Multi-Fractal Traffic and Anomaly Detection in Computer Communications

Description

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. 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