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                    Master’s Thesis

Optimizing Allocation and Handover Processes in
Mobile Networks

Geymerson dos Santos Ramos
geymerson@ic.ufal.br

Advisors:
Dr. André Luiz Lins de Aquino
Dr. Rian Gabriel Santos Pinheiro

Maceió
October 27, 2021

Geymerson dos Santos Ramos

Optimizing Allocation and Handover Processes in
Mobile Networks

A thesis submitted by Geymerson dos Santos Ramos
in partial fulfillment of the requirements for the degree
of Master of Science in Informatics at the Federal University of Alagoas, Computing Institute.

Advisers:

Dr. André Luiz Lins de Aquino
Dr. Rian Gabriel Santos Pinheiro

Maceió
October 27, 2021

A thesis submitted by Geymerson dos Santos Ramos in partial fulfillment of the requirements for the degree of Master of Science in Informatics at the Federal University of Alagoas,
Computing Institute, approved by the examination committee which signs bellow.

Dr. André Luiz Lins de Aquino - Adviser
Computing Institute
Federal University of Alagoas

Dr. Rian Gabriel Santos Pinheiro - Co-Adviser
Computing Institute
Federal University of Alagoas

Dr. Alexandre Mendes - Committee Member
School of Information and Physical Sciences
University of Newcastle

Dr. Erick de Andrade Barboza - Committee Member
Computing Institute
Federal University of Alagoas

Dr. Marilia Pascoal Curado - Committee Member
Department of Informatics Engineering
University of Coimbra

Maceió
October 27, 2021

Catalogação na Fonte
Universidade Federal de Alagoas
Biblioteca Central
Divisão de Tratamento Técnico
Bibliotecário: Marcelino de Carvalho Freitas Neto – CRB-4 - 1767
R175o

Ramos, Geymerson dos Santos.
Optimizing allocation and hadover processes in mobile networks /
Geymerson dos Santos Ramos. – 2021.
49 f. : il.
Orientador: André Luiz Lins de Aquino e Rian Gabriel Santos
Pinheiro.
Dissertação (mestrado em Informática) - Universidade Federal de
Alagoas. Instituto de Computação. Maceió, 2021.
Bibliografia: f. 44-49.
1. Redes móveis. 2. Alocação de usuários. 3. Otimização de processos. 4.
Handover. 5. Redes locais sem fio. I. Título.
CDU: 004.72

UNIVERSIDADE FEDERAL DE ALAGOAS/UFAL
Programa de Pós-Graduação em Informática – PPGI
Instituto de Computação/UFAL
Campus A. C. Simões BR 104-Norte Km 14 BL 12 Tabuleiro do Martins
Maceió/AL - Brasil CEP: 57.072-970 | Telefone: (082) 3214-1401

Folha de Aprovação
GEYMERSON DOS SANTOS RAMOS
OTIMIZAÇÃO DE PROCESSOS DE ALOCAÇÃO E HANDOVER EM REDES
MÓVEIS

Dissertação submetida ao corpo docente do Programa
de Pós-Graduação em Informática da Universidade
Federal de Alagoas e aprovada em 27 de outubro de
2021.
Banca Examinadora:

________________________________________
Prof. Dr. ANDRE LUIZ LINS DE AQUINO
UFAL – Instituto de Computação
Orientador

__________________________________________
Prof. Dr. ERICK DE ANDRADE BARBOZA
UFAL – Instituto de Computação
Examinador Interno

__________________________________________
Prof. Dr. RIAN GABRIEL SANTOS PINHEIRO
UFAL – Instituto de Computação
Coorientador

________________________________________
Prof. Dr. ALEXANDRE MENDES
Examinador Externo

________________________________________
Prof. Dra. MARILIA PASCOAL CURADO
Examinador Externo

Acknowledgement

Kill the boy, Jon Snow [...]. Kill the boy and let the man be born.

– Aemon Targaryen to Jon

Snow (George R.R. Martin, A Dance with Dragons).

For the last months, I have been fighting against emotions that I can only describe as anxiety
due to fear of change. This work should have been done a long time ago. The plan for the past
two years was simple: Before leaving home, I wanted to create my financial protection for study
expenses, help my parents with their house renovation, present my thesis, and start a Ph.D. But
then, the pandemic hit. I am feeling very compelled not to write about the covid-19, but it has
inflicted massive pain and distress for people. I can not ignore the context in which this work is
being conceived. I am a very fortunate person, for all my family made it through and is doing
well. My friends are healthy, and I am also healthy... physically. The pandemic brought us dread
and isolation. Doubt and uncertainty slowly infiltered me over time.
My plans seemed to make no sense anymore, something from a distant reality. The world
was closed, and I was worried about the growing disconnection with my peers, my eagerness
for learning, and the feeling of overcoming obstacles. Helplessness everywhere and idleness
through the day. These were the gates to the transition to the void, and I needed to get out of
there. Fortunately, I achieved most of my initial goals and took the time to make amends with
myself. Things seem to be in motion again, and I still have some work in progress.
It is 1:56 am, and I need to end this monologue and go to sleep. But not before expressing
my gratitude to Professor Rian Pinheiro, which I only met at the end of my undergraduate course
but proved to be very important through the following years. And once again, thank you too,
Professor André Aquino, the man who will not let me lose sight of my goals. Gratitude to my
parents Cícera and Sandro, who raised and supported me to be who I am. There is no point in
postponing it further. I recognize that there is apprehension, almost fear. Fear of the path that
I need to follow. Fear of cutting the cord. It seems like it is time to go. May the light guide me
through my journey, may my will be reforged from steel to gold. Let the change embrace me. Kill
the boy.
Digna Factis Recipimus.
– Luke 23:41

iii

Resumo
O número crescente de dispositivos conectados à Internet tem exigido avanços em tecnologias
de comunicação sem fio. A rede 4G e suas antecessoras estão sendo gradativamente substituídas pela 5G, que promete maior velocidade, heterogeneidade e escalabilidade. A 5ª geração
oferece suporte amplo para aplicações de redes definidas por software, aumentando a flexibilidade para modelagem de processos e protocolos que antes eram embarcados e de difícil
atualização.
Este trabalho tem como objetivo melhorar processos em redes móveis através de modelos
matemáticos, que podem impactar mobilidade, balanceamento de carga na rede e redução
de custos operacionais. Nossa proposta visa a alocação de usuários em torres ou estações
bases de redes de telecomunicação, minimizando handovers e melhorando a qualidade de
comunicação.
O trabalho oferece as seguintes contribuições: i) Um modelo matemático para alocação de
usuários em estações bases de redes de telefonia móvel, com a redução de transferências;
ii) Uma solução meta-heurística como alternativa a modelos exatos, visto que estes podem
se tornar inviáveis em condições de restrição de recursos de tempo e computacionais; iii) A
avaliação dos modelos em cenários simulados de mobilidade, avaliando o processo de handover
e a distribuição de usuários na rede em função de largura de banda disponível.
A modelagem, que considera a frequência média de handover de cada estação base e o
sinal indicador de qualidade de comunicação, foi avaliada com soluções exatas e heurísticas,
sendo estas o algoritmo de branch and bound, busca local iterativa, e solução gulosa. Através
dos métodos heurísticos o algoritmo de busca local iterativa obteve uma redução de aproximadamente 82% do tempo de execução em comparação ao algoritmo exato branch and bound.
Com relação ao indicador de qualidade de conexão, a solução obteve um ganho médio de 1.45%
em comparação à solução da literatura, mantendo o número handovers. Apesar do ganho reduzido, o que torna nossa proposta estatisticamente equivalente, oferecemos a vantagem de
não computar todas possíveis e futuras rotas dos usuários, sendo suficiente a posição atual.
Adicionalmente, nossa solução considera a capacidade de largura de banda de cada estação
base, respeitando a capacidade de rede e mantendo o controle de alocação.
Palavras-chave: Redes Móveis, Alocação, Otimização, Handover.

iv

Abstract
The growing number of devices connected to the Internet has required advances in wireless
communication technologies. As a result, 5G networks gradually replace 4G and its predecessors, offering more speed, heterogeneity, and scalability. The fifth-generation provides broad
support for software-defined networking (SDN) applications, increasing the programming flexibility of processes and protocols previously embedded and difficult to update.
This work aims to improve processes in mobile networks through mathematical models. Our
work focuses on optimizing the allocation of users in base stations of telecommunication networks, minimizing the handover of users between base stations, and improving network communication quality.
The contributions of this work are: i) A mathematical model for allocating users of mobile
networks at base stations, also aiming handover reduction; ii) A metaheuristic solution as an alternative to exact models since exact models can prove to be non-scalable and present unfeasible solving times under computationally restricted conditions; iii) A model evaluation in simulated
mobility scenarios considering the handover process and the network user distribution according
to available bandwidth.
Our allocation model considers the average handover frequency of each base station and
the Reference Signal Received Quality (RSRQ) indicator between users and base stations. The
model evaluation used exact and heuristic methods: the branch and bound algorithm, iterated
local search, and a greedy solution. On average, the iterated local search algorithm obtained
an execution time reduction of approximately 82% compared to the branch and bound exact algorithm. Regarding the RSRQ indicator, the solution reached a 1.45% average gain, and the
number of performed handovers was maintained, compared to a similar literature model. Despite the modest improvement, which makes our proposal statistically equivalent to the literature
model, we offer the advantage of not predicting the users’ possible and future routes. Only the
current position is required. Furthermore, our solution also considers base stations’ bandwidth
capacity, controlling the allocation and network occupation limits.

Keywords: Mobile Networks, Allocation, Optimization, Handover.

v

Contents
Abbreviation List

vii

Figure List

ix

Table List

x

Algorithm List

xi

1

INTRODUCTION

1

2

TECHNOLOGIES AND CONCEPTS
2.1 Mobile networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Handover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Linear programming and simplex method . . . . . . . . . . . . . . . . .
2.3.2 Branch and bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Iterated local search . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.4 Variable neighborhood descent . . . . . . . . . . . . . . . . . . . . . . .
2.3.5 Generalized assignment problem . . . . . . . . . . . . . . . . . . . . . .

5
5
9
10
11
13
15
16
17

3

METHODOLOGY
3.1 Handover and communication cost optimization . . . . . . . . . . . . . . . . . .
3.2 Proposed model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19
19
21

4

RESULTS AND DISCUSSION
4.1 Performance of ILP formulation . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Heuristic performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Simulation of the proposed model . . . . . . . . . . . . . . . . . . . . . . . . .

