Fast, Approximate Synthesis of Fractional Gaussian Noise for Generating Self-Similar Network Traffic

Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically self-similar processes instead of traditional Poisson processes [LTWW94,PF95]. One difficulty in dealing with self-similar models is how to efficiently synthesize traces (sample paths) corresponding to self-similar traffic. We present a fast Fourier transform method for synthesizing approximate self-similar sample paths for one type of self-similar process, Fractional Gaussian Noise, and assess its performance and validity. We find that the method is as fast or faster than existing methods and appears to generate close approximations to true self-similar sample paths. We also discuss issues in using such synthesized sample paths for simulating network traffic, and how an approximation used by our method can dramatically speed up evaluation of Whittle's estimator for H, the Hurst parameter giving the strength of long-range dependence present in a self-similar time series.Comment: 14 page

Video traffic modeling and delivery

Video is becoming a major component of the network traffic, and thus there has been a great interest to model video traffic. It is known that video traffic possesses short range dependence (SRD) and long range dependence (LRD) properties, which can drastically affect network performance. By decomposing a video sequence into three parts, according to its motion activity, Markov-modulated self-similar process model is first proposed to capture autocorrelation function (ACF) characteristics of MPEG video traffic. Furthermore, generalized Beta distribution is proposed to model the probability density functions (PDFs) of MPEG video traffic. It is observed that the ACF of MPEG video traffic fluctuates around three envelopes, reflecting the fact that different coding methods reduce the data dependency by different amount. This observation has led to a more accurate model, structurally modulated self-similar process model, which captures the ACF of the traffic, both SRD and LRD, by exploiting the MPEG structure. This model is subsequently simplified by simply modulating three self-similar processes, resulting in a much simpler model having the same accuracy as the structurally modulated self-similar process model. To justify the validity of the proposed models for video transmission, the cell loss ratios (CLRs) of a server with a limited buffer size driven by the empirical trace are compared to those driven by the proposed models. The differences are within one order, which are hardly achievable by other models, even for the case of JPEG video traffic. In the second part of this dissertation, two dynamic bandwidth allocation algorithms are proposed for pre-recorded and real-time video delivery, respectively. One is based on scene change identification, and the other is based on frame differences. The proposed algorithms can increase the bandwidth utilization by a factor of two to five, as compared to the constant bit rate (CBR) service using peak rate assignment

Using Digital Filtration for Hurst Parameter Estimation

We present a new method to estimate the Hurst parameter. The method exploits the form of the autocorrelation function for second-order self-similar processes and is based on one-pass digital filtration. We compare the performance and properties of the new method with that of the most common methods

Fractal-based models for internet traffic and their application to secure data transmission

This thesis studies the application of fractal geometry to the application of covert communications systems. This involves the process of hiding information in background noise; the information being encrypted or otherwise. Models and methods are considered with regard to two communications systems: (i) wireless communications; (ii) internet communications. In practice, of course, communication through the Internet cannot be disassociated from wireless communications as Internet traffic is 'piped' through a network that can include wireless communications (e.g. satellite telecommunications). However, in terms of developing models and methods for covert communications in general, points (i) and (ii) above require different approaches and access to different technologies. With regard to (i) above, we develop two methods based on fractal modulation and multi-fractal modulation. With regard to (ii), we implement a practical method and associated software for covert transmission of file attachments based on an analysis of Internet traffic noise. In both cases, however, two fractal models are considered; the first is the standard Random Scaling Fractal model and the second is a generalisation of this model that incorporates a greater range of spectral properties than the first—a Generalised Random Scaling Fractal Model. [Continues.

Wavelet-based simulation of fractional Brownian motion revisited

We reexamine the wavelet-based simulation procedure for fractional Brownian motion proposed by Abry and Sellan. We clarify in what sense the wavelet-based simulation procedure works, shed light on the structure of associated fractional low- and high-pass filters, and consequently suggest some modifications to the simulation algorithm

Multifractal stationary random measures and multifractal random walks with log-infinitely divisible scaling laws

We define a large class of continuous time multifractal random measures and processes with arbitrary log-infinitely divisible exact or asymptotic scaling law. These processes generalize within a unified framework both the recently defined log-normal Multifractal Random Walk (MRW) [Bacry-Delour-Muzy] and the log-Poisson "product of cynlindrical pulses" [Barral-Mandelbrot]. Our construction is based on some ``continuous stochastic multiplication'' from coarse to fine scales that can be seen as a continuous interpolation of discrete multiplicative cascades. We prove the stochastic convergence of the defined processes and study their main statistical properties. The question of genericity (universality) of limit multifractal processes is addressed within this new framework. We finally provide some methods for numerical simulations and discuss some specific examples.Comment: 24 pages, 4 figure

Distinguishing DDoS attacks from flash crowds using probability metrics

Both Flash crowds and DDoS (Distributed Denial-of-Service) attacks have very similar properties in terms of internet traffic, however Flash crowds are legitimate flows and DDoS attacks are illegitimate flows, and DDoS attacks have been a serious threat to internet security and stability. In this paper we propose a set of novel methods using probability metrics to distinguish DDoS attacks from Flash crowds effectively, and our simulations show that the proposed methods work well. In particular, these mathods can not only distinguish DDoS attacks from Flash crowds clearly, but also can distinguish the anomaly flow being DDoS attacks flow or being Flash crowd flow from Normal network flow effectively. Furthermore, we show our proposed hybrid probability metrics can greatly reduce both false positive and false negative rates in detection.<br /

A study of self-similar traffic generation for ATM networks

This thesis discusses the efficient and accurate generation of self-similar traffic for ATM networks. ATM networks have been developed to carry multiple service categories. Since the traffic on a number of existing networks is bursty, much research focuses on how to capture the characteristics of traffic to reduce the impact of burstiness. Conventional traffic models do not represent the characteristics of burstiness well, but self-similar traffic models provide a closer approximation. Self-similar traffic models have two fundamental properties, long-range dependence and infinite variance, which have been found in a large number of measurements of real traffic. Therefore, generation of self-similar traffic is vital for the accurate simulation of ATM networks. The main starting point for self-similar traffic generation is the production of fractional Brownian motion (FBM) or fractional Gaussian noise (FGN). In this thesis six algorithms are brought together so that their efficiency and accuracy can be assessed. It is shown that the discrete FGN (dPGN) algorithm and the Weierstrass-Mandelbrot (WM) function are the best in terms of accuracy while the random midpoint displacement (RMD) algorithm, successive random addition (SRA) algorithm, and the WM function are superior in terms of efficiency. Three hybrid approaches are suggested to overcome the inefficiency or inaccuracy of the six algorithms. The combination of the dFGN and RMD algorithm was found to be the best in that it can generate accurate samples efficiently and on-the-fly. After generating FBM sample traces, a further transformation needs to be conducted with either the marginal distribution model or the storage model to produce self-similar traffic. The storage model is a better transformation because it provides a more rigorous mathematical derivation and interpretation of physical meaning. The suitability of using selected Hurst estimators, the rescaled adjusted range (R/S) statistic, the variance-time (VT) plot, and Whittle's approximate maximum likelihood estimator (MLE), is also covered. Whittle's MLE is the better estimator, the R/S statistic can only be used as a reference, and the VT plot might misrepresent the actual Hurst value. An improved method for the generation of self-similar traces and their conversion to traffic has been proposed. This, combined with the identification of reliable methods for the estimators of the Hurst parameter, significantly advances the use of self-similar traffic models in ATM network simulation