ABSTRACT
Forecasting of voice traffic using an accurate model is important to the telecommunication
service provider in planning a sustainable Quality of Service (QoS) for their mobile networks.
This work is aimed at forecasting Erlang C – based voice traffic using a hybrid forecasting model
that integrates fuzzy C-means clustering (FCM) and particle swarm optimization (PSO)
algorithms with fuzzy time series (FTS) forecasting model. Fuzzy C-means (FCM) clustering,
which is an algorithm for data classification, is adopted at the fuzzification phase to obtain
unequal partitions. Particle swarm optimization (PSO), which is an evolutional search algorithm,
is adopted to optimize the defuzzification phase; by tuning weights assigned to fuzzy sets in a
rule.This rule is a fuzzy logical relationship induced from a fuzzy set group (FSG). The
clustering and optimization algorithms were implemented in programs written in C#. Daily
Erlang C traffic observations collected over a three (3) month period from 1 December, 2012 –
28 February, 2013 from Airtel, Abuja region, was used to evaluate the proposed hybrid model.To
evaluate the forecasting efficiency of the proposed hybrid model, its statistical performance
measures of mean square error (MSE) and mean absolute percentage error (MAPE), were
calculated and compared with those of a conventional fuzzy time series (FTS) model and, a
fuzzy C-means (FCM) clustering and fuzzy time series (FTS) hybrid model.Statistical results of
MSE 0.9867 and MAPE 0.47 %were obtained during training of the proposed hybrid
forecasting model. Compared with the training results ofMSE 845.122 andMAPE 13.47 %,
for Chen‟s (1996) FTS model and; MSE 856.145 and MAPE 13.37 %, for Cheng‟s (2008);
the proposed hybrid forecasting model resulted in a relatively higherforecasting accuracy and
precision. Also, performancemeasures of MSE 59.22 and MAPE 3.85 %were obtained
during thetesting phase of the proposed model. Compared with the test results of MSE 1567.4
and MAPE 23.98 %obtained for Cheng‟s (2008) FCM/ FTS hybrid model, the proposed
hybrid forecasting model also showed a relatively higher forecasting accuracy and precision.
Finally, it was determined that reversing the weights of the forecasting rules, during training,
resulted to a lesser performance;MSE 42.73 and MAPE 0.88 %. Thus, reversing the weights
of forecasting rule affected the forecasting accuracy.
TABLE OF CONTENTS
TITLE PAGE ………………………………………………………………………………………………………………… i
DECLARATION ………………………………………………………………………………………………………….. ii
CERTIFICATION ……………………………………………………………………………………………………….. iii
DEDICATION …………………………………………………………………………………………………………….. iv
ACKNOWLEDGEMENTS …………………………………………………………………………………………… v
TABLE OF CONTENTS ……………………………………………………………………………………………… vi
LIST OF APPENDICES………………………………………………………………………..ix
LIST OF FIGURES ………………………………………………………………………………………………………. x
LIST OF TABLES ……………………………………………………………………………………………………….. xi
LIST OF ABBREVIATIONS ……………………………………………………………………………………… xiii
ABSTRACT ……………………………………………………………………………………………………………….. xvi
CHAPTER ONE: INTRODUCTION
1.1 Background Information …………………………………………………………………………………………. 1
1.2 Aim and Objectives ………………………………………………………………………………………………….. 2
1.3 Statement of the Problem …………………………………………………………………………………………. 2
1.4 Methodology ……………………………………………………………………………………………………………. 3
1.5 Significant Contributions………………………………………………………………………..5
1.6 Thesis Organization …………………………………………………………………………………………………. 5
CHAPTER TWO: LITERATURE REVIEW
2.1 Introduction …………………………………………………………………………………………………………….. 6
2.2 Review of Fundamental Concepts …………………………………………………………………………….. 6
2.2.1 Time Series………………………………………………………………………………….6
2.2.2 Fuzzy Set Theory ………………………………………………………………………………………………….. 6
2.2.3 Fuzzy Time Series and Fuzzy Logic Relationship …………………………………………………… 7
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2.2.4 Universe of Discourse ……………………………………………………………………………………………. 9
2.2.5 Fuzzy Set Groups ………………………………………………………………………………………………… 10
2.2.6 Data Mining and Clustering ………………………………………………………………………………… 11
2.2.6.1Distance Measure ……………………………………………………………………………………………….. 13
2.2.7Fuzzy C-Meeans Clustering ………………………………………………………………………………….. 13
2.2.8Cluster Validity Index ………………………………………………………………………………………….. 16
2.2.9 Particle Swarm Optimization ………………………………………………………………………………. 17
