Modelling computer network traffic using wavelets and time series analysis (original) (raw)
Related papers
A unified framework for understanding network traffic using independent wavelet models
2002
Abstract Properties of heterogeneous network traffic have been investigated from different aspects, resulting in different understanding. Specifically, one previous work discovers that the variance of network traffic exhibits a linear relationship with respect to the mean. Such a linear relation suggests that the traffic is" Poisson-like", and thus" smooth". On the other hand, prior work has shown that the heterogeneous traffic can be long-range dependent, and is thus bursty.
Modeling network traffic in wavelet domain
This work discovers that although network traffic has a complicated short- and long-range temporal dependence, the corresponding wavelet coefficients are no longer long-range dependent. Therefore, a “short-range” dependent process can be used to model network traffic in the wavelet domain. Both independent and Markov models are investigated. Theoretical analysis shows that the independent wavelet model is sufficiently accurate in terms of the buffer overflow probability for fractional Gaussian noise traffic. Any model which captures additional correlations in the wavelet domain only improves the performance marginally. The independent wavelet model is then used as a unified approach to model network traffic including VBR MPEG video and Ethernet data. The computational complexity is O(N) for developing such wavelet models and generating synthesised traffic of length N, which is among the lowest attained.
Comparison of the independent wavelet models to network traffic
2000
Abstract Cheng Ma and Chuanyi Ji (1998) and Chuanyi Ji et al.(1999) showed empirically that independent (Haar) wavelet models were parsimonious, computationally efficient and accurate in modeling heterogeneous network traffic measured by both auto-covariance functions and buffer loss rate. We also proved analytically that such models were capable of capturing any decay rate of auto-covariance functions at large lags.
Modeling heterogeneous network traffic in wavelet domain
2001
Abstract Heterogeneous network traffic possesses diverse statistical properties which include complex temporal correlation and non-Gaussian distributions. A challenge to modeling heterogeneous traffic is to develop a traffic model which can accurately characterize these statistical properties, which is computationally efficient, and which is feasible for analysis. This work develops wavelet traffic models for tackling these issues. In specific, we model the wavelet coefficients rather than the original traffic.
Modeling Heterogeneous Network Traffic in Wavelet Domain: Part I--Temporal Correlationi
1999
Heterogeneous network traffic possesses diverse statistical properties such as (1) complex temporal correlation,(2) higher-order statistics and (3) a certain (such as periodic) structure. The Part I of this workfocuses on modeling temporal correlation (the second-order statistics) of heterogeneous traffic, and the PartII will be on modeling non-Gaussian (high-order statistics) and periodic traffic.
Modeling heterogeneous network traffic in wavelet domain: Part II-non-gaussian traffic
1999
Following our work described in Part I of this paper that modeled various correlation structures ofGaussian traffic in wavelet domain, we extend our previous models to heterogeneous network traffic witheither a non-Gaussian distribution or a periodic structure. To include a non-Gaussian distribution, we firstinvestigate what higher-order statistics are pertinent by exploring a relationship between time-scale analysisof wavelets and cumulative traffic.
Wavelet analysis of long-range-dependent traffic
IEEE Transactions on Information Theory, 1998
A wavelet-based tool for the analysis of long-range dependence and a related semi-parametric estimator of the Hurst parameter is introduced. The estimator is shown to be unbiased under very general conditions, and efficient under Gaussian assumptions. It can be implemented very efficiently allowing the direct analysis of very large data sets, and is highly robust against the presence of deterministic trends, as well as allowing their detection and identification. Statistical, computational, and numerical comparisons are made against traditional estimators including that of Whittle. The estimator is used to perform a thorough analysis of the long-range dependence in Ethernet traffic traces. New features are found with important implications for the choice of valid models for performance evaluation. A study of mono versus multifractality is also performed, and a preliminary study of the stationarity with respect to the Hurst parameter and deterministic trends.
Topics in Intelligent Engineering and Informatics, 2012
The significant increase of trunk channel bandwidth makes much easier to integrate different types of traffics on the tier links without activating high processing power consuming QoS (Quality of Service) mechanisms in the intermediate nodes. Self-similarity, long range dependence and fractal characteristics of packet flows are strongly influenced by the QoS parameters in congested network environment. Several models are proposed for the qualitative and quantitative evaluation of physical phenomenon supervened on different OSI layers at the routers and switches. Most of these claims relatively long traces for evaluating both scale independence and fractal characteristics. In this chapter are evaluated the highlights of common usage of wavelet and ON/(ON+OFF) transformations for network traffic analysis are evaluated. We take into consideration the channel load and the channel intensity as complex time series for evaluation the statistical characteristics of changes in time of the flows nature in packet switched networks. UDP and TCP traffics in tier and LAN networks are considered and statistically analyzed based on MRA (Multi Resolution Analysis) wavelets method. Fast detection algorithm of data and real time traffic burstiness is presented for QoS based packet switched network environment with congestion.
A Multifractal Wavelet Model with Application to Network Traffic
… , IEEE Transactions on, 1999
In this paper, we develop a new multiscale modeling framework for characterizing positive-valued data with longrange-dependent correlations (1=f noise). Using the Haar wavelet transform and a special multiplicative structure on the wavelet and scaling coefficients to ensure positive results, the model provides a rapid O(N ) cascade algorithm for synthesizing Npoint data sets. We study both the second-order and multifractal properties of the model, the latter after a tutorial overview of multifractal analysis. We derive a scheme for matching the model to real data observations and, to demonstrate its effectiveness, apply the model to network traffic synthesis. The flexibility and accuracy of the model and fitting procedure result in a close fit to the real data statistics (variance-time plots and moment scaling) and queuing behavior. Although for illustrative purposes we focus on applications in network traffic modeling, the multifractal wavelet model could be useful in a number of other areas involving positive data, including image processing, finance, and geophysics.
Approximation capability of independent wavelet models to heterogeneous network traffic
1999
Abstract In our previous work, we showed empirically that independent wavelet models were parsimonious, computationally efficient, and accurate in modeling heterogeneous network traffic measured by both auto-covariance functions and buffer loss rate. In this work, we focus on auto-covariance functions, to establish a theory of independent wavelet models as unified models for heterogeneous network traffic.