Multiscale queuing analysis of long-range-dependent network traffic (original) (raw)

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.

A Multifractal Wavelet Model of Network Traffic

ensc.sfu.ca

In this paper, a new Multifractal Wavelet Model (MWM) is studied and simulation results are presented. We conclude that MWM has captured most of the properties of network traffic and the computational complexity of MWM is only O(N). The efficiency of MWM makes it possible in the real-time applications.

Modeling network traffic with multifractal behavior

2003

The traffic engineering of IP networks requires accurate characterization and modeling of network traffic, due to the growing diversity of multimedia applications and the need to efficiently support QoS differentiation in the network. In recent years several types of traffic behavior, that can have significant impact on network performance, were discovered: longrange dependence, self-similarity and, more recently, multifractality. The extent to which a traffic model needs to incorporate each of these characteristics is still the subject of much research. In this work, we address the modeling of network traffic multifractality by evaluating the performance of four models, which cover a wide range of traffic types, as mathematical descriptors of measured traffic traces showing multifractal behavior. We resort to traffic traces measured both at the University of Aveiro and at a Portuguese ISP. For the traffic models, we selected a Markov modulated Poisson process as an example of a Markovian model, the well known fractional Gaussian noise model as an example of a self-similar process and two examples of models that are able to capture multifractal behavior: the conservative cascade and the L-system. All models are evaluated comparing the density function, the autocovariance and the loss ratio queuing behavior of the measured traces and of traces synthesized from the fitted models. Our results show that the fractional Gaussian noise model is not able to perform a good fitting of the first and second order statistics as well as the loss rate queuing behavior, whereas the Markovian, the conservative cascade and the L-system models give similar and very good results. The cascade and the L-system models are intrinsically multifractal in the sense that they are able to capture and synthesize traffic multifractality, thus the obtained results are not surprising. The good performance of the Markovian model can be attributed to the parameter fitting procedure, that aggregates distinct sub-processes operating in different time scales, and matches closely both the first and second order statistics of the traffic. The poor performance of the self-similar model can be explained mainly by its lack of parameters.

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.

Modelling computer network traffic using wavelets and time series analysis

2019

Modelling of network traffic is a notoriously difficult problem. This is primarily due to the ever-increasing complexity of network traffic and the different ways in which a network may be excited by user activity. The ongoing development of new network applications, protocols, and usage profiles further necessitate the need for models which are able to adapt to the specific networks in which they are deployed. These considerations have in large part driven the evolution of statistical profiles of network traffic from simple Poisson processes to non-Gaussian models that incorporate traffic burstiness, non-stationarity, self-similarity, long-range dependence (LRD) and multi-fractality. The need for ever more sophisticated network traffic models has led to the specification of a myriad of traffic models since. Many of these are listed in [91, 14]. In networks comprised of IoT devices much of the traffic is generated by devices which function autonomously and in a more deterministic fa...

The multiscale nature of network traffic: Discovery, analysis, and modelling

IEEE Signal …, 2002

The complexity and richness of telecommunications traffic is such that one may despair to find any regularity or explanatory principles. Nonetheless, the discovery of scaling behavior in tele-traffic has provided hope that parsimonious models can be found. The statistics of scaling behavior present many challenges, especially in non-stationary environments. In this paper, we overview the state of the art in this area, focusing on the capabilities of the wavelet transform as a key tool for unravelling the mysteries of traffic statistics and dynamics.

Framework based on stochastic L-Systems for modeling IP traffic with multifractal behavior

Computer Communications, 2004

In a previous work we have introduced a multifractal traffic model based on so-called stochastic L-Systems, which were introduced by biologist A. Lindenmayer as a method to model plant growth. L-Systems are string rewriting techniques, characterized by an alphabet, an axiom (initial string) and a set of production rules. In this paper, we propose a novel traffic model, and an associated parameter fitting procedure, which describes jointly the packet arrival and the packet size processes. The packet arrival process is modeled through a L-System, where the alphabet elements are packet arrival rates. The packet size process is modeled through a set of discrete distributions (of packet sizes), one for each arrival rate. In this way the model is able to capture correlations between arrivals and sizes. We applied the model to measured traffic data: the well-known pOct Bellcore, a trace of aggregate WAN traffic and two traces of specific applications (Kazaa and Operation Flashing Point). We assess the multifractality of these traces using Linear Multiscale Diagrams. The suitability of the traffic model is evaluated by comparing the empirical and fitted probability mass and autocovariance functions; we also compare the packet loss ratio and average packet delay obtained with the measured traces and with traces generated from the fitted model. Our results show that our L-System based traffic model can achieve very good fitting performance in terms of first and second order statistics and queuing behavior.

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.

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.

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.