2.2.10 Defuzzification Operator ……………………………………………………………………………………. 19
2.2.11Erlang Based Voice Traffic …………………………………………………………………………………. 20
2.2.12 Performance Measure ……………………………………………………………………………………….. 20
2.2.13 Programming Language…………………………………………………………………………………….. 23
2.2.13.1C programming Language ………………………………………………………………………………….. 23
2.2.13.2 C++ Programming Language ……………………………………………………………………………. 24
2.2.13.3 Java Programming Language ……………………………………………………………………………. 24
2.2.13.4 C# Programming Language ………………………………………………………………………………. 24
2.3 Review of Similar Works ……………………………………………………………………………………….. 25
CHAPTER THREE: MATERIAL AND METHODS
3.1 Introduction …………………………………………………………………………………………………………… 30
3.2Data Collection and Processing …………………………………..……..…………………30
3.3 Fuzzification Module……………………………………..…………………………………31
3.3.1 Coding fuzzy C-Means (FCM) Clustering Algorithm in C#…………………………………….31
3.3.2 Applying Time Series Data on Fuzzy C-Means Code…………………………………..36
3.3.3 Ranking Clusters in Ascending Order ………………………………………………….40
3.3.4 Fuzzifying Time Series Data …………………………………………………………….41
3.4 Defuzzification Module…………………………………………………………………….43
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3.4.1 Establishing Fuzzy Set Groups (FSGs)………………………………………………………………….43
3.4.2 Converting Fuzzy Set Groups into “if – then” Rules………………………………………………47
3.4.3 Tuning “if – then” Rules Using Particle Swarm Optimization (PSO)………………………50
3.4.4 Deriving Forecasts………………………………………………………………………………………………..63
3.5 Investigating the Effect of Reversed Weights……………………………………………………………64
3.6 Forecasting Test Data Set………………………………………………………………………………………..67
3.7 Forecasting Using Chen’s (1996) Fuzzy Time Series Model………………………………………71
3.8 Forecasting Using Cheng et al (2008) Hybrid Model…………………………………………………72
CHAPTER FOUR: RESULTS AND DISCUSSIONS
4.1 Introduction……….………………………………………………………………………..75
4.2 Forecasting Results for Training Data Set………………………………………………………………..75
4.3 Forecasting Result for Test Data SetForecasts…………………………………………………………80
4.4 Validation………………………………………………………………………………………………………………82
4.5 Significance of Forecasting Results…………………………………………………………………………..95
CHAPTER FIVE: CONCLUSION AND RECOMMENDATIONS
5.1 Summary ……………………………………………………………………………………………………………….. 96
5.2 Conclusion …………………………………………………………………………………………………………….. 96
5.3 Limitations …………………………………………………………………………………………………………….. 97
5.4 Recommendations for Further Works …………………………………………………………………….. 97
REFERENCES ……………………………………………………………………………………………………………. 99
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CHAPTER ONE
INTRODUCTION
1.1 BACKGROUND INFORMATION
Since its inception over three decades ago, mobile telecommunication call centres have witnessed exponential growth. Call centres are on the increase owing to the large number of mobile subscribers and the need for telecommunication operators to lower cost of providing services while increasing time access of their services. Understanding voice traffic pattern of a call centre becomes critical to service providers in predicting traffic, planning and budgeting for future changes of their mobile networks. This is important for sustaining a good Quality of Service (QoS). Forecasting is used to predict, model and simulate the future from past events in virtually all fields of endeavours. In the telecommunication industry, forecasting is a useful tool in planning, budgeting, evaluating and verifying network resources (Eleruja et al, 2012).
Voice traffic is one of the critical measures in mobile telecommunication systems. Since this measure is non – linear and dynamic with time, forecasting Erlang based voice traffic observations using fuzzy time series (FTS) models seems to be more suitable than conventional statistical models. Fuzzy time series (FTS) models take care of uncertainties in observations over time and does not require any restrictive assumptions and too much background knowledge of the data; like in the case of conventional statistical forecasting methods.The use of fuzzy time series (FTS) in forecasting was first introduced by Song and Chissom (1993). This approach comprises two phases; fuzzification and defuzzification. Fuzzification is a technique for conversion of real observations into discrete or linguistic fuzzy sets. Defuzzification is a technique for converting linguistic observations to real values.
