Multifractal Wavelet Model Research Articles

FRACTAL CHARACTERISTICS OF NETWORK TRAFFIC AND ITS CORRELATION WITH NETWORK SECURITY

Based on the analysis of the self-similarity of network traffic, a network anomaly detection technology is proposed by combining with the fuzzy logic so as to explore the fractal characteristics of network traffic. The concepts of network traffic and network security are introduced. Then, a network traffic model of network traffic is proposed based on the fractal theory and wavelet analysis. Finally, a distributed denial of service (DDoS) that attacks the monitoring and intensity judgment method is put forward based on the fuzzy logic theory. The results show that the autocorrelation function of the multifractal wavelet model constructed based on the local Hurst exponent (LHE) can reach a mean square error (MSE) of [Formula: see text], which proves that the network traffic model proposed can reduce the impact of the non-stationary characteristics of the network traffic on the modeling accuracy. The network security detection method proposed can monitor the DDoS attacks and can accurately judge the attack intensity in real time. The research in this study provides an important reference for the scientific operation of the network.

Models of monitoring of self-like traffic of information and communication networks for attack detection systems

Autoregressive, fractal and multifractal models of network self-similar traffic are con-sidered, which allow to form an adequate reference model (template) of "normal" traffic and to detect traffic anomalies in attack detection and prevention systems. Models of fractal Brownian motion and fractal Gaussian noise were considered as models of fractal motions, because they have self-similarity and long-term dependence properties that correspond to the properties of experimental data, as well as the possibility of their analytical interpretation. When evaluating and identifying processes for the implementation of autoregressive models use adaptive filters-approximators, among which there are neural network and neuro-wavelet. The following were used as multifractal models: a multifractal wavelet model with a beta distribution and a hybrid multifractal wavelet model in which the beta distribution is used on a coarse scale and the dis-tribution of point masses on an accurate scale By modeling as a result of adaptation and learning of models, autocorrelation functions, spectra and variances of model signals qualitatively correspond to the graphs of the experimental signal. In addition, the qualitative and numerical values of the characteristics of the model signals generally correspond to the characteristics of the experimental signal. In this case, beta multifractal wavelet models have a smaller error of determination of characteristics than hybrid multifractal wavelet models, and the relative root mean square error of approximation of the experimental signal using a neural network adaptive filter approximator does not exceed 0.046. Statistical verification by non-parametric criterion of signs allowed to establish the adequacy of experimental and model signals with a significance level of 0.01. Further research should be aimed at developing and using predictive models of self-similar traffic in attack detection and prevention systems, which will increase the efficiency of attack detection.

USING TIME SCALES WHILE APPROXIMATING THE LENGTH OF COMPUTER NETWORKS

The subject of the research is to predict the queue length for the communication device of a high-speed computer network with non-Gaussian traffic. The goal of this article is to examine the probabilities of the application of time scales used to study the organization of queues of modern high-speed computer networks. The following methods were used: the fractal analysis, scaling methods, methods of approximation. The following results were achieved: the results of the time scale selection for constructing adequate models of modern traffic were presented. The use of such models, in particular, enables studying the dynamics of the queues of active network devices, which is important for planning and distributing the network load. The use of statistical characteristics of traffic on a small number of time scales enables expanding theoretical concepts for critical time scales, which makes this approach applicable to any traffic process including the long-term traffic. In addition, the issues of describing the behaviour of queue tails for modern high-speed computer networks are considered and the properties of the proposed model approximations are determined. The analysis of the independent Gaussian model of a wavelet domain and the multifractal wavelet model showed the advantage of the first one for the fractal traffic and a slight discrepancy in the results for traffic close to the Gaussian one. Conclusions . Various approaches to the selection of time scales used in the study of the organization of queues of modern high-speed data networks were studied. The effect of the necessary accuracy and computational power required for calculating the maximum approximation were analyzed and it was established that exponential time scales are optimal for the fractal traffic. The impact of the tails of distributions in different time scales on the process of queue organization was also shown. It was noted that in the context of non-Gaussian traffic scenarios, the correlation structure (both short-term and long-term ones) does not describe the queues behaviour adequately enough.

Study on the Prediction of Urban Traffic Flow Based on ARIMA Model

Because the traffic flow has the characteristics of nonlinear and strong interference, good traffic model can accurately describe the flow characteristics, predict the changing trend of the flow and carry out the corresponding control measures to ensure the normal operation of traffic, thus improving the traffic pressure. In this paper, wavelet analysis is applied to analyze the complex network traffic. Time series are decomposed into approximate uncorrelated time series, and the time series are smoothed. The wavelet analysis is carried out by using the mathematical model, independent wavelet model and multi fractal wavelet model. Matlab and SPSS are used to analyze the data of traffic flow. The wavelet analysis and ARIMA model are used to predict the sequence of single branch reconstruction, which reduces the error and improves the feasibility.

