Pr{Du

vj=

du

vj}2. Expression (13) is reformulated as,

Pr{Eu

vj=t}=X

du

vj∈Dvj

Pr nSu

vj=nvj

Du

vj=du

vjoδvj.(14)

Recall that the staying duration Du

vjat vjis independent

from the starting time Su

vjof vj. It follows that the

value of Pr nSu

vj=nvj

Du

vj=du

vjois in similar form

of (12).

C. Probability of a user staying in a speciﬁc location

within a period of state

The joint probability of ending a state vjwith the

possibility of being at different locations is expressed

as,

Pr nEu

vj=t, Lu

vjo=X

l∈Lu

vj

Pr nEu

vj=t

Lu

vj=loPr{Lu

vj=l},

(15)

where Lu

vjis the random variable that spans all possible

locations for the same state, i.e., Lu

vj. Recall our assump-

tion that the user selects the location of the activity in

state vjindependent from the starting and ending time of

that activity. Hence, the probability in (15) is calculated

as follows,

Pr nEu

vj=t, Lu

vjo=X

l∈Lvj

Pr nEu

vj=t

Lu

vj=loPr{Lu

vj=l}

=X

l∈Lu

vj

X

du

vj∈Du

vj

Pr nSu

vj=nvj

Du

vj=du

vjoPr{Lu

vj=l}δvj.

(16)

In similar lines, we link the probability of starting a

state vjat a time twith the set of locations Lu

vj, from

(12), as in (17).

D. Expected number of users at each time tin each BS

In this subsection, we calculate the expected value of a

number of users at speciﬁc time and location. We begin

by ﬁnding the probability of a single user ubeing in

location lat time t, using the probabilities found in (16)-

(17), as follows,

2Recall that Du

vjis a Normal distributed random variable, with

mean and variance µDvjand σDvj, hence, the probability of δvj=

Pr nDu

vj=du

vjois known.

Pr{Su

vj=t}=X

i<j

j∈{1,...,V }

Pr ht−1≤Su

vi+Du

vi≤t, tSl

vj≤Su

vi+Du

vi≤tSu

vj

tDl

vi≤Du

vi≤tDu

vi, t ≤tSu

vi+tDu

vii

hFDu

vi(tDu

vi)−FDu

vi(tDl

vi)iIt≤tSu

vi+tDu

vimvi,vj(t),∀j∈[1, V ].

=X

i<j

j∈{1,...,V }

Pr ht−1≤Su

vi+Du

vi≤t

tDl

vi≤Du

vi≤tDu

vi, t ≤tSu

vi+tDu

vii

hFDu

vi(tDu

vi)−FDu

vi(tDl

vi)iItSl

vj≤t≤tSu

vjIt≤tSu

vi+tDu

vimvi,vj(t),∀j∈[1, V ].

(12)

Pr nSu

vj=t, Lu

vjo=X

l∈Lu

vj

Pr nSu

vj=t

Lu

vj=loPr{Lu

vj=l}

=X

l∈Lu

vj

X

i<j

i∈V

Pr nt−1≤Su

vi+Du

vi≤t

Lu

vj=l, tDl

vi≤Du

vi≤tDu

vi, t ≤tSu

vi+tDu

vio

Pr{Lu

vj=l}hFDu

vi(tDu

vi)−FDu

vi(tDl

vi)iItSl

vj≤t≤tSu

vjIt≤tSu

vi+tDu

vimvi,vj(t),∀j∈[1, V ].

(17)

Pr nuvj|t, Lu

vj=lo= Pr nSu

vj≤t, Eu

vj≥t|Lu

vj=lo

=X

su∈{0,...,t}X

eu∈{0,...,t}

Pr nSu

vj=su|Eu

vj=eu, Lu

vj=lo

Pr nEu

vj=eu|Lu

vj=lo,

(18)

where suand euare the starting and ending time

deterministic values of the random variables Su

vjand

Eu

vj, respectively, and in notation they are replaced by t

at (12) and (13).

Utilizing the probability of each user being in location

lat time t, expressed in (18), the expected numbers of

users is obtained as,

E{NU(t, l)}=X

u∈UX

vj(u):j∈J

Pr nuvj|t, Lu

vj=lo. (19)

E. Search minimum number of active cells at a time t

in a time range

The time segment t∗at which the minimum number

of active cells is enough to serve all subscribed users

for a content can be found by solving the following

optimization problem,

t∗= arg min

tX

l∈BS

I(E{NU(t, l)}> mu), (20)

where muis the threshold of the minimum number of

user to declare that a BS lis active.

