A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ten lectures on wavelets
On the self-similar nature of Ethernet traffic
SIGCOMM '93 Conference proceedings on Communications architectures, protocols and applications
Wavelets and subband coding
Wide area traffic: the failure of Poisson modeling
IEEE/ACM Transactions on Networking (TON)
Essential wavelets for statistical applications and data analysis
Essential wavelets for statistical applications and data analysis
On estimating the intensity of long-range dependence in finite and infinite variance time series
A practical guide to heavy tails
Meaningful MRA intitialization for discrete time series
Signal Processing - Special issue on current topics in adaptive filtering for hands-free acoustic communication and beyond
Estimation of the self-similarity parameter in linear fractional stable motion
Signal Processing - Signal processing with heavy-tailed models
Does fractal scaling at the IP level depend on TCP flow arrival processes?
Proceedings of the 2nd ACM SIGCOMM Workshop on Internet measurment
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Long-range dependence in a changing Internet traffic mix
Computer Networks: The International Journal of Computer and Telecommunications Networking - Special issue: Long range dependent trafic
Cluster processes: a natural language for network traffic
IEEE Transactions on Signal Processing
Wavelet analysis of long-range-dependent traffic
IEEE Transactions on Information Theory
A wavelet-based joint estimator of the parameters of long-range dependence
IEEE Transactions on Information Theory
Statistical study of the wavelet analysis of fractional Brownian motion
IEEE Transactions on Information Theory
Correlation structure of the discrete wavelet coefficients of fractional Brownian motion
IEEE Transactions on Information Theory - Part 2
Performance Issues in Optical Burst/Packet Switching
Towards Digital Optical Networks
Scaling Analysis of Wavelet Quantiles in Network Traffic
TMA '09 Proceedings of the First International Workshop on Traffic Monitoring and Analysis
Traffic generator model for an n-node network
HSI'09 Proceedings of the 2nd conference on Human System Interactions
Real-Time and Self-adaptive Method for Abnormal Traffic Detection Based on Self-similarity
WISM '09 Proceedings of the International Conference on Web Information Systems and Mining
Global modeling of backbone network traffic
INFOCOM'10 Proceedings of the 29th conference on Information communications
A LoSS based on-line detection of abnormal traffic using dynamic detection threshold
ICICS'09 Proceedings of the 11th international conference on Information and Communications Security
Systolic traffic modelling in network on chip
International Journal of Wireless and Mobile Computing
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The fluctuations of Internet traffic possess an intricate structure which cannot be simply explained by long-range dependence and self-similarity. In this work, we explore the use of the wavelet spectrum, whose slope is commonly used to estimate the Hurst parameter of long-range dependence. We show that much more than simple slope estimates are needed for detecting important traffic features. In particular, the multi-scale nature of the traffic does not admit simple description of the type attempted by the Hurst parameter. By using simulated examples, we demonstrate the causes of a number of interesting effects in the wavelet spectrum of the data. This analysis leads us to a better understanding of several challenging phenomena observed in real network traffic. Although the wavelet analysis is robust to many smooth trends, high-frequency oscillations and non-stationarities such as abrupt changes in the mean have an important effect. In particular, the breaks and level-shifts in the local mean of the traffic rate can lead one to overestimate the Hurst parameter of the time series. Novel statistical techniques are required to address such issues in practice.