A multifractal wavelet model for the generation of long-range dependency traffic traces with adjustable parameters

The available multifractal traffic finite-length time series to implement performance test of the management, control and admission algorithms, and level of service about M/M/1 models for WAN/LAN communication systems are very few and their recollection through current mechanisms is very slow due to the amount of data that must be obtained. Hence, it is necessary to develop a tool which synthesizes traces with multifractal features and allows the stochastic parameters configuration as its average, Hurst parameter and, multifractal spectrum width. This article describes the development of a proposed algorithm to generate multifractal traffic finite-length time series with a Hurst parameter and the multifractal spectrum width, sampling and adjustable, called MultiFractal Hurst Spectrum Width (MFHSW). The MFHSW algorithm is based on the MultiFractal Hurst model (MFH) and on the Multifractal Wavelet Model (MWM), to construct the time series through a binomial multiplicative cascade. The main contribution of the MFHSW algorithm is to allow adjusting both the Hurst parameter and the multifractal spectrum width, the aforementioned is achieved by appropriately modifying the beta distributions that conform the binomial cascade. Consequently, the impact developed by the algorithm to the trace generation with multifractal features will be the improvement in the simulation and data network modeling.The MFHW algorithm behaves as an expert system when inferring to distribution of the beta coefficients present in the scales that make part of the binomial cascade starting from the stochastic parameters configured by the user, and obtaining the corresponding time series through an inference engine. To validate the algorithm effectiveness, a trace with the Hurst parameter sampling and the multifractal spectrum width similar to the presented in a network traffic time series are synthetized. The MFHSW happens to be a promising tool for the modeling of time series applicable to diverse fields as the traffic engineering, finances, biomedical signals, among other real traces with multifractal features.

Design of a Novel Variable Bit Rate Video Traffic Prediction Model Based on Neural Networks

The video business has gradually become the main business of the network traffic, video traffic is Variable Bit Rate (VBR), which has nonlinear and sudden features, a single prediction model is not fit for describing those features, and prediction accuracy is not high. Because of wavelet analysis has advantages of multi-resolution and dealing with unexpectedness, and the neural network has better nonlinear fitting characteristics, in order to improve the prediction performance, the paper researched on the problem of VBR video traffic prediction based on neural networks, a novel prediction model AMWM is proposed, the model firstly introducing BP neural network to multi-fractal wavelet model, and designing prediction method, which introduced multi-fractal wavelet model to model VBR video traffic, and then applying BP neural network to forecast scale coefficient decomposed, and forecast multiplier using AR model, and predict traffic generated by wavelet reconstruction. Finally, the model is built and simulated. The experimental result shows that prediction performance based AMWM is better compared with multi-fractal wavelet model.

Distributed multipliers in MWM for analyzing job arrival processes in massive HPC workload datasets

There are three distributed multipliers multifractal wavelet model (MWM) on network traffic. The β multifractal wavelet model (β MWM) recently has been introduced as a good choice to yield long range dependence (LRD) and fractal behavior for a job arrival process for parallel workload analysis. In this paper, based on the Multifractal Wavelet Model (MWM), we choose the three kinds of distributions for the multipliers, namely the symmetric β-distribution, a symmetric point-mass distribution, and a hybrid distribution, the influence which distributed multipliers had on the MWM was analyzed with the analysis and comparison between the real job arrival process and the synthesized one. We find that the choice of β-distribution wavelet multipliers Aj,k is not necessary. For the job arrival process, we can use different distributed multipliers to control the wavelet energy decay in MWM.

An End-to-End Traffic Estimation Algorithm via Multifractal Wavelet Model and Principal Component Analysis in Smart Grid

In this paper, we study the problem of end-to-end network traffic estimation in the electric power communication network. Based on principal component analysis and multifractal wavelet model, we propose an effective and precise approach to estimate each origin-destination pair. Numeral results state that our method can capture the changes of end-to-end network traffic accurately in electric power communication network.

Estimação de envelope efetivo de tráfego de redes baseada em Modelagem Multifractal para controle de admissão de usuários com qualidade de serviço

In this paper, first we present an effective bandwidth equation for multifractal traffic based on a multiplicative cascade model. Merging the effective bandwidth to the effective envelope concept from the Statistical Network Calculus, we compute end-to-end performance bounds for real multifractal network traffic. Using these bounds, we propose an admission control scheme that guarantees quality service in terms of data loss probability and delay through the obtained effective envelope for the MWM (Multifractal Wavelet Model) multifractal model. Through simulations, we compare the number of flows admitted using effective service curves corresponding to different types of traffic flow schedulers for the fBm (fractional Brownian motion) and MWM traffic models.

A reconstructing approach to end‐to‐end network traffic based on multifractal wavelet model

SUMMARYThis paper studies the reconstructing method of end‐to‐end network traffic. Due to the development of current communication networks, our networks become more complex and heterogeneous. Meanwhile, because of time‐varying nature and spatio‐temporal correlations of the end‐to‐end network traffic, to obtain it accurately is a great challenge. We propose to exploit discrete wavelet transforms and multifractal analysis to reconstruct the end‐to‐end network traffic from time–frequency domain. First, its time–frequency properties can be characterized in detail by discrete wavelet transforms. And then, we combine discrete wavelet transforms and multifractal analysis to reconstruct end‐to‐end network traffic from link loads. Furthermore, our method needs to measure end‐to‐end network traffic to build the statistical model named multifractal wavelet model. Finally, simulation results from the real backbone networks suggest that our method can reconstruct the end‐to‐end network traffic more accurately than previous methods. Copyright © 2013 John Wiley & Sons, Ltd.

