scholarly journals The Associative Multifractal Process: A Novel Model for Computer Network Traffic Flows

2021 ◽  
Author(s):  
Ginno Millán ◽  
Gastón Lefranc ◽  
Román Osorio-Comparán
Keyword(s):  
Mathematical Model ◽  
Time Series ◽  
High Speed ◽  
Computer Network ◽  
Traffic Flows ◽  
Multifractal Formalism ◽  
Proposed Model ◽  
Self Similar ◽  
Speed Computer ◽  
Novel Model

A novel constructive mathematical model based on the multifractal formalism in order to accurately characterizing the localized fluctuations present in the course of traffic flows today high-speed computer networks is presented. The proposed model has the target to analyze self-similar second-order time series representative of traffic flows in terms of their roughness and impulsivity.

scholarly journals The Associative Multifractal Process: A Novel Model for Computer Network Traffic Flows

2021 ◽  
Author(s):  
Ginno Millán ◽  
Gastón Lefranc ◽  
Román Osorio-Comparán
Keyword(s):  
Mathematical Model ◽  
Time Series ◽  
High Speed ◽  
Computer Network ◽  
Traffic Flows ◽  
Multifractal Formalism ◽  
Proposed Model ◽  
Self Similar ◽  
Speed Computer ◽  
Novel Model

A