29
29
34
37

5

FINAL CONSIDERATIONS
5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42
42
43

REFERENCES

44

vi

Abbreviation List
CAGR

Compound Annual Growth Rate

D2D

Device-to-Device

DC

Data Center

eNB

evolved Node B

EPS

Evolved Packet System

GAP

Generalized Assignment Problem

GPS

Global Positioning System

GRASP

Greedy Randomized Adaptive Search Procedure

HSS

Home Subscriber Server

ILP

Integer Linear Programming

ILS

Iterated Local Search

IoT

Internet of Things

LTE

Long Term Evolution

LP

Linear Programming

LPP

Linear Programming Problem

LPWA

Low-Power Wide-Area

M2M

Machine-to-Machine

MBS

Macro Base Station

MME

Mobile Management Entity

PDN-GW Packet Data Network Gateway
RAT

Radio Access Technology

RSRP

Reference Signal Received Power

RSRQ

Reference Signal Received Quality

RSSI

Received Signal Strength Indication

SBS

Small Base Station

SDN

Software-Defined Networking

S-GW

Serving Gateway
vii

Abbreviation List

SUMO

Simulation of Urban MObility

UE

User Equipment

VND

Variable Neighborhood Descent

viii

List of Figures
1.1 Handover example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Global projections for the number of network connections . . . . . . . . . . . . .
2.2 5G network architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Intra macro-cell, inter macro-cell and multi-RAT handover. . . . . . . . . . . . .
2.4 The relation between problem classes and complexity. . . . . . . . . . . . . . .
2.5 The simplex execution process. . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 The branch and bound tree . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7 Expected ILS perturbation result. . . . . . . . . . . . . . . . . . . . . . . . . .
2.8 Attribution of jobs to agents according to costs, a general assignment problem. .
3.1 EPS architecture for LTE networks. . . . . . . . . . . . . . . . . . . . . . . . .
3.2 An example of an UE moving along a set of eNBs. . . . . . . . . . . . . . . . .
3.3 Simulation flowchart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 The two neighborhood structures for swap and insertion operations. . . . . . . .
4.1 Path Traveled by the User . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 eNB in which the UE was allocated over the travel time. . . . . . . . . . . . . . .
4.3 eNBi in which UE1 is allocated according to its position. . . . . . . . . . . . . .
4.4 Number of connected UEs in each eNB over time. . . . . . . . . . . . . . . . .
4.5 Available bandwidth in each eNB at instant t. . . . . . . . . . . . . . . . . . . .
4.6 Network occupation levels for different max capacity limits per eNB. . . . . . . .
4.7 Experiment’s eNBs positions at the city of São Paulo, Brazil. . . . . . . . . . . .
4.8 UE simulated route generate with SUMO. . . . . . . . . . . . . . . . . . . . . .
4.9 User allocation through the route. . . . . . . . . . . . . . . . . . . . . . . . . .
4.10 UE’s allocation eNBs for each model. . . . . . . . . . . . . . . . . . . . . . . .
4.11 User’s RSRQ connection value through the route. . . . . . . . . . . . . . . . . .
4.12 Boxplot of the average RSRQ value for 100 random instances of eNB placement.

ix

2
6
7
10
11
13
14
16
17
20
21
23
26
31
31
32
33
33
36
37
38
39
39
40
40

List of Tables
2.1
2.2
3.1
4.1
4.2
4.3
4.4

Comparative of the different generations of wireless communication technology. .
Base station range and users capacity per cell type . . . . . . . . . . . . . . . .
LTE signal quality indicators. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Distance model’s average execution time . . . . . . . . . . . . . . . . . . . . .
The number of UEs and eNBs according to the instance type. . . . . . . . . . .
Overall execution time results. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Exact and heuristic models result. . . . . . . . . . . . . . . . . . . . . . . . . .

x

6
8
24
30
34
35
35

List of Algorithms
2.1
2.2
3.1
3.2

General iterated local search . . . . . . . . . . . . . . . . . . . . . . . . . . . .
General variable neighborhood descent . . . . . . . . . . . . . . . . . . . . . .
Iterated local search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Variable neighborhood descent . . . . . . . . . . . . . . . . . . . . . . . . . .

xi

15
16
26
27

1
INTRODUCTION
The evolution of communication technologies has significantly impacted protocols and data
transfer solutions. With the arrival of the Internet of Things (IoT) (Al-Fuqaha et al., 2015)
paradigm, devices are becoming more integrated, and Wireless Networks (Akyildiz et al., 2002)
are showing to be essential resources. Through devices such as smartphones, users can communicate from practically anywhere, make use of location services, and exchange information
with technologies such as Wi-Fi, Bluetooth, 3G, 4G, and the most recent 5G (Panwar et al.,
2016). The fifth-generation promises more incredible speeds, ubiquitous connection, support to
denser, heterogeneous, and scalable networks. Among the fundamentals pillars of 5G networks,
we highlight:

• Uninterrupted and ubiquitous connection: Users will able to connect from anywhere at
any time;

• Zero-latency: Granted support to real-time applications, critical systems, and services
with low tolerance to network delay;

• High-speed connections: Support to applications that rely on virtually zero latency. The
connection speed will be in the order of Gigabit per second.
The new scenario offers the opportunity for innovation, improvement of existing solutions, and
the use of new computational paradigms, such as Software-Defined Networking (SDN) (Nunes
et al., 2014), which allows flexible programming and management of resources such as scalability, privacy, security, traffic control, and allocation. In the current state of mobile wireless networks, the 5G technology will demand applications to be faster, more efficient, heterogeneous,
and scalable.
Existing solutions will require improvement or rethinking to a zero-latency context. The handover process is one of the many problems that we can approach and propose several improvements. Figure 1.1 shows a handover process (Yan et al., 2010). It occurs when a user connected to some device (UE — User Equipment) changes its base station (here represented by
1

INTRODUCTION

2

the evolved Node B — eNB). This process can affect mobility, connection discontinuity perception, and commutation between different wireless communication technologies such as Wi-Fi,
4G, or Bluetooth. Therefore, handovers need to occur imperceptibly, within short time intervals,
and in areas that do not negatively affect mobility and connectivity experience.

Coverage Area 1

Coverage Area 2

eNB1

eNB2

UE

MOVEMENT

Figure 1.1: Handover of UE from eNB1 within coverage area 1 to eNB2 in the coverage area 2.
Our work is motivated by the current state of mobile networks, which is transitioning to a
technology (5G) with a growing adoption of optimization models run through SDN applications,
which consider a logically centralized controller to execute models that dynamically optimize,
manage, and improve network features such as mobility and load distribution.
Using mathematical models, we aim to optimize the handover and allocation of users in base
stations of telecommunication networks. As a starting point, our proposal extends a model that
minimizes both handovers between base stations and the communication cost between base
stations and data centers (Taleb et al., 2015). The authors did not consider the direct relation
user-base station, so we extended their model by proposing an optimization solution to allocate
users. We later compare our proposal to a similar literature model (Ahmadi et al., 2020). We do
not evaluate our solution in wireless SDN controllers, but it is appliable in this context.
The resulting allocation model first considered the average handover frequency of each base
station and their distance from users. However, since we deal with wireless communication, the
distance parameter can be non-responsive to noise and environment interference. We updated
the allocation model by replacing the distance parameter with the RSRQ (Reference Signal Received Quality), which indicates the quality of communication between users and base stations.
We evaluate the allocation models in two simulated mobility scenarios. The first considers
a 13.7 km route at Maceió City, Brazil, with eNBs artificially placed. The distance-based model
computes the distance and allocates the user in base stations according to the latitude and
longitude of GPS (Global Positioning System) collected data. In the second scenario, we use
a heuristic approach to solve the model instead of an exact algorithm, and modify the model to
consider the RSRQ indicator instead of distance. We use a map region of the city of São Paulo,
Brazil. The map region has the real position of 26 eNBs from a local phone carrier, provided by

INTRODUCTION

3

Telebrasil (2021), and we simulate the user routes with the SUMO (Simulation of Urban MObility)
simulator (Krajzewicz et al., 2012).
In our final evaluations, on average, the iterated local search algorithm obtained an execution
time reduction of approximately 82% compared to the branch and bound exact algorithm. Comparing results with Ahmadi et al. (2020) in the second scenario, the RSRQ indicator reached a
1.45% average gain, and the models performed the same number of handovers.
We found in the literature several related works about the topic of this work. For instance,
Kuklinski et al. (2015) present a discussion on how to apply technologies such as SDN to increase the efficiency of mobile networks. They consider the handover process according to 3
architectures: i) centralized: uses one controller; ii) semi-centralized: multiple controllers acting
on different domains or geographic regions; iii) hierarchical: multiple layers and a master controller on the top of the hierarchy that communicates with other controllers on the lower levels.
Prados-Garzon et al. (2016) propose a handover implementation for a partially virtualized
LTE (Long Term Evolution) networks. The authors implemented the process’s message exchange, simulated the transmission delays, propagation, network processing, and handover finalization.
Lee and Yoo (2017) present a 5G handover scheme considering users’ mobility information.
The controller receives mobility data and base station information to select in which cell to allocate the users. They observed that the proposal could select the cells that offer greater signal
strength and fit the user’s movement direction through simulation.
Qiang et al. (2016) discuss a solution to a handover multi-objective problem for hybrid 5G
environments. The authors consider maximizing the data receiving rate and minimizing the
probability of handover process failure. The probability is calculated based on other users of the
network and limited information (due to privacy restrictions). In a previous work (Qiang et al.,
2014), a controller executes this process using private information.
Duan and Wang (2015) proposal focuses on privacy and authentication tools for 5G SDN
heterogeneous networks handover processes. Authentication uses attributes such as location,
direction, and features of the physical network layer to generate unique identifiers. Cryptography
is not required, thus simplifying the authentication process.
This work will mainly contribute with the following aspects:

• Proposition of a mathematical allocation model to allocate users in base stations of mobile
networks;

• Proposition and evaluation of heuristic solving methods to the allocation model as an alternative to exact solving approaches;

• Evaluation of allocation on different mobility simulations, one of which considers the real
position of base stations from a local mobile carrier;

• A evaluation and comparison of our model with existing literature work.

INTRODUCTION

4

Additionally, some results of our proposal have already been published and are available
(Ramos et al., 2019b,a).
The remainder of this work is structured as follows: Chapter 2 presents general concepts
on mobile networks, handover and optimization. Chapter 3 shows the proposal, which contains
description of our allocation models, mainly the distance-based model, the RSRQ allocation
model, and the heuristic solution. Next, Chapter 4 discusses the results. Finally, Chapter 5
presents the final considerations and future work.

This chapter briefly introduced relevant topics such as mobile networks and what is the
handover process. We also discussed objectives, related literature, and contributions
of this work.

2
TECHNOLOGIES AND CONCEPTS

This chapter presents the concepts and technologies related to our work. In Section 2.1, we
will discuss wireless technologies such as 5G and its predecessors. Section 2.2 presents an
overview of handover processes. We end the chapter with Section 2.3 discussing optimization,
mainly the algorithms and methods which contribute to the understanding of our proposal.