Improved multi-fractal network traffic model and its performance analysis

This paper demonstrates the limitation of the traditional multi-fractal wavelet model (MWM). Through analyzing the multi-resolution behaviors of the real video traffic, we propose an improved MWM model. It synthesizes the traffic traces using another wavelet basis, and can adjust wavelet coefficients and multiplicative coefficients at each time scale, based on the network measurement. Subsequently, multifractal spectra and queue performances of the new model have been analyzed. The simulation proves it can capture the multifractal behaviors of network traces.

Markov and multifractal wavelet models for wireless MAC-to-MAC channels

Statistical understanding of bit-errors above the physical layer facilitates the design and verification of wireless protocols and applications. In this paper, we provide analysis and modeling of bit-errors at the 802.11b MAC layer. We show that MAC-to-MAC bit-errors at 2 and 5.5 Mbps are Markov, whereas those at 11 Mbps are long-range dependent (LRD). For the 2 and 5.5 Mbps channels, we observe that low-complexity hierarchical and hidden Markov models cannot characterize the bit-error processes, and consequently high-order full-state Markov chains are employed for accurate channel characterization. A multifractal wavelet model is employed to accurately capture the LRD 11 Mbps bit-error process.

Effective congestion control for QoS enhancement of self-similar multimedia traffic

Owing to the existence of noticeable concentrated periods of contention and idleness, self-similar traffic can greatly increase packet delay and loss probability and thus reduce system resource utilisation. The development of efficient congestion control mechanisms plays a central role in the improvement of network quality of service (QoS), in particular for real-time multimedia applications. By exploiting the property of scale-invariant burstiness and correlation inherent in self-similar traffic, the authors propose an effective congestion control scheme, named adaptive wavelet and probability-based scheme (AWP), which concurrently operates over multiple time scales. AWP adopts the extended multifractal wavelet model (EMWM) for analysing estimated traffic volume across multiple time scales. Furthermore, a new auto-correction algorithm based on Bayes’ theory for confidence analysis is employed to examine the validity of the predicted information. The analysis results can be used to enhance the adaptability of the prediction algorithm. In particular, the AWP framework can be easily extended to more than two time scales by increasing the level of wavelet transforms, which brings AWP a natural advantage in implementation and scalability. A series of simulation experiments have demonstrated that the proposed AWP scheme is superior to TCP and TFRC as it can greatly improve the QoS of multimedia data transmission while avoiding congestion collapse on the network.

Conservative Cascades for Multifractal Traffic Prediction

In this paper we propose a novel traffic prediction method, based on the statistical analysis of the coefficients of a multifractal wavelet model. The predictor is computationally efficient because it is based on a simple equation on the coefficients of the wavelet transform. It is also highly accurate because it takes into account several higher order statistics over a wide range of time scales. We verify these characteristics using the predictor over several real traffic traces.

A New Approach to Cell Loss Analysis for Long-Range Dependent Network Traffic

A new expression for cell/packet loss probability in an ATM and packet switched queue system with a finite buffer is presented. Cell and packet loss analysis is based on the new concept of a buffer overflow cluster and the overflow probability for a queue with an infinite buffer. This approach holds for a wide variety of long-range dependent traffic sources typical of wide-area networks, as well as Internet and other communication traffics. The method is verified by simulations of two long-range dependent traffic scenarios: fractional Gaussian noise and multifractal wavelet model traffic with a beta marginal distribution.

Modelling and control of broad band traffic using multiplicative multifractal cascades

We present the results on the modelling and synthesis of broad-band traffic processes namely ethernet inter-arrival times using the VVGM (variable variance gaussian multiplier) multiplicative multifractal model. This model is shown to be more appropriate for modelling network traffic which possess time varying scaling/self-similarity and burstiness. The model gives a simple and efficient technique to synthesise Ethernet inter-arrival times. The results of the detailed statistical and multifractal analysis performed on the original and the synthesised traces are presented and the performance is compared with other models in the literature, such as the Poisson process, and the Multifractal Wavelet Model (MWM) process. It is also shown empirically that a single server queue preserves the multifractal character of the process by analysing its inter-departure process when fed with the multifractal traces. The result of the existence of a global-scaling exponent for multifractal cascades and its application in queueing theory are discussed. We propose tracking and control algorithms for controlling network congestion with bursty traffic modelled by multifractal cascade processes, characterised by the Holder exponents, the value of which at an interval indicates the burstiness in the traffic at that point. This value has to be estimated and used for the estimation of the congestion and predictive control of the traffic in broadband networks. The estimation can be done by employing wavelet transforms and a Kalman filter based predictor for predicting the burstiness of the traffic.

A multifractal wavelet model with application to network traffic

We develop a new multiscale modeling framework for characterizing positive-valued data with long-range-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 N-point 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.