69 research outputs found
Time series classification based on fractal properties
The article considers classification task of fractal time series by the meta
algorithms based on decision trees. Binomial multiplicative stochastic cascades
are used as input time series. Comparative analysis of the classification
approaches based on different features is carried out. The results indicate the
advantage of the machine learning methods over the traditional estimating the
degree of self-similarity.Comment: 4 pages, 2 figures, 3 equations, 1 tabl
The Dynamics of Internet Traffic: Self-Similarity, Self-Organization, and Complex Phenomena
The Internet is the most complex system ever created in human history.
Therefore, its dynamics and traffic unsurprisingly take on a rich variety of
complex dynamics, self-organization, and other phenomena that have been
researched for years. This paper is a review of the complex dynamics of
Internet traffic. Departing from normal treatises, we will take a view from
both the network engineering and physics perspectives showing the strengths and
weaknesses as well as insights of both. In addition, many less covered
phenomena such as traffic oscillations, large-scale effects of worm traffic,
and comparisons of the Internet and biological models will be covered.Comment: 63 pages, 7 figures, 7 tables, submitted to Advances in Complex
System
Wavelet and Multiscale Analysis of Network Traffic
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 behaviour 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 describe 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
Multifractal Analysis of a Class of Additive Processes with Correlated Non-Stationary Increments
International audienc
Renewal of singularity sets of statistically self-similar measures
This paper investigates new properties concerning the multifractal structure
of a class of statistically self-similar measures. These measures include the
well-known Mandelbrot multiplicative cascades, sometimes called independent
random cascades. We evaluate the scale at which the multifractal structure of
these measures becomes discernible. The value of this scale is obtained through
what we call the growth speed in H\"older singularity sets of a Borel measure.
This growth speed yields new information on the multifractal behavior of the
rescaled copies involved in the structure of statistically self-similar
measures. Our results are useful to understand the multifractal nature of
various heterogeneous jump processes
On the multiresolution structure of Internet traffic traces
Internet traffic on a network link can be modeled as a stochastic process.
After detecting and quantifying the properties of this process, using
statistical tools, a series of mathematical models is developed, culminating in
one that is able to generate ``traffic'' that exhibits --as a key feature-- the
same difference in behavior for different time scales, as observed in real
traffic, and is moreover indistinguishable from real traffic by other
statistical tests as well. Tools inspired from the models are then used to
determine and calibrate the type of activity taking place in each of the time
scales. Surprisingly, the above procedure does not require any detailed
information originating from either the network dynamics, or the decomposition
of the total traffic into its constituent user connections, but rather only the
compliance of these connections to very weak conditions.Comment: 57 pages, color figures. Figures are of low quality due to space
consideration
Local Effective Hölder Exponent Estimation on the Wavelet Transform Maxima Tree
We present a robust method of estimating an effective H\"older exponent locally at an arbitrary resolution. The method is motivated by the multiplicative cascade paradigm, and implemented on the hierarchy of singularities revealed with the wavelet transform modulus maxima tree. In addition, we illustrate the possibility of the direct estimation of the scaling spectrum of the effective H\"older exponent, and we link it to the established partition functions based multifractal formalism. We motivate both the local and the global multifractal analysis by showing examples of computer generated and real life time series
Uniform convergence for complex -martingales
Positive -martingales were developed as a general framework that extends
the positive measure-valued martingales and are meant to model intermittent
turbulence. We extend their scope by allowing the martingale to take complex
values. We focus on martingales constructed on the interval and
replace random measures by random functions. We specify a large class of such
martingales for which we provide a general sufficient condition for almost sure
uniform convergence to a nontrivial limit. Such a limit yields new examples of
naturally generated multifractal processes that may be of use in multifractal
signals modeling.Comment: Published in at http://dx.doi.org/10.1214/09-AAP664 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Bio-inspired route estimation in cognitive radio networks
Cognitive radio is a technique that was originally created for the proper use of the radio electric spectrum due its underuse. A few methods were used to predict the network traffic to determine the occupancy of the spectrum and then use the ‘holes’ between the transmissions of primary users. The goal is to guarantee a complete transmission for the second user while not interrupting the trans-mission of primary users. This study seeks the multifractal generation of traffic for a specific radio electric spectrum as well as a bio-inspired route estimation for secondary users. It uses the MFHW algorithm to generate multifractal traces and two bio-inspired algo-rithms: Ant Colony Optimization and Max Feeding to calculate the secondary user’s path. Multifractal characteristics offer a predic-tion, which is 10% lower in comparison with the original traffic values and a complete transmission for secondary users. In fact, a hybrid strategy combining both bio-inspired algorithms promise a reduction in handoff. The purpose of this research consists on deriving future investigation in the generation of multifractal traffic and a mobility spectrum using bio-inspired algorithms
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