2.1

Mobile networks

The number of connected devices is increasing, and due to the aggressive volume of data, we
also observed the surging of new computational paradigms, such as Cloud Computing (Mell and
Grance, 2010) and Big Data (Chen et al., 2014), to redesign data storage and analysis. Wireless
communication technologies, which also should support applications in this new panorama, have
found themselves in a hostile scenario against dense, heterogeneous, and high connectivity
demands.
In such a scenario, the 5th-generation introduces itself to mobile communication. The 5G
networks will allow the deployment of computational paradigms that will help the expansion of
information and communication technologies, which are very important for Smart Cities (Mohanty et al., 2016). If compared to the 4th-generation, we can list the following improvements:
100 times more connected devices; 1000 times more data volume from connected devices; 100
times faster; 1-millisecond latency; almost 100% coverage; information processing in real-time
and reduced energy consumption (GSMA Intelligence, 2014). In addition, the fifth generation is
coming to significantly reduce operational infrastructure costs by offering ubiquitous connection,
scalability, heterogeneity, and software solutions.
Table 2.1 shows a comparison of the five generations of mobile technologies. 1G mostly offered voice communication support through analog signals. Handover solutions were precarious
and horizontal, which means transfers between access points did not happen between different

5

TECHNOLOGIES AND CONCEPTS

6

communication technologies (e.g., 1G and 2G). Besides slow speed, the first generation had severe security problems because of the reproduction of conversations in the base stations, which
made them susceptible to external access (Vora, 2015). 2G technology surpassed the previous generation’s speed, adopted digital signals, images, and text messages. Its obsolescence
became apparent as the Internet and the dissemination of multimedia data gained popularity,
starting the 3G era.
Table 2.1: Comparative of the different generations of wireless communication technology.
Generation

Features

Speed

Latency (ms)

Handover

Limitations

1G
2G

Analog signals, voice message
Digital signal, voice messaging, text e images
Voice message,
Access to home and mobile Internet,
Video calls

< 2.4 Kbps
< 64 Kbps

< 1000

Horizontal
Horizontal

Low security
weak support to Internet service

< 3.1 Mbps

< 500

Horizontal
and Vertical

Slow speed

3G
4G

Greater speed connection

< 300 Mbps

< 100

5G

Ubiquitous connection and high speed,
scalability, heterogeneous

> 1 Gbps

<1

Horizontal
and Vertical
Horizontal
and Vertical

Low scalability and connectivity,
support to dense networks
-

In the 3G era, the connections’ speed reached the megabit per second order, and the Internet
gained access through cell phones. As a result, multimedia streaming services increased significantly. Besides the horizontal approach, we found a new vertical architecture regarding handover
processes, which allowed transfers between different wireless communication technologies (e.
g. 3G to 2G). The following demands incurred on the network’s speed, which resulted in the development of the 4G. Since then, the fourth generation became the main access option, reaching
theoretical speeds of 300 Mpbs.
According to CISCO’s annual internet report (CISCO, 2020) shown in Figure 2.1(a), the
number of 4G network users will surpass the previous generation after 2019. The projection
estimates that the fourth generation will correspond to 46.0% of connections by the year 2023.
The figure also includes LPWA connections (Low-Power Wide-Area), essential in M2M commu-

(a) Global mobile device and connection growth.

Billions of Mobile
Subscribers

Billions of Devices
or Connections

nication (Machine-to-Machine).

(b) Global mobile subscriber growth.

Figure 2.1: Global projection for the number of devices and connections according to network
type and for the global number of mobile subscribers. Adapted from (CISCO, 2020).
Figure 2.1(b) shows the growth and projection of mobile subscribers between 2018 and 2023

TECHNOLOGIES AND CONCEPTS

7

with a 2% CAGR (Compound Annual Growth Rate). These increasing numbers put pressure on
the infrastructure of 4G networks, already being replaced by the upcoming technology, which is
5G.
Compared with its predecessor, the fifth generation is not simply a speed increase. It is
a redefinition in applications, efficient use of resources, models, and architectures to support
data loads and various devices with different radio communication technologies. It will support
heterogeneous frameworks with software-defined networks, D2D (Device-to-Device), and fullduplex radio communication (Panwar et al., 2016). Figure 2.2 illustrates an example of the
plurality that 5G network architectures can achieve. This figure also represents a multi-layered
architecture.
Industry
SBS

Hospital
SBS

Home
SBS

MBS

Vehicular
Network
D2D
Communication

Direct
Communication

Mobile
Cell

MACRO CELL
Figure 2.2: 5G network architecture composed of a macro cell, which contains stationary and
mobile small cells, direct and D2D communication.
In this architecture, a macro cell with an MBS (Macro Base Station) in the upper layer receives requests from the lower layers, divided into small cells containing SBS (Small Base Stations) for different application profiles. For example, in a small mobile cell, its occupants can
access the external network through an SBS attached to the bus, which communicates with the
MBS of the macrocell. In addition, mobile devices such as smartphones can communicate directly with the MBS or create small dynamic D2D communication cells, in which only some of
these devices connect to the MBS while the others transmit requests and responses.
SBS can be installed in diverse environments such as homes, hospitals, and industries,
constituting different natures of applications and small cells. Depending on the radius range and
number of users, cells can be distinguished as presented in Table 2.2.
The use of small cells increases macro cells range, and it also:

• Increases transfer rates: A local SBS, which communicates with an MBS, serves better the indoor devices reducing the signal attenuation effects that would occur in direct
communication between MBS and devices;

TECHNOLOGIES AND CONCEPTS

8

Table 2.2: Range and total users capacity according to cell types. Adapted from Panwar et al.
(2016)

Range
Users

Femtocell

Picocell

Microcell

Macrocell

10 - 20 m
< 20

200 m
20 - 40

2 km
> 100

30 - 35 km
Many

• Improves the use of the radio communication spectrum: There are fewer devices in
direct communication with MBS;

• Increases energy efficiency: Communication intermediated by an SBS reduces the required range for data transmission, which significantly impacts the battery usage of the
devices;

• Reduces cost: An SBS has lower installation and operating costs if compared to an MBS.
We can mention the optimized use of computational and energy resources among the problems to be addressed by the fifth generation. Base stations operate at peak periods in the
existing mobile phone networks, and their processing power is only for connected users. Energy consumption for peak or near-inactivity times is similar (Correia et al., 2010), increasing the
network’s operating costs.
Base stations in commercial areas get overloaded during the daytime, while residential areas
have little activity (Wu et al., 2015). The scenario reverses for different day times. Instead of being restricted to connected users, we can achieve better usage and load-balancing by distributing
idle computing resources.
Also, there are solutions for the redundant use of two channels (operating at different frequencies) for communicating with base stations. The devices have a channel transferring data
(uplink) to the base station and another transfer channel in the opposite direction (downlink).
This practice is considered inefficient. 5G networks present full-duplex communication using a
single channel for sending and receiving data, with no co-interference.
Until now, mobile network architectures have not distinguished between indoor and outdoor
users. As a result, devices communicate directly with the base stations, regardless of location,
which implies severe attenuation and loss of signal quality if walls or obstacles surround the user.
The fifth-generation introduces the SBS as a bridge between users and MBS, allowing indoor
and outdoor distinction and improving transmission quality.
As for heterogeneous wireless networks (Damnjanovic et al., 2011), Bluetooth, 3G, and WiFi, 5G’s solution framework proposes significant contributions. 4G technology already provides
some support, but not as a primary purpose since a device can only connect the uplink and
downlink channels to the same base station.
The fifth-generation must implement decoupling, allowing users to have the channels associated with different base stations. According to Boccardi et al. (2016), decoupling reduces

TECHNOLOGIES AND CONCEPTS

9

required transmission power, interference, achieves higher transmission rates, reduces costs,
and differentiates load balancing for uplink and downlink channels.
Mobility and handover processes also require attention because transfers between different
wireless technologies have become common nowadays. When moving between commercial
and residential areas, users’ connection must be sustained, with no perception of discontinuity
or drop in transfer rates. 5G solutions must guarantee user services, even in high mobility
scenarios with speeds of up to 500 km/h (Zhang et al., 2017).
It is noticeable that mobile wireless networks are converging for a highly connected ecosystem, in which users seamlessly transit between environments and communication technologies.
We aim to contribute to this integrated ecosystem by improving the allocation and connection
transitioning processes, namely handovers. In our experiments, we will consider simulated scenarios of mobility in which users are transferred regularly between base stations. As long as
the technology can provide the input data, our model will calculate which base station offers the
best service. We do not distinguish wireless cell types (small or macro) or base stations, but our
solution ensures that each eNB has enough bandwidth for the requiring users.

2.2

Handover

The handover process is the transferring of a user connected to one access point to another.
In general, we divided the process into 3 phases: preparation, execution, and completion. The
preparation includes the analysis of a series of user information, such as position, services
consumed, possible future routes, neighboring access points, and provided services’ quality.
The information allows the best access points to be selected. Different solutions apply machine learning techniques as auxiliary selecting tools (Al et al., 2016). In the execution phase, the
solutions use messages for synchronization and recognition elements involved in the handover
process: users, access points, and upper-level entities that generally coordinate the process.
The types of handover can also vary. In 5G networks, it is possible to execute transfer
between two SBS belonging to the same macro cell, between different macrocells, and even to
another type of radio communication technology, as shown in Figure 2.3. If the base stations
are in the same macro cell, the handover is an intra-macro cell. This process is the case of a
transfer between SBS1 and SBS2. When transferring from SBS2 to SBS3, the device migrates
to another cell and performs an inter-macro cell handover. When the device disconnects from
the 5G network towers to another type of communication technology, such as 4G, we have the
multi-RAT (Radio Access Technology) handover.
Intra-macro cell transfers have a lower cost when compared to inter-macro cells because only
SBSs are involved in the process. However, at the inter-macro cell level, not only do SBSs need
to be analyzed, but MBSs are also involved, and this consequently increases the complexity of
handover, which can become even more costly for multi-RAT transfers.

TECHNOLOGIES AND CONCEPTS

10

MBS1 (5G)

MBS2 (5G)

BS (4G)
SBS2

SBS1

Intra macro-cell
handover

SBS3

Inter macro-cell
handover

MACRO CELL 1

multi-RAT
handover

MACRO CELL 2

Figure 2.3: Intra macro-cell, inter macro-cell and multi-RAT handover.
Considering that we have the required data, such as user and base station location, the
list of allowed eNBs, RSRQ values, etc., our model determines the most suited or the best
allocation. There is no need to know eNBs technology types (multi-RAT handover) or handover
level (intra-cell or inter-cell). Knowing and handling different types of wireless technologies, the
management, preparation, and execution phases is a task of the network entity (such as an SDN
controller) which executes our allocation model.

