This book provides a comprehensive theory of mono- and multi-fractal traffic, including the basics of long-range dependent time series and 1/f noise, ergodicity and predictability of traffic, traffic modeling and simulation, stationarity tests of traffic, traffic measurement and the anomaly detection of traffic in communications networks.
Proving that mono-fractal LRD time series is ergodic, the book exhibits that LRD traffic is stationary. The author shows that the stationarity of multi-fractal traffic relies on observation time scales, and proposes multi-fractional generalized Cauchy processes and modified multi-fractional Gaussian noise. The book also establishes a set of guidelines for determining the record length of traffic in measurement. Moreover, it presents an approach of traffic simulation, as well as the anomaly detection of traffic under distributed-denial-of service attacks.
Scholars and graduates studying network traffic in computer science will find the book beneficial.
Author(s): Ming Li
Publisher: CRC Press
Year: 2023
Language: English
Pages: 296
City: Boca Raton
Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
Acknowledgments
Part I: Fundamentals
Chapter 1: Fractal Time Series
1.1. BACKGROUND
1.2. FRACTAL TIME SERIES: A VIEW FROM FRACTIONAL SYSTEMS
1.3. BASIC PROPERTIES OF FRACTAL TIME SERIES
1.4. SOME MODELS OF FRACTAL TIME SERIES
1.5. SUMMARY
REFERENCES
Chapter 2: On 1/f Noise
2.1. INTRODUCTION
2.2. PRELIMINARIES
2.3. HYPERBOLICALLY DECAYED ACFS AND 1/f NOISE
2.4. HEAVY-TAILED PDFS AND 1/f NOISE
2.5. FRACTIONALLY GENERALIZED LANGEVIN EQUATION AND 1/f NOISE
2.6. SUMMARY
REFERENCES
Chapter 3: Power Laws of Fractal Data in Cyber-Physical Networking Systems
3.1. BACKGROUND
3.2. BIREF OF POWER LAWS
3.3. CASES OF POWER LAWS IN CPNS
3.4. SOME EQUATIONS FOR POWER-LAW-TYPE DATA
3.5. SUMMARY
REFERENCES
Chapter 4: Ergodicity of Long-Range-Dependent Traffic
4.1. BACKGROUND
4.2. PRELIMINARIES
4.3. PROBLEM STATEMENTS
4.4. RESULTS
4.5. DISCUSSIONS AND SUMMARY
REFERENCES
Chapter 5: Predictability of Long-Range-Dependent Series
5.1. INTRODUCTION
5.2. PROBLEM STATEMENTS
5.3. PREDICTABILITY OF LRD SERIES
5.4. SUMMARY
REFERENCES
Part II: Traffic Modeling and Traffic Data Processing
Chapter 6: Long-Range Dependence and Self-Similarity of Daily Traffic with Different Protocols
6.1. BACKGROUND
6.2. DATA
6.3. PRELIMINARIES: BRIEF OF GENERALIZED CAUCHY PROCESS
6.4. MODELING RESULTS
6.5. DISCUSSIONS
6.6. SUMMARY
REFERENCES
Chapter 7: Stationarity Test of Traffic
7.1. BACKGROUND
7.2. CORRELATION METHOD FOR STATIONARITY TEST OF LRD TRAFFIC
7.3. CASE STUDY
7.4. DISCUSSIONS
7.5. SUMMARY
REFERENCES
Chapter 8: Record Length Requirement of LRD Traffic
8.1. BACKGROUND AND PROBLEM STATEMENTS
8.2. THEORETICAL RESULTS
8.3. PRACTICAL CONSIDERATIONS
8.4. CASE STUDY
8.5. DISCUSSIONS
8.6. SUMMARY
REFERENCES
Part III: Multi-fractal Models of Traffic
Chapter 9: Multi-Fractional Generalized Cauchy Process and Its Application to Traffic
9.1. INTRODUCTION
9.2. THE MGC PROCESS
9.3. PSD OF THE MGC PROCESS
9.4. COMPUTATIONS OF D(T) AND H(T)
9.5. CASE STUDY
9.6. DISCUSSIONS
9.7. SUMMARY
REFERENCES
Chapter 10: Modified Multi-fractional Gaussian Noise and Its Application to Traffic
10.1. INTRODUCTION
10.2. MODIFIED MULTI-FRACTIONAL GUASSIAN NOISE
10.3. ON STATIONARITY OF MMFGN
10.4. APPLICATION TO STATIONARITY TEST OF TRAFFIC
10.5. SUMMARY
REFERENCES
Chapter 11: Traffic Simulation
11.1. INTRODUCTION
11.2. SIMULATIONS BASED ON GIVEN PDF/PSD/ACF
11.3. GENERATION OF LRD TRAFFIC OF GC TYPE
11.4. DISCUSSIONS
11.5. SUMMARY
REFERENCES
Part IV: Anomaly Detection of Traffic
Chapter 12: Reliably Identifying Signs of DDOS Flood Attacks Based on Traffic Pattern Recognition
12.1. BACKGROUND
12.2. FEATURE EXTRACTION
12.3. IDENTIFICATION DECISION
12.4. CASE STUDY
12.5. DISCUSSIONS AND SUMMARY
REFERENCES
Chapter 13: Change Trend of Hurst Parameter of Multi-Scale Traffic under DDOS Flood Attacks
13.1. BACKGROUND
13.2. TEST DATA
13.3. BRIEF OF DATA TRAFFIC
13.4. USING H TO DESCRIBE ABNORMALITY OF TRAFFIC UNDER DDOS FLOOD ATTACKS
13.5. CHANGE TREND OF H
13.6. SUMMARY
REFERENCES
Chapter 14: Postscript
14.1. LOCAL VERSUS GLOBAL OF FRACTAL TRAFFIC
14.2. STATIONARITY VERSUS MULTI-FRACTAL PROPERTY OF TRAFFIC
14.3. OPEN PROBLEMS
REFERENCES
APPENDIX
INDEX