IV. PERFORMANCE EVALUATION

In this section, a real-life simulation is presented to

illustrate the relationship between the human mobility

and the optimization objective, which is searching for a

time segment with the minimum number of active cells.

A. Setup

1) Location: A small town located in Thuwal,

Makkah Province, Saudi Arabia, is considered in the

simulation. It is a moderate density living compound that

facilitates both working and living environment. In the

simulation, there are about 2000 townhouses and 80 two-

story apartment buildings. Each townhouse populates a

family or 3-8 people and an apartment building populates

Fig. 1. The simulation area with buildings in the following coloring,

green: townhouses, cyan: apartment buildings, blue: university campus,

magenta: recreational and dining areas, yellow: primary and secondary

schools. 45 base stations with their name and sectors are shown. The

black straight and dotted color lines are the cell boundaries.

about 20-40 people. In the compound, the university

campus is the major working area for the residents and

three schools for primary and secondary school students.

Furthermore, there are six buildings for recreation, din-

ing, and shopping. For the mobile network, it is a typical

hexagonal cell deployment with about 540 meters inter-

BS distance. There are 45 BSs are deployed in the

simulation area and named as a 4-digit number from

1001 to 1045. Each BS consists of three 120 degree

sectors and each sector is considered as a cell with a

5-digit number name. The sector name is constructed by

extended one more digit from the BS name to the right

most digit, such as 10011(northeast), 10022(southeast),

and 10033(west) for three sectors of BS 1001. In total,

135 cells are deployed in the 9.57 km2simulation area.

A map of the simulation with the BS deployment and

cell boundaries is shown in Figure 1.

2) Mobility: In the simulation, a daily life of a user

is modeled with random locations and durations. The

Day 1

12AM

Day 2

12AM

Day 3

12AM

Day 4

12AM

Day 5

12AM

0

200

400

600

800

Number of Mobile Nodes

Number of users of Group 1 in each cell

10011

10053

10063

10143

10183

(a) Staff

Day 1

12AM

Day 2

12AM

Day 3

12AM

Day 4

12AM

Day 5

12AM

0

200

400

600

800

1000

Number of Mobile Nodes

Number of users of Group 2 in each cell

10011

10053

10063

10143

10183

(b) School Students

Day 1

12AM

Day 2

12AM

Day 3

12AM

Day 4

12AM

Day 5

12AM

0

50

100

150

200

250

300

Number of Mobile Nodes

Number of users of Group 3 in each cell

10011

10053

10063

10143

10183

(c) University Students

Day 1

12AM

Day 2

12AM

Day 3

12AM

Day 4

12AM

Day 5

12AM

0

20

40

60

80

100

120

Number of Mobile Nodes

Number of users of Group 4 in each cell

10011

10053

10063

10143

10183

(d) Dependents

Fig. 2. Number of users of each group in ﬁve selected cells

model ﬁrst randomly selects a home and a work location

for certain user. These locations are static for a user

throughout the simulation period. Then, the durations

of staying are randomly generated following various

truncated normal distributions. Furthermore, a user has a

certain probability of visiting different recreational and

dining places. Four groups of mobile users with different

daily mobility patterns employed in the simulation are

described in the following.

Staff: A model for the movements of ofﬁce staff

is adopted for 2200 users. There are 75% of users

live in townhouses and 25% of users live in apartment

buildings. Their ofﬁce locations are static and randomly

chosen in university campus buildings. The daily mobil-

ity patterns start by staying at home at the midnight until

morning. Then, users start moving to ofﬁces and stay

until lunch hours. After an average one-hour lunch break,

users go back to ofﬁces until evening. A percentage of

people will go to the recreational and dining areas after

work. Finally, users return to home in the evening.

School Students: This group includes 1400 primary

and secondary school students who live in townhouses.

Starting at midnight, the mobility of this user group is

similar to the others, staying at home until morning.

At 7am-7:30am, all of the school students go either to

the primary or secondary school areas and stay until

3-3:30pm. After school, school students start to travel

around the community actively. In the evening, they

return to home. This group of users are signiﬁcantly

synchronized to travel and stay in the school period.

University Students: There are 900 university students

live in apartment buildings. The mobility patterns start

from the midnight, while most of the university students

stay in apartments until morning. In the morning and

afternoon, university students move between the campus

buildings and stay for classes and activities. In the

evening, students may go to recreational and dining areas

or go home. The major difference between adult staff

and university students is that university students have

the higher mobility to move inside the campus and a

shorter average staying period.