2.3

Optimization

The urge to increase efficiency, or more specifically, optimize a process, seems only natural after
the discovery or creation stage. Our cognitive capacity and math domain has led us to maximize
gains and minimize costs, such that optimization became a whole study field. When proposing
an efficient solution to a problem, one must consider the most relevant variables, correlations,
and constraints.
Different classes of problems require distinct computational effort to solve. Figure 2.4 shows
a Venn diagram of the classes and their solving difficulty in regards to P . If we consider the
input size n of a given problem p ∈ P and some constant k, then p is solvable with a polynomialtime complexity O (nk ) (Cormen et al., 2009, chapter 34). There is no known efficient solution
for the problems in the N P -hard class, and P 6= N P or P = N P is an assumption yet to be
proven. Garey and Johnson (1979) provides a more detailed discussion of the problem classes
and NP-Completeness.
We can achieve optimization through exact or heuristic methods. Exact methods are guaranteed to find an optimal solution, while heuristic methods are more flexible, fine-tuned, and
specific to a given problem. It can find solutions that may not be global optima, but good enough
if we consider the available resources. Metaheuristics, similarly to heuristics, do not guarantee
a globally optimal solution but are more general solving problem frameworks.

TECHNOLOGIES AND CONCEPTS

11

The following topics of this section discuss relevant algorithms to this work, such as the
simplex method, the generalized assignment algorithm, branch and bound, and iterated local
search.

P

NP

NP-Complete

EASY

MEDIUM

HARD

NP-HARD

HARDEST

DIFFICULTY
Figure 2.4: The relation between problem classes and complexity.

2.3.1

Linear programming and simplex method

The Simplex Algorithm solves Linear Programming Problems (LPP), widely found in real-world
industry and business models. Linear optimization models play a major role in minimizing processes’ expenses and maximizing gain. The general structure of an LPP contains three important components:
1. Decision Variables: It is a set of controllable, continuous, and non-negative values. Such
variables guide the decisions and courses of action of an optimization model. For example,
the employees of a factory and their respective tasks can be considered decision variables
in an optimization model that aims to maximize the number of tasks per employee.
2. Objective function: It is a mathematical function containing a set of constants and the
decision variables. Depending on the problem, the optimal value of this function can represent the minimum cost, maximum profit, and best efficiency.
3. Constraints: It is a set of mathematical expressions that limits the number of valid solutions. For example, a business analyst may create an objective function that models profit
according to available resources and produced products. As a constraint, the available
budget only allows the purchase of a limited number of resources. This process limits the
number of produced products and maximum profit.
Equation (2.1) (Sharma, 2017, chapter 2) defines the relationship between these three main
components. Z is the objective function that we aim to maximize or minimize, c j is the cost or
profit value associated with the decision variable x j . The input-output coefficient (or technological

TECHNOLOGIES AND CONCEPTS

12

coefficients) of the constraints’ inequations are represented by ai j , and bi establishes lower or
upper bounds for each constraint inequation. All the decision variables must be greater than
zero (non-negativity condition).

Objective function (min or max) Z = c1 x1 + c2 x2 + ... + cn xn

(2.1)

subject to

(2.2)

a11 x1 + a12 x2 + ... + a1n xn (≤, =, ≥) b1

(2.3)

a21 x1 + a22 x2 + ... + a2n xn (≤, =, ≥) b2

(2.4)

..
.

..
.

..
.

am1 x1 + am2 x2 + ... + amn xn (≤, =, ≥) bm
with x1 , x2 , ..., xn ≥ 0

(2.5)
(2.6)

Dantzig (1990) proposed the simplex method, used to solve general LP problems. Thus,
when we consider n decision variables, the simplex method has exponential performance and
visits O (2n ) vertices in the worst-case scenario (Klee and Minty, 1972), but Spielman and Teng
(2004) showed that the algorithm had expected polynomial behavior for most of the real-world
linear problems.
In mathematics, a simplex is an object connecting n + 1 points in an n-dimensional space, if
we consider the dimension D = 1, the simplex is a line segment connecting 2 points (Sharma,
2017, ch 4, p. 101). Considering the LP defined in (2.1)—(2.6), and its linear problem standard
form definition (2.7)—(2.9), the simplex method can find global optima by iterating between a
finite set of vertices, provided by the intersection of the problem’s constrains (2.8).

max Z = cT x

(2.7)

subject to Ax = b

(2.8)

x≥0

(2.9)

The gray area in Figure 2.5 represents the problem’s feasible region, and the intersection red
dots are the primary feasible solution vertices. In each iteration step, the algorithm evaluates the
objective function (2.7) according to the current vertex and then visits the next one until it finds
the optimal basic feasible solution.
Through Integer Linear Programming (ILP), we can model and solve integer linear problems,
which belong to the N P -hard problem class. A typical integer linear problem has the standard
form of Equation (2.10)–(2.13), and as established by (2.13), each of its variables have integer

TECHNOLOGIES AND CONCEPTS

13

Figure 2.5: The simplex execution process.
values. There are classic and well-established algorithms to solve integer linear problems, such
as the branch and bound (Lawler and Wood, 1966), branch and cut (Padberg and Rinaldi, 1987),
and the cutting-plane method (Kelley, 1960).

2.3.2

max Z = cT x

(2.10)

subject to Ax = b

(2.11)

x≥0

(2.12)

x∈Z

(2.13)

Branch and bound

The Branch and Bound algorithm is an exact method for solving integer problems, proposed by
Land and Doig (2010). It has application in many classic optimization problems, such as the
traveling salesman problem (Applegate et al., 2006), the generalized assignment problem (Ross
and Soland, 1975), and the knapsack problem (Kolesar, 1967). The branch and bound algorithm
organizes the search method as a tree. Thus, it creates a source node split into subproblems
connected to the source. As an example, we can consider the general linear problem (2.14)
(a simplified form of Equation (2.1)), in which x is a decision variable vector and the set of
constraints presented in Expression (2.15).

TECHNOLOGIES AND CONCEPTS

14

max cT x

(2.14)

subject to Ax ≤ b

(2.15)

x∈Z

(2.16)

The method starts by solving the linear programming relaxation of an instance of the problem
defined in Equation (2.14)–(2.15), i.e., we remove the integrality constraint of each variable. We
test if the solution x∗ is composed of integer values. If x∗ contains any fractional value, it is not
a valid solution, and the algorithm selects a non-integer variable x∗j ∈ x∗ to generate two new
00

0

variables β (floor, greatest integer less than x∗j ) and β (ceiling, the smallest integer greater than

x∗j ), as established by Equation (2.17). We use these values to create the new subproblem’s
branches, as defined by Equations (2.18)—(2.19).

0

00

(β , β ) = (bx∗j c, dx∗j e)

(2.17)
0

max cT x subject to

Ax ≤ β , x in S

max cT x subject to

00

Ax ≥ β , x in S

Figure 2.6: The branch and bound tree (Applegate et al., 2006).

(2.18)
(2.19)

TECHNOLOGIES AND CONCEPTS

15

In Figure 2.6, problem (2.14) represents the root node as initial state of the algorithm, followed by the branching subproblems (2.18) and (2.19). Each branch and bound tree node has
a value for the objective function, according to its x variables. The algorithm decides if it is worth
expanding new nodes by evaluating the objective function value and checking if x∗ contains any
fractional value. We achieve a final solution if there is no feasible solution or if x∗ for a given tree
node is integer only and contains the best value for the objective function. We use the branch
and bound algorithm to find optimal solutions for the simulated mobility scenarios.

2.3.3

Iterated local search

The Iterated Local Search (ILS) is a sequence of solutions built iteratively by an embedded
heuristic. (Lourenço et al., 2019). In its history, it received many names and propositions (Baxter, 1981; Martin et al., 1991; Martin and Otto, 1996), and the demand for new approaches
for different surging problems continues to push the efficiency boundaries through evolutionary
optimization (Cao et al., 2018).
Algorithm 2.1 describes the general framework of the iterated local search. The procedure is
simple and starts by generating the initial solution S0 from the starting instance I . In the following
step, the algorithm performs a local search to obtain a new solution S, stores it in S∗ , which
is an improvement S0 . Thus, the local search method aims to find better solutions by making
calculated adjustments in the current input instance.
Algorithm 2.1 General iterated local search
1: procedure ILS(I, maxIter)
2:
S0 ←Initialize(I)
3:
S ←Local_Search(S0 )
4:
S∗ ← S
5:
iter ← 0
6:
while iter < maxIter do
7:
S0 ←Perturbate(S)
8:
S0 ←Local_Search(S0 )
9:
Accept(S, S0 )
10:
Update_Best_Solution(S, S∗ )
11:
iter ← iter + 1
12:
end while
13:
return S∗
14: end procedure

The loop structure updates the number of performed iterations iter to avoid exceeding the
maximum limit maxIter. The iterations repeat a series of perturbations, local searches, and
cost checks to provide the best result as the final output. Since the iterative process is prone
to get trapped in local maximum or minimum values, the perturbation function Perturbate can
randomly change the current solution variables. As the expected result 2.7, the algorithm steers
0

0

the solution away from local optima. The acceptance function Accept(S, S ) compares S and S ,
allowing that the function Update_Best_Solution(S, S∗ ) update their current values to the new

TECHNOLOGIES AND CONCEPTS

16

0

best if cost(S ) < cost(S).

Cost

Perturbation

Solution Space S

Figure 2.7: Expected ILS perturbation result.

2.3.4

Variable neighborhood descent

The Variable Neighborhood Descent (VND) (Mladenović and Hansen, 1997) is one of the most
used and efficient local search algorithms.

In the context of our work, we implement the

Local_Search(S0 ) with the VND Algorithm 2.2, which seeks the best solution through a search
of sorted neighborhood sets. Considering V = {V 1 , . . . ,V r } a set of neighborhoods of the graph
G, the VND starts V . Starting from k = 1 until a max of kmax iterations, the algorithm looks for
neighborhood sets that reduce a defined cost g∗ of the graph G. As long as it is possible to find
a neighborhood G0 with a lower cost, which we will consider as the solution S, the algorithm will
try to find better neighborhoods, and if not possible, we move on to the next neighborhood k + 1.
We will use the VND as the local search of the ILS Algorithm 3.1, this combination presents
successful cases in the literature (Penna et al., 2011).
Algorithm 2.2 General variable neighborhood descent
1: procedure VND(G)
2:
start V
3:
k←1
4:
g∗ ← Cost(G)
5:
repeat
6:
G0 ← V k (G)
7:
if Cost(G0 ) < g∗ then
8:
S ← G0
9:
k←1
10:
else
11:
k ← k+1
12:
end if
13:
until k = kmax
14:
return S
15: end procedure

TECHNOLOGIES AND CONCEPTS

2.3.5

17

Generalized assignment problem

We will reserve some time to discuss the GAP (Generalized Assignment Problem) (Cattrysse
and Van Wassenhove, 1992), as shown in Figure 2.8, as our proposition can be defined as one
of its specific case. This problem is part of the N P -hard complexity class (Sahni and Gonzalez,
1976), and is generally defined according to Equation (2.20). The value of ci j represents the
cost of assigning a job j ∈ J to the agent i ∈ I . The variable xi j indicates if i receives the job

j, and in this case xi j = 1. If the job j is not assigned to the agent, then xi j = 0. In Figure
2.8, which is a complete bipartite graph, the jobs J = {1, 2, ..., m} are assigned to the agents I =
{1, 2, ..., n} according to the blue colored edges. Each job is assigned to at least one agent, and
there is a occurrence of one agent (i = 1) with more than one job.