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Recently, due to the need for improving forecasting accuracy, hybrids of fuzzy time series approaches have become the research trends in literature. In this study a novel hybrid fuzzy time series that integrates fuzzy C-means (FCM) clustering and particle swarm optimization, in the fuzzification and defuzification phases respectively, with fuzzy time series (FTS) model was proposed.
1.2 AIM AND OBJECTIVES
The aim of this research is the application of fuzzy C-means (FCM) clustering and particle swarm optimization (PSO) algorithms in fuzzy time series (FTS) forecasting model in order to improve the forecasting accuracy. The objectives of the research are as follows:
I. Development of a GUI based fuzzy C-means (FCM) clustering model to objectively partition the universe of discourse into unequal lengths (cluster centres) and to learn the memberships in hidden data structure.
II. Development of a GUI based particle swarm optimization (PSO) model to optimize the defuzzification process.
III. Reduction of computational complexities of the forecasting process in using FCM clustering and particle Swarm optimization (PSO) by implementation of the algorithms in C#.
IV. Validation using Erlang based voice traffic data obtained from Airtel, Abuja Call Centre.
V. Comparison of the results obtained using the developed hybrid model with results obtained using other models (Chen‟s (1996) model and Cheng et al (2008) hybrid model).
1.3 STATEMENT OF PROBLEM
Accurate and robust fuzzy time series models capable of determining objective interval length, memberships that explains unknown structures in data sets, minimizing loss of forecasting rules,
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and reducing computational complexities are challenging issues facing fuzzy time series
forecasting. It has become necessary to solve these challenges using hybrid fuzzy time series
models. As a consequence, employing fuzzy C-means (FCM) clustering algorithm in fuzzification,
fuzzy set groups (FSGs) to generate logical relationships, and particle swarm optimization (PSO)
algorithm in defuzzification will improve fuzzy time series forecasting accuracy. Coding thevarious
algorithms used in the forecasting process in high – level or object – oriented programming
languages like matlab, C++ or C# will reduce computational complexity. C# was chosen in this
work because of its pure object – oriented programming features which can be integrated with
Windows operating systems.
1.4 METHODOLOGY
The following methodology was adopted in carrying out this research:
1. Collection and processing voice (Erlang) traffic observations for Airtel, Abuja call centre.
2. The fuzzification module comprises the following steps:
a. Code fuzzy C-means (FCM) clustering algorithm in C#.
b. Apply voice (Erlang) traffic observations on the fuzzy C-means (FCM) clustering code
to compute cluster centres, i v , and membership degrees (partition matrix).
c. Rank cluster values, i v , in ascending order to determine ordered linguistic variables,
A r c r 1,2,3,…., .
d. Fuzzify the voice traffic data sets using the partition matrix and the rank.
3. The defuzzification module comprises the following steps:
a. Establish disambiguated fuzzy set groups (FSGs).
b. Convert fuzzy set groups (FSGs) to “if – then” rules.
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c. Tune the “if – then” rules using particle swarm optimization (PSO) algorithm coded in C#.
d. Based on the results of the training, derive the possible outcomes of the voice traffic forecast, using a defuzzification operator.
4. Investigate the effect of reversed weights.
5. Validate and compare forecasts using measured data from Airtel, Abuja Call Centre.
The flowchart for the model design is shown in Figure 1.1.
Figure 1.1: Flowchart of the Proposed Hybrid Model.
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1.5 SIGNIFICANT CONTRIBUTIONS
The significant contributions derivable from this work are as follows:
1) Development of a GUI based FTS model that incorporates fuzzy C-means clustering and particle swarm optimization which reduces the computational cost whilst easing the forecasting process.
2) Development of a hybrid fuzzy time series forecasting model that has improved forecasting performance in terms of mean square error (MSE). In comparison with the Chen‟s (1996) fuzzy time series model and Cheng‟s (2008) hybrid model, during the training phase, the developed model has improved mean square errorperformance by over 99 % in forecasting the Airtel voice traffic, Abuja region.When compared with the Cheng‟s (2008), the developed model showedimprovement in mean square error performance by over 96 % during the testing phase.
1.6 DISSERTATION ORGANIZATION
The general introduction has been presented in Chapter One. The remaining chapters were structured as follows: A detailed review of the relevant literature and pertinent fundamental conceptswas carried out in Chapter Two.Chapter Three discussed the methodology adopted in achieving the set objectives.The results obtained were analyzed and discussed in Chapter Four. Chapter Five discussed the conclusion and recommendations for further work. Quoted references and Appendices are also provided at the end of the thesis.
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