Dependents: There are 1700 dependents in the sim-

ulation. They have a ﬁxed home location but without

a ﬁxed working location. Their staying locations and

durations are more random and unpredictable than the

other groups. In general, the mobility patterns start from

midnight while users stay at home, until morning. Then

users travel and stay randomly in the area.

B. Results

These four user groups have distinct mobility patterns.

From the mobile network operator perspective, these

movements generate various daily periodic patterns re-

garding the number of users in each cell. For instance,

the cells covering the university campus area has a

larger number of users in working hours. The cells

covering primary and secondary schools have a signif-

icant decrease in users after the school hours. Figure 2

shows the number of users of each user group in the

ﬁve selected cells over a ﬁve-days simulation period.

Each cell covers a particular type of buildings. Cell

10011 covers two schools and some staff housing. Cell

10053 covers apartment buildings only, where mostly

occupied by university students and a few staff. Cell

10063 covers staff housings only. Cell 10143 covers

half of the university campus and the campus diner.

Cell 10183 covers a recreational and dining building.

In Figure 2a, the number of staff increases steadily in

Cell 10143 starting in the morning and reaches the peak

roughly at noon on a daily basis. Furthermore, Cell

10183 shows two peaks are observed daily. The ﬁrst

lower peak is the lunch hours and the second peak is

the evening time before midnight when the people are

seeking for recreation or dining. In Figure 2b, the Cell

10011, where the secondary school located, shows a

signiﬁcant sharp increase of school students from no

users to over 900 users during the school hours. In

Figure 2c, Cell 10143 and 10183 have similar patterns

observed in the staff, but with a different number of

users. In the Cell 10053, which cover one-fourth of

the university student apartments, the peak numbers of

university students appear in the night daily. In Figure

2d, the dependents have no static locations to travel or

stay. Therefore, the numbers of users in Cell 10053 and

10063 are chaotic. However, the cells covering the dining

area, Cell 10143 and 10183, have distinct daily patterns

as described in Figure 2a. Figure 3 shows the aggregated

number of users in these ﬁve selected cells. It clearly

Day 1

12AM

Day 2

12AM

Day 3

12AM

Day 4

12AM

Day 5

12AM

0

200

400

600

800

1000

1200

Number of users

Number of users in each cell

10011

10053

10063

10143

10183

Fig. 3. Number of total users in ﬁve selected cells

Day 1

12AM

Day 2

12AM

Day 3

12AM

Day 4

12AM

Day 5

12AM

0

10

20

30

40

50

60

70

Number of active cells

Number of active cells

Staff School S. University S. Dependents All Users

Fig. 4. Number of active cells

shows each cell has different periodic patterns and peak

hours according to its coverage area.

Recall that the period of having the minimum number

of active cells is the best timing for broadcasting contents

to the user groups regarding using the minimum radio

resources. In Figure 4, the numbers of active cells for

each user group are illustrated. Three phenomena can

be observed in this ﬁgure. First, in most of the time, the

average number of active cells for staff, school students,

and dependents are ranged from 55 to 62, but the

university students have a lower number of active cells

compare to the others. It is because those three groups of

users are mainly living in the low-density housing area.

When users go home in the evening, they spread evenly

over a large area. For the university students, they live

in the higher density apartment buildings and this area

is located closely to the campus buildings. In general,

they are more congregated in the evening and moves

within a closer area than the other users. Therefore, the

average number of active cells of university students is

less than the others. Second, the periods of having the

minimum number of active cells for the school students

are longer than the other groups. School students arrive

at the school on time and stay in the school for several

hours every day. It is easier to look for a time segment

for delivering contents to school students in the school

area. However, although the minimum number of active

cells for staff is relatively small compare to its average, it

has only a short period in a day to achieve the minimum.

In contrast, the university students have a longer period

on maintaining the minimum number of active cells

in the early morning when students are mainly in the

apartments. Finally, since the mobility patterns of depen-

dents group were mostly random, the minimum number

of active cells of dependents are large comparing to

other groups. In summary, among these four user groups,

searching a time segment for broadcasting content to the

school students are relatively easier than the other users,

and consuming the minimum amount of radio resources.

V. CONCLUSION

In this paper, we conduct a comprehensive analysis

on the human activity mobility model tied with an

efﬁcient content broadcasting system in 5G networks.

The analysis was conducted by using the concept of

random events and associated conditional probabilities. It

shows the relationship between the human mobility and

the optimization objective of the content broadcasting

system. A real-life simulation is presented to indicate

the connection further. In the future, it is essential to

evaluate the time complexity of the statistical analysis

to investigate the cost of predicting an optimal solution

for the delivery system.

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