(GAP) min

∑ ∑ ci j xi j
i

subject to

(2.20)

j

∑ ai j xi j ≤ bi

∀i∈I

(2.21)

∑ xi j = 1

∀ j∈J

(2.22)

∀ i ∈ I, ∀ j ∈ J

(2.23)

j

i

xi j ∈ B

The assignments aim to minimize the overall costs of an objective function by performing
multiple combinations. The solution must satisfy conditions such as the Knapsack (Salkin and
De Kluyver, 1975) set of constraints (2.21), and the restriction that each job must be assigned
for at least one agent in this particular case (2.22). Each agent has an individual level of effort
or capacity ai j to offer, and if a job exceeds this effort level, we must assign it to another agent.
Considering the set of agents I , the sum of their capacity must not exceed the established max
capacity bi .

...

2

1
Agents
c

c
c
c

Jobs
1

2

3

...

Figure 2.8: Attribution of jobs to agents according to costs, a general assignment problem.

TECHNOLOGIES AND CONCEPTS

18

In real-life scenarios, the GAP appears in different ways, such as creating efficient schedules for workers or building timetables for teachers and classes. It also has variations such
as the multilevel, the nonlinear capacity constrained, and the bottleneck GAP (Öncan, 2007).
Literature has extensive documentation and solution, and the most classical approaches propose approximation methods (Shmoys and Tardos, 1993), and lower/upper bound manipulation
through the branch and bound algorithm (Ross and Soland, 1975). Modern approaches usually
propose minor changes to the classic algorithms, hybrid solutions, or genetic and evolutionary
based-solutions (Srivarapongse and Pijitbanjong, 2019; Jia et al., 2018).
We will see in Chapter 3 that our allocation models, defined in Equations (3.8) and (3.19),
have the same standard form of the GAP (2.20). Similarly to assigning jobs to agents, our model
allocates (assigns) users to base stations according to a set of constraints. Each user must
connect to at least one base station, and each base station can receive as many users as its
maximum bandwidth capacity allows.

This chapter introduced key concepts related to this work. In Section 2.1, we discussed the advances in mobile networks technologies, which are mainly transitioning
to the fifth-generation. By allocating users in base stations, our contribution impacts
mobile networks and their handover processes mentioned in Section 2.2. In regards
to optimization, our solution can be deployed by using some of the exact or heuristic
methods discussed in Section 2.3.

3
METHODOLOGY

In this chapter, we introduce Taleb et al. (2015) optimization model in Section 3.1. The authors
propose a multi-objective function to minimize handovers between eNBs, and the communication
cost between eNBs and data centers. Their work is a starting point for our proposal, which extends their model. In Section 3.2, we present our contribution by first showing a distance-based
allocation model, followed by the heuristic solution 3.2. We change to a heuristic approach as
an alternative to the exact method and consider the RSRQ (Reference Signal Received Quality) indicator instead of distance. The RSRQ informs the quality of the wireless communication
between UEs and eNBs.

3.1

Handover and communication cost optimization

Based on the Multi-Objective model of Taleb et al. (2015), our proposal aims to improve the
mobility and connection in wireless networks. The authors consider the EPS (Evolved Packet
System) architecture (Figure 3.1). The S-GW (Serving Gateway) is responsible for routing packages, mobility management, and handover processes. The HSS (Home Subscriber Server)
saves identification and location of UEs, and it also has authentication and authorization functionalities. The PDN-GW (Packet Data Network Gateway) bridges networks (the Internet) containing
several data centers and entities such as the eNBs and UEs. The MME (Mobile Management
Entity) contains UE’s mobility management functionalities and location information, interacting
with the HSS entity to execute authentication. The eNBs connect UEs with the rest of the network.
Taleb et al. (2015) work establishes a model to minimize the communication cost between
eNBs and data centers and a model that minimizes UE’s handover between coverage areas.
These two models compose a multi-objective optimization problem. The authors consider an
SDN context with virtual network infrastructure, in which the S-GW and the PDN-GW have virtual

19

METHODOLOGY

20

Figure 3.1: EPS architecture for LTE networks.
function sets allocated for distinct entities depending on the user’s demand and behavior. In the
communication cost minimization problem, a solution is to allocate the virtual functionalities of
the PDN in the data centers of the nearby eNBs. To minimize handovers, the authors place
virtual functions of S-GW in more distant regions, creating more significant coverage areas.
Considering a set of eNBs = {i1 , i2 , ..., iN−1 , iN }, where N is the total base stations, and a
set of data centers = {s1 , s2 , ..., sDC−1 , sDC } containing a total of DC data centers, Taleb et al.
(2015) complete model is defined as follows:

min ( f (hi j , xi j ), g(cis , yis ))

(3.1)

subject to yis + y js ≤ 1 + xi j

∀ i, j ∈ N, ∀ s ∈ DC

(3.2)

yis − y js ≤ 1 − xi j

∀ i, j ∈ N, ∀ s ∈ DC

(3.3)

∑ yis = 1

∀i∈N

(3.4)

yis , xi j ∈ B

∀ i, j ∈ N, ∀ s ∈ DC

(3.5)

s∈DC

The y js variable is equal to 1 if eNB j is connected to the data center s, and 0 otherwise.
The multi-objective function (3.1) uses two criteria f and g. The constraints (3.2) states that
two eNBs must not connect to the same data center, which means (xi j = 0) =⇒ (yis = 0) ∨

(y js = 0). Constraints (3.3) states that two connected eNBs must not be connected to different
data centers, which implies (xi j = 1) =⇒ (yis = y js ). According to (3.4), every eNB must be
connected to only one data center, and the variables yis and xi j belong to the binary domain, as
we can see in (3.5).
The objective functions f e g are respectively defined by (3.6) for handover and (3.7) for
cost. The values of hi j represent the average handover frequency between eNBi and eNB j .
Base stations connected to the same data center belong to the same coverage area, and in such
cases, there is no handover between the eNBs. The values of cis represent the communication
cost between the eNBi and the data center s. The purpose of the objective function (3.7) is to
select an eNBsi near a data centers s of the set DC, assuring the smaller communication cost.

METHODOLOGY

21

f (hi j , xi j ) = min ∑ ∑ hi j (1 − xi j )

(3.6)

g(cis , yis ) = min ∑ ∑ cis yis

(3.7)

i∈N j∈N

i∈N s∈DC

Since Taleb et al. (2015) model (3.1) did not consider the allocation of UEs in eNBs, our
proposal extends the current model by implementing it. The proposed model allocates users in
base stations by using distance, average handover frequency for each eNB, and the bandwidth
requirements of UEs and eNBs. It is worth mentioning that the handover and cost criteria f
and g have opposite natures since to decrease handover between coverage areas, we need to
increase the distance between eNBs and data centers to create more significant coverage areas.
On the other hand, we need to reduce this distance to reduce the communication cost between
eNBs and data centers. As a consequence, we need to find the ideal exchange between these
two objectives. We can use multi-objective optimization approaches (Marler and Arora, 2004).

3.2

Proposed model

We introduce the allocation of UEs in eNBs, which can occur according to available bandwidth,
distance, and each eNBs’ handover average. Figure 3.2 illustrates an example that is not covered
in Taleb et al. (2015). In this example scenario, composed of 5 eNBs, horizontally spaced by 50
units of distance, consider the max bandwidth capacity Li = 20 Mbps for each eNBi . Each user
UEk has a minimum bandwidth requirement lk = 3 Mbps. Therefore, each eNBs can not support
service to more than six users simultaneously. We recalculate the solution dynamically when the
UE moves between eNBs.

Figure 3.2: An example of an UE moving along a set of eNBs.
For such a scenario, we can apply the new objective function defined by (3.8). Notice that
our allocation model has the GAP (2.20) standard form. We will use this property to evaluate
the results of the heuristic method presented in Subsection 3.2. The variable bki , if its value
is equal to 1, maps a UEk that is connected to an eNBi , and if they are not connected, bki =
0. Equation (3.8) establishes that the users connect to nearby base stations with the smallest
handover average hi .

METHODOLOGY

22

min

z(bki , dki , hi ) = ∑ ∑ bki (dki + hi )

(3.8)

k∈U i∈N

Equation (3.9) gives the formula for calculating hi , which can be found with the sum of the
average handover frequency hi j for each eNBs j ∈ N , connected to eNBi , divided by N − 1 (we
remove eNBi from N ). The value of dki represents the distance between UEk and eNBi .

hi =

hi j
(N − 1)
j∈N\{i}

∑

∀i∈N

(3.9)

The model constraints are given by (3.10) — (3.12). We establish in (3.10) that every user
must be connected to only one base station. By constraints (3.11), the max bandwidth capacity

Li of a base station i must not exceed the sum of the bandwidth minimum requirements lk for
each user k ∈ U . The binary domain of bki if defined in (3.12).

∑ bki = 1

∀ k ∈U

(3.10)

∑ lk bki ≤ Li

∀i∈N

(3.11)

∀i∈N

(3.12)

i∈N

k∈U

bki ∈ B

To find the value of dki in a Cartesian coordinate systems, we use Equation (3.13). Therefore,

dki = dcart is the Euclidean distance between UEk at position pk = (xk , yk , zk ), and eNBi at position pi = (xi , yi , zi ). To geographic coordinate systems, dki = dharv , according to the Haversine
formula (3.14) to spherical surfaces (Sinnott, 1984). In this case, (ψi , βi ) represents respectively
eNBi ’s latitude and longitude. In the same way, (ψk , βk ) is UEk ’s latitude and longitude. The
Earth is our sphere, and R is its radius, which is approximately 6317 Km.

q
dcart = (xi − xk )2 + (yi − yk )2 + (zi − zk )2
s



!
ψ
−
ψ
β
−
β
i
i
k
k
dharv = (2R) arcsin
sin2
+ cos (ψk ) cos (ψi ) sin2
2
2

(3.13)
(3.14)

Equations of handover (3.6), cost (3.7), and user allocation (3.8) are used as criteria in a
Multi-Objective Function (COMP). We will use the weighted sum method described by Equation
(3.16) and (3.17). This approach provides a multi to mono-objective conversion for a set with m

METHODOLOGY

23

optimization criteria, in which each Fi criterion will be weighted by a value wi ∈ [0, 1]. The sum
of all the criterion weights must be equal to 1. Varying the value of wi means assigning different
importance to a specific objective function. If w2 = 0.6, then g(cis , yis ) has a greater contribution
for worsening the optimal solution of (COMP). As a consequence, smaller values of cis will be
required, which means that we are prioritizing communication cost minimization. The complete
proposed formulation is given by:

(COMP) : min ob j = w1 × f (hi j , xi j ) + w2 × g(cis , yis ) + w3 × z(bki , dki , hi )

(3.15)

subject to (3.2 − 3.5) and (3.10 − 3.12)

m

∑ wiFi(x)

(3.16)

∑ wi = 1

(3.17)

i=1
m

i=1

We could execute the complete formulation (COMP) in network entities such as the mobile
manage entity presented in Figure 3.1. If we consider an SDN context, a controller executes the
model and distributes virtual network functions of PDN-GW and S-GW according to results. This
strategy should create coverage areas with reduced handovers, minimum communication cost
between eNBs and data centers, and the allocation of UEs in the best candidate eNB. We must
connect every user to one base station, keeping network bandwidth limits. When executed, the
model must run periodically, collecting and updating information about eNBs and UEs.
Read UE, eNB and
DC input data

Update UEs
position

Execute Model

Create coverage
area with best
handover and
communication cost

No

No

END

YES

Stop
Simulation?

Handover
required?

YES

Update UEs and
eNBs Data

Allocate UE in new
eNB

Figure 3.3: Simulation flowchart.
We can implement this model in the linear programming solver CPLEX (IBM, 2017), which
uses the branch and bound exact method. The simulation process follows Figure 3.3, starting by

METHODOLOGY

24

reading the eNBs’ handover average, position, and bandwidth requirements for UEs and eNBs.
It proceeds with reading updates of UEs’ position and execution of (COMP).
As a result, (COMP) provides a set of coverage areas connecting the eNBs with minimum
handover frequency. These eNBs connect to the data centers with lower communication costs.
If handover is required, the model allocates users to a new eNB and proceeds to update users’
and eNBs data. If the simulation does not end, we read UE’s position data to restart the process.

Heuristic approach
Our previous user allocation model defined in Equation (3.8) allocates UEs based on the distance and the eNB individual handover frequency average. However, due to noise and physical
environment interference, the distance may not be the best indicator for connection quality. We
can improve this model by considering indicators such as the Received Signal Strength Indication (RSSI), the Reference Signal Received Quality (RSRQ), or the Reference Signal Received
Power (RSRP).
The RSSI is an indicator of wireless signal strength. The RSRP presents the base station
average signal power perceived by the users. Finally, the RSRQ informs the received signals’
quality. It is a commonly used parameter in handover solutions since it contains information on
noise and interference levels. We will simulate the RSRQ value according to Equation (3.18), in
which the signal degrades with distance. For example, if we consider the RSRQ values in Table
3.1, the maximum transmission radius Ri of a given base station i, and the distance dki = Ri for
the user k, then Θki = −12 dB, which is a poor RSRQ value (dki = 0 =⇒ Θki = −5 dB).

Θki = −[

dki
(|Θmin | − |Θmax |) + |Θmax |]
Ri

(3.18)

Table 3.1 presents the signals’ quality classification according to their respective values. In
ideal conditions, users with poor signal reception are further away from the eNB or located at
cell edges. Excellent or good signal reception means that the user is closer to the base station.
Table 3.1: LTE signal quality indicators.
Signal Quality

RSSI (dBm)

RSRQ (dB)

RSRP (dB)

Excellent
Good
Fair
Poor

-65
-65 to -75
-75 to -85
-85

-5
-9 to -5
-12 to -9
-12

-84
-85 to -102
-103 to -111
-111

We will reformulate the user allocation model (3.8) to consider the average handover frequency hi of each eNB, and the RSRQ value Θki , which represents the communication quality

METHODOLOGY

25

between the user k and eNBi . The model p in Equation (3.19) allocates users in the eNBs with
the minor handover frequency average hi and with the best signal quality Θki .

min

p(bki , hi , Θki ) = ∑ ∑ bki (hi + Θki )

(3.19)

k∈U i∈N

subject to (3.10 − 3.12)

We will not consider Taleb et al. (2015) models in the next evaluations, but similarly to
(COMP), we can use the solving constraints and weighted sum method to define (COMP2).

(COMP2) : min

ob j = w1 × f (hi j , xi j ) + w2 × g(cis , yis ) + w3 × p(bki , hi , Θki )

(3.20)

subject to (3.2 − 3.5) and (3.10 − 3.12)
We will evaluate heuristic methods to solve our allocation model as an alternative to the
branch and bound exact algorithm. Heuristic approaches do not guarantee optimal results. However, there are scenarios in which the optimal solution exceeds the time limit or computational
resources are limited, so we have to use a solution sufficiently good that does not exceed hardware, software, or time limitations.
Our heuristic method uses the iterated local search (ILS) metaheuristic (Lourenço et al.,
2019) coupled with the variable neighborhood descent (VND) (Hansen et al., 2018) in the local
search phase. Also, to complement the search algorithms, two neighborhood structures are
defined to execute swap and insertion operations: swap_ue(UEui , UEv j ), and insert_ue(UEui ,
eNB j ). These structures can only be executed if the model constraints are obeyed.

• swap_ue(UEui , UEv j ): This neighborhood structure swaps a user UEu , allocated in eNBi ,
with a user UEv , allocated in eNB j , as shown in Figure 3.4(a). This procedure stops
the local search at the first swap that improves the current solution. It has a worst case
complexity O (n2 ) for a instance with n users.

• insert_ue(UEui , eNB j ): This neighborhood structure removes a user UEu , allocated in
eNBi , and inserts (or allocates) it in eNB j . Figure 3.4(b) illustrates an example of a insert
operation between two eNBs. This procedure stops the local search at the first insertion
that improves the current solution. It has a worst case complexity O (nm) for a instance
with n UEs and m eNBs .
The cost improvement evaluations of the insertion and swap neighborhood structures take

O (1) complexity. Algorithm 3.1 presents the iterated local search. Starting from a graph G that
will represent our network, an initial solution S0 is generated with a greedy algorithm (Cormen

METHODOLOGY

26

eNBi

eNBj

eNBi

eNBj

SWAP
UEu

UEu

UEv

UEv

(a) User swap neighborhood structure.
eNBi

eNBj

eNBi

eNBj

INSERT
UEu

UEu

(b) User insert neighborhood structure.

Figure 3.4: The two neighborhood structures for swap and insertion operations.
et al., 2009, chapter 16), implemented in the function GenerateInitialSolution(G). This function
randomly selects UEs and allocates them in the eNB with minimum cost. The initial solution S0
represents users connected to eNBs. Upon S0 , we use the VND based local search Algorithm
3.2 to find a new solution, denoted by S.
Algorithm 3.1 Iterated local search
1: procedure ILS(G)
2:
S0 ← GenerateInitialSolution(G)
3:
S ← LocalSearch(S0 )
4:
counter ← 0
5:
while !(stop condition) do
6:
S0 ← Perturbation(S)
7:
S0 ← LocalSearch(S0 )
8:
counter ← counter + 1
9:
if Cost(S0 ) ≤ Cost(S) then
10:
S ← S0
11:
else if counter ≥ n then
12:
counter ← 0
13:
S0 ← GenerateInitialSolution(G)
14:
end if
15:
end while
16:
return S
17: end procedure

The VND starts by setting the improvement index k and its maximum value kmax . There is
an improvement variable to indicate if any of the neighborhood structures found improvement
(returning true) at the current iteration and a flag that resets the k value in this situation. To pre-

METHODOLOGY

27

vent the algorithm from running indefinitely, we increment k each time a neighborhood structure
improvement fails (returning false). If the two neighborhood improvements fail, then k = 3, and
the VND algorithm ends.
Algorithm 3.2 Variable neighborhood descent
1: procedure VND
2:
k←1
3:
kmax ← 3
4:
improvement ← f alse
5:
f lag ← f alse
6:
repeat /*eNBs and UEs randomly chosen*/
7:
if k = 1 then
8:
f lag = insert _ue(UEui ,UEv j )
9:
end if
10:
if k = 2 then
11:
f lag = swap_ue(UEui , eNB j )
12:
end if
13:
if (flag) then /*Reset k if any neighborhood structure returns true (improvement found)*/
14:
k←1
15:
else
16:
k ← k+1
17:
end if
18:
until k = kmax
19:
return improvement
20: end procedure

The local search generates different solutions by performing the insert and swap operations
with the mentioned neighborhood structures. Subsequently, we enter the loop of the iterated
local search, which contains a perturbation function to avoid local minimums. Finally, from the
disturbed solution S0 , we execute a local search again. Considering that the global costs of the
networks S and S0 , if the condition Cost(S0 ) ≤ Cost(S) is satisfied, then S0 is assigned to S as a
new solution. The final result is a minimized cost in the relationships between users and base
stations.
In terms of allocation and handover, we can compare our proposed model of Equation (3.19)
with the solution proposed by Ahmadi et al. (2020). To allocate users, their model builds a base
station score rank, in which each eNB receives a score according to Equation (3.21). From
(3.22), if a user is approaching a given eNB and simultaneously the RSRQ value is improving,
then f actordirection = 1, and 0 otherwise. The f actordistratio depends on the user’s current
position and all possible future routes. The eNBs which cover most future routes receive the
highest scores. As for the RSRQ parameter, the better the signal, the better the score. All values
are normalized (0 to 1).

score = RSRQ + Factor prediction

(3.21)

Factor prediction = f actordirection + f actordistratio

(3.22)

METHODOLOGY

This chapter mainly discussed this work’s mathematical models. Taleb et al. (2015)
propose a handover and communication cost minimization model, which we discussed
in Section 3.1. As a contribution, we proposed an allocation model to address the
relation between users and base stations in Section 3.2. We refined our model by
considering parameters such as the RSRQ signal indicator and providing a heuristic
approach.

28

4
RESULTS AND DISCUSSION

This chapter presents the computational experiments conducted to evaluate the effectiveness
of our proposed approaches. The experiments are divided into three sections. First, in Section
4.1, we analyze the performance of the new ILP formulation applied in the simulation process
described in Figure 3.3. Second, in Section 4.2 we evaluate the quality of the solutions found by
the ILS metaheuristic. Finally, in Section 4.3, we conduct an extensive simulation, and compare
our proposal with Ahmadi et al. (2020) approach, considering allocation (RSRQ impact) and
handover.

4.1

Performance of ILP formulation

This experiment evaluates the proposed distance-based model (COMP), implemented with the
IBM ILOG CPLEX Optimization Studio v12.5.0 solver and executed on Intel Core i5-6200U
(2.30GHz and 4 cores) with 4GB of RAM, Ubuntu 16.04 LTS operating system.

Execution time
Table 4.1 shows the average execution time for different combinations of the weights w1 , w2
and w3 . For this test case, we considered 10 data centers and a sample of 60 base stations
in the city of Maceió, Alagoas, available in Telebrasil (2021) database, which has latitude and
longitude data of several base stations of different mobile carriers in Brazil. Ten users are randomly placed and maintained in positions near eNBs so that the model can calculate distances.
Since handover data and communication costs between data centers and eNBs are not available, we considered a random uniform distribution to generated 30 instances of these values for
each eNB. We compute the execution time for every instance, and in the end, we calculate the
average execution time for the different weight combinations.

29

RESULTS AND DISCUSSION

30

Table 4.1: Average execution time for different weights combinations. Total number of instances
= 30, eNBs = 60, data centers = 10, UEs = 10.
w1 w2 w3 Average execution time (seconds)
1
0
0
0.75
0
1
0
1.09
0
0
1
1.13
0.8 0.1 0.1
2.04
0.1 0.8 0.1
4.44
0.1 0.1 0.8
2.42
0.4 0.3 0.3
2.69
0.3 0.4 0.3
2.70
0.3 0.3 0.4
2.42
0.9 0.1
0
1.69
0.1 0.9
0
4.17
In the the formulation (COMP), the weight configurations (1, 0, 0), (0, 1, 0) and (0, 0, 1) verify the execution time in an isolated manner for f (xi j , hi j ), g(cis , yis ) and z(bki , dki , hi ), since
only one of the three criteria is considered. In a case of assigning higher priority to a specific
criterion, it is observable that the execution time increases considerably for the weights combination (0.1, 0.8, 0.1), which is when the costs of communication between eNBs and data centers
need to be strictly optimized. If an approximately uniform combination such as (0.4, 0.3, 0.3),

(0.3, 0.4, 0.3) or (0.3, 0.3, 0.4) is to be taken, the average execution times are similar. We can
verify Taleb et al. (2015) base model average execution time by making z(bki , dki , hi ) = 0, which
results in Equation (3.1). Configuration (0.1, 0.9, 0) shows that it takes longer to find an optimized solution to minimized communication costs with high priority, and low priority for reduced
number of handover between coverage areas. In the opposite case, (0.9, 0.1, 0), a considerable
smaller average execution time is required.

User allocation
We collected latitude and longitude data from the Google Maps location history of a moving UE.
Figure 4.1(a) shows the starting point of a 13.7 km displacement, traversed in a time interval of
42 minutes. The user followed the path from the starting point to the highest-numbered base
station (21 in total), some of them illustrated by Figure 4.1(b). In addition, we found several base
station locations in the database provided by Telebrasil (2021). In this study case, for every new
UE’s location, the model must evaluate if it is worth keeping it allocated in the same eNB or if it
is better to transfer it to another one. Haversine Equation (3.14) gives the distance between user
and base station in this scenario.
Figure 4.2 shows the eNBs where the system allocates the UE over the 13.7 km path. According to its GPS information, the initial UE position was nearby eNB1 and eNB2 , with respective
distances of 0.08 km and 0.45 km. The average handover of these base stations is 5.3 for the

RESULTS AND DISCUSSION

31

STARTING
POINT

(a) eNBs placement along the path traveled by UE. (b) eNBs in which the UE was allocated over the
path.

Figure 4.1: Path traveled by UE over time, moving forward from the starting point to the highestnumbered eNB.
first and 3.75 for the second. The formulation (COMP) allocates UEs in eNBs with the smallest
sum of distance and handover average. Thus, it is observable in Figure 4.2 the correct allocation
in eNB2 . During the last 10 minutes of the traveled path, eNB19 , eNB20 and eNB21 are closer, at
a respective distance of 0.78, 0.91, and 0.53 kilometers. Their handover averages are 3.8, 6.25,
5.5, which causes the permanence of UE in eNB19 .

Figure 4.2: eNB in which the UE was allocated over the travel time.

RESULTS AND DISCUSSION

32

Bandwidth management
To evaluate the model (COMP) bandwidth management, we simulated a second mobility scenario with 20 UEs and 5 eNBs. The bandwidth restrictions for eNBs and UEs are respectively

Li = 20 Mbps and lk = 3 Mbps (hypothetical values). The model does not have time as a direct
parameter, but the position (which influences the value of dki ) changes over time. In this test
case, UE’s position x is given by the function x = t , and t represents a time instant. As previously illustrated in the flowchart of Figure 3.3, the model is executed periodically, at an instant

t . Figure 4.3 shows the base station that the model allocates a user (namely UE1 ). From the
moment it becomes very costly to remain connected to a base station (because of distance or
eNB handover average), e. g., eNB1 , the system will transfer the user to another eNB, Fig 4.3.
The transition from eNB1 to eNB2 is performed near position x = 30.

Figure 4.3: eNBi in which UE1 is allocated according to its position.
The process repeats as UE1 moves towards other base stations. The remaining 19 UEs are
not moving so we can easily see the behavior of the network. The graphs in Figure 4.4 and 4.5
show respectively the number of UEs allocated and the available bandwidth in each eNB, which
changes as UE1 is transferred between eNBs. We can see in Figure 4.4 that eNB1 initially has
2 connected UEs. It is also known that UE1 has its position determined by x = t . Therefore, at

t = 0, UE1 is at x = 0 and allocated in eNB1 . Observing the bandwidth availability of eNB1 in
Figure 4.5 at t = 0, for 2 connected users with minimum requirements of 3 Mbps, it is verifiable
that the base station has only 14 Mbps, from a total L1 = 20 Mbps.
We can verify the rearrangement of the network as UE1 moves. As previously shown, the
transfer of eNB1 to eNB2 occurs approximately at x = 30. We can see the change in the number
of UEs in eNB1 (from 2 to 1) and eNB2 (from 3 to 4) in Figure 4.4 at t ≈ 30. The gain or loss of

RESULTS AND DISCUSSION

33

Figure 4.4: Number of connected UEs in each eNB over time.

Figure 4.5: Available bandwidth in each eNB at instant t.
available bandwidth is observable in Figure 4.5 at the same instant t . Since eNB4 and eNB5 are
always operating with 6 users, their bandwidth availability is low and insufficient to serve another
UE. However, when approaching these base stations, UE1 will certainly connect to them, as is
observable in Figure 4.4. This behavior is possible because even if operating in full capacity, the
network will rearrange UEs in different eNBs, ensuring a base station connection.

RESULTS AND DISCUSSION

4.2

34

Heuristic performance

In this section, we present the results for the allocation model (3.19) considering RSRQ and
the average handover frequency of each eNB. We will compare the results of the iterated local
search, and a GRASP algorithm. To validate the results, we executed an exact model with the
IBM ILOG CPLEX Optimization Studio V12.10, which provides the optimal solution through the
branch-and-bound algorithm.
We created the problem’s instances according to the standard GAP generation scheme (Chu
and Beasley, 1997). They are divided per difficulty and number of variables, being A the easy
instances, B moderate, and C presents the same difficulty as B, but with more variables. Table
4.2 presents the total number of UEs and eNBs in each instance.
Table 4.2: The number of UEs and eNBs according to the instance type.
Instance
1
2
3
4
5
6
1
2
3
4
5
6

Type

A/B

C

UEs Quantity

eNBs Quantity

100
100
100
200
200
200
1200
1200
1200
1500
1500
1500

5
10
20
5
10
20
5
10
20
5
10
20

Execution time
The algorithms were executed 30 times per instance on a computer with an Intel Core i7 @2.7
GHz x 4 processor, 16 GB of RAM, and the Ubuntu 18.04 LTS operating system. Table 4.3
summarizes the overall average execution time of the algorithms. The results presented in Table
4.4 contains the instances’ optimal value provided by the branch and bound exact model, the
average execution time of each solution, the best value achieved by the heuristic methods, the
number of times that the best value was found Nbests , and the average solution result.
The worst performing was the GRASP algorithm with a 3.38 s overall average execution time.
The ILS heuristic achieves the best performance, with an 11.09 ms overall average execution
time.
If we compare the average execution time of the exact model, 61.43 ms, with the ILS algorithm, there is a reduction in the average execution time by approximately 82%. Table 4.4 also

RESULTS AND DISCUSSION

35

Table 4.3: Overall execution time results.
Exact MD GRASP
Overall Average Time (ms)
61.43
3381.76

ILS
11.09

shows that the ILS algorithm found the optimal solution for every instance. Column Nb est indicates the number of times the instance evaluation and the algorithm found the optimal solution.
The GRASP solution presented the worst results, with an overall longer execution time when
compared to the ILS and exact model solution. Also, it barely found the instances’ optimal results.
Briefly discussing The GRASP algorithm, its general structure contains a greedy function that
starts by shuffling a list of users and base stations. We look for the base station that offers the
minimum allocation cost for each user, generating a solution.
We apply the local search algorithm to improve the results, store it to a temporary best
variable, and start the process again, looping until the algorithm reaches its time limit. The two
key aspects that impact the algorithm’s performance are the repeated generation of solutions per
iteration, and the susceptibility to local minimum, since there is no diversification of perturbation
mechanisms.

Table 4.4: The results for the exact, GRASP, and the ILS model.
Instance
1
2
3
4
5
6
1
2
3
4
5
6
1
2
3
4
5
6

Type

A

B

C

Exact MD
Optimal AVG Time (ms)
101.77
5.80
94.82
9.65
89.17
16.34
209.67
8.36
179.97
17.46
169.15
31.09
102.64
5.35
91.96
8.68
88.38
19.37
235.75
7.91
197.79
19.53
158.65
34.29
1221.85
47.87
1057.96
109.02
1020.05
237.66
1636.13
76.29
1397.8
143.22
1248.36
307.77

Best
101.77
94.87
89.21
209.67
180.04
169.24
102.64
91.96
88.40
235.75
197.87
158.74
1221.85
1057.96
1020.22
1636.13
1397.84
1248.59

GRASP
Average AVG Time (ms)
101.80
3.04
95.02
4.14
89.32
4.30
209.87
31.48
180.18
33.00
169.39
36.52
102.71
2.44
92.06
3.07
88.54
4.15
235.77
26.90
198.03
32.23
158.86
35.20
1221.88
5880.62
1058.10
7320.85
1020.41
7638.71
11998.06
1398.15
13146.96
1248.78
14670.06

Nbests
13/30
0
0
5/30
0
0
15/30
4/30
0
23/30
0
0
22
4
0
30/30
0
0

Best
101.77
94.82
89.17
209.67
179.97
169.15
102.64
91.96
88.38
235.75
197.79
158.65
1221.85
1057.96
1020.05
1636.13
1397.8
1248.36

Average
-

ILS
AVG Time (ms)
0.18
0.21
0.24
0.72
0.67
1.02
0.19
0.22
0.26
0.88
0.77
1.00
23.57
25.15
26.88
37.10
38.28
42.25

Nbests
30/30
30/30
30/30
30/30
30/30
30/30
30/30
30/30
30/30
30/30
30/30
30/30
30/30
30/30
30/30
30/30
30/30
30/30

RESULTS AND DISCUSSION

36

Bandwidth distribution evaluation
Evaluating new bandwidth management results, Figure 4.6 shows that as long as there is enough
network bandwidth 4.6(a), we can freely allocate the users to the eNB which provides the best
service. The network occupation rates are somewhat irregular. By decreasing the network available bandwidth per eNB while maintaining the same number of users and network requirements,
we can see the occupation levels tend to have a more uniform distribution, which is more explicit
in Figure 4.6(c). Under bandwidth restrained scenarios, the model will prioritize serving all the
network users as best as possible at the sacrifice of service quality since we will allocate the
users to secondary or tertiary transmission sources.

Max Bandwidth (5 Gbps)

Max Bandwidth (4 Gbps)

Occupied Bandwidth

100%

75%

50%

25%

75%

50%

25%

0%

0%
1

2

3

4

5

1

2

eNB

3

4

5

eNB

(a) 5 Gbps bandwidth maximum limit.

(b) 4 Gbps bandwidth maximum limit.
Max Bandwidth (3.3 Gbps)

100%
Occupied Bandwidth

Occupied Bandwidth

100%

75%

50%

25%

0%
1

2

3

4

5

eNB

(c) 3.3 Gbps bandwidth maximum limit.

Figure 4.6: Network occupation levels for different max capacity limits per eNB.

RESULTS AND DISCUSSION

4.3

37

Simulation of the proposed model

User allocation
In this section, we evaluate the user allocation provided by the ILS metaheuristic. The simulation process is similar to the flowchart presented in Figure 3.3, but this time we do not have the
coverage area creation and data center communication cost step. The evaluation of the allocation process considers the region of São Paulo city, Brazil, shown in Figure 4.7. This region
can be obtained through the OpenStreetMap (OSMF, 2021) website by informing the coordinates: latitudemin = -23.558, latitudemax = -23.5426, longitudemin = -46.642, longitudemax =
-46.6249. We can use this region’s perimeter data to extract a set of real eNBs positions from
the Telebrasil (2021) base station dataset. The simulation region has a 1947.65 m x 1878.95
m area and contains 26 eNBs from a local phone carrier. For our experiment, we will consider
a 300 meters transmission range, and the base stations are labeled from 0 to 25. We use the
SUMO (Simulation of Urban MObility) simulator to generate the route shown in Figure 4.8, which
has 432 positions. The UE starts at the bottom left and proceeds to the final destination at the
top right.
eNB12

eNB6

eNB16
eNB24

eNB19

eNB11
eNB10

eNB22

eNB21
eNB23

eNB15

eNB3

eNB4
eNB13

eNB14 eNB7
eNB25

eNB5

eNB17

eNB2

eNB9

eNB0

eNB18

eNB8

eNB1
eNB20

Figure 4.7: Experiment’s eNBs positions at the city of São Paulo, Brazil.

RESULTS AND DISCUSSION

38

Figure 4.8: UE simulated route generate with SUMO.
Figure 4.9 shows the eNBs in which we allocate the user throughout the route (highlighted
in green). We can see that the allocations are very similar, differing for a moment around the
time-step 200. Our model kept the UE connected for a longer time in eNB5 , but the number of
handovers had not changed as the final result. Each model performed 7 handovers if we discard
the initial allocation at eNB20 (the route starts at the bottom left).
The mobility simulation process reads one position per iteration until the final destination (top
right). The models receive the positions to compute the best candidate eNB. Both Ahmadi et al.
(2020) and our solution are affected by the RSRQ. The farther away, the worst the RSRQ value.
The eNB’s average handover frequency hi and the RSRQ value Θki (which is a function of the
distance that we compute with the UE’s current position) are enough for our allocation model to
compute the best candidate eNB, as established in Equation (3.19).
On the other hand, Ahmadi et al. (2020) proposal requires all the possible routes connecting a user’s current position and final destination to perform the allocation. For simplification
purposes, this simulation only considered the route of Figure 4.8 as the possible path, which is
a best-case scenario where we can calculate the ideal point as the route’s middle point, which
changes every time the current position is updated.
Figures 4.10(a) and 4.10(b) show respectively the allocation sequence for Ahmadi et al.
(2020) and our proposal, with the period of each allocation. As previously stated, our solution
maintained the user in eNB5 for a longer period. Each model performed 7 handovers, starting

RESULTS AND DISCUSSION

39

Allocation Model

Ahmadi et al

Our Proposal

25

eNB ID

20
15
10
5
0

100

200

300

400

Time step

Figure 4.9: User allocation through the route.
from eNB20 , proceeding to eNB8 and continuing until eNB19 .

eNB 20

eNB 20

eNB 8

eNB 8

eNB 25

eNB 25

eNB 5

eNB ID

eNB ID

eNB 5

eNB 2

eNB 2

eNB 3

eNB 3

eNB 13

eNB 13

eNB 19

0

100

200
Allocation period

300

(a) Ahmadi’s model

eNB 19

400

0

100

200
Allocation period

300

400

(b) Our proposal.

Figure 4.10: UE’s allocation eNBs for each model.
On the evaluation of other metrics besides the allocation and handover behavior, Figure 4.11
shows the user’s RSRQ status through the route. The closer to zero, the better. It is in our
interest to always choose the best RSRQ eNB to maintain the users’ connection quality. The
models’ results are mostly overlapped through the route, with short periods when our proposal
is better. We can now understand why we kept the user allocated in eNB5 for a more extended

RESULTS AND DISCUSSION

40

period around the 200 time-step mark since this eNB provides a better RSRQ.
Allocation Model

Ahmadi et al

Our Proposal

−5

RSRQ (dB)

−10

−15

−20

0

100

200

300

400

Time step

Figure 4.11: User’s RSRQ connection value through the route.
According to Figure 4.11, achieved better RSRQ results for short periods, but to investigate
further and reduce the influence of the eNBs position, we generated 100 instances with different
random eNBs placement. We consider the São Paulo map region of Figure 4.7, 26 eNBs, and
the same user’s travel route 4.8. For each instance, we save travel’s RSRQ time series and
calculate its average value.
-8

Average RSRQ (dB)

-10

-12

-14

-16
Ahmadi et al

Our proposal

Figure 4.12: Boxplot of the average RSRQ value for 100 random instances of eNB placement.

RESULTS AND DISCUSSION

41

Figure 4.12 presents the boxplot of the RSRQ averages for each placement instance. The
overall RSRQ average for Ahmadi’s and our proposal are -11.03 dB, and -10.87 dB, which gives
a 1.45% gain to our allocation model. The boxplot shows that the models produce very similar
solutions, and the two-sided Kolmogorov-Smirnov test considering a 5% significance provides pvalue = 0.3667 (> 0.05), which reinforces that the models are statistically equal. The advantage
of our solution is that our allocation considers the network’s bandwidth limits, and also, we do not
need to know or predict the users’ future routes. Instead, we require only the current position.
Ahmadi et al. (2020) rely on third-party applications to compute, for every network user, all
possible routes to reach the final destination. These routes are the inputs to calculate an ideal
point that aims to cover most paths, and the eNBs closer to the ideal point receive higher scores
than distant ones.
Realistically, this approach may face severe time response overhead due to third-party applications network delay. Furthermore, finding all the possible paths between two points is a

N P -hard problem (Chatterjee and Banerjee, 2014). Performing this operation for each user is
an expensive task.

This chapter presented the results of the allocation model. In Section 4.1, we evaluated the average execution time, user allocation, and bandwidth management for the
distance-based model solved with the branch and bound algorithm. In Section 4.2, we
discussed the results of our heuristic approach considering the RSRQ parameter. Similar to the previous evaluation, we observed the heuristic approach average execution
time, bandwidth management according to base station’s bandwidth occupation, and
allocation results were discussed in Section 4.3.

5
FINAL CONSIDERATIONS

5.1

Conclusion

The transition to the 5G generation brings new possibilities for improving application and models.
In this work, we presented a mathematical model to improve allocation and handover processes
considering users (UEs) and base stations (eNBs) of mobile networks. Our first proposal considered the shortest distance between base stations and users, the handover average, and
the bandwidth requirements. Since distance does not consider wireless communication factors
such as noise and environment interference, we replaced the distance parameter with the RSRQ
(Reference Signal Received Quality) indicator, which measures communication quality between
users and base stations.
As the main mobility simulation scenarios, we considered a 13.7 Km route at Maceió City,
Brazil. A user provides its current location at the route with GPS collected data. In the second
mobility scenario, we use a map region of the city of São Paulo, Brazil. The map region has the
real position of 26 eNBs from a local phone carrier, and we simulate the user routes with the
SUMO simulator.
We implemented the allocation models with a heuristic method and the CPLEX optimization
solver, which solves linear integer problems with the branch and bound algorithm, an exact
solution. In resource-constrained scenarios, exact algorithms might exceed the limits of available
resources. Heuristic approaches are better for these situations, and at the sacrifice of optimal
values for good enough solutions, we can obtain better resource management and faster-solving
methods.
On average, the iterated local search obtained an execution time reduction of approximately
82% compared to the branch and bound exact algorithm. The GRASP-based algorithm showed
the worst results due to its recurrent solution construction and lack of mechanisms to avoid local
minimum. Regarding the RSRQ indicator, the solution reached a 1.45% average gain, and the

42

Conclusion

43

number of performed handovers was maintained, compared to a similar literature model. Despite the modest improvement, which makes our proposal statistically equivalent to the literature
model, we offer the advantage of not predicting the users’ possible and future routes. Only the
current position is required. Furthermore, our solution also considers base stations’ bandwidth
capacity, controlling the allocation and network occupation limits.
We conclude by stating the following contributions: i) A mathematical model to allocate users
in base stations of mobile wireless networks; ii) Proposition and evaluation of a heuristic method
as an alternative to exact solving approach; iii) Evaluation of allocation on different mobility
simulations, one of which considers the real position of base stations from a local mobile carrier;
iv) A evaluation and comparison of our model with existing literature work. Also, some of our
work results have already been published (Ramos et al., 2019b,a).

5.2

Future work

Designing allocation models to wireless networks, we can consider characteristics such as prediction factors, user’s traveling speed, and estimation of failure probability. Future work includes
the study of new characteristics and their impacts on the mathematical formulation. We consider the development of a hybrid approach combining the advantages of ILS-VND with an
exact method. Heuristic approaches can provide satisfactory results, but it is susceptible to
non-optimal values. We can improve our proposal by generating initial solutions with heuristic
methods and using the result as an input to exact methods. This approach would impact the
average execution time of the exact method and provide an optimal solution. As for new mobility
scenarios, we consider integration and real-time simulation with the SUMO mobility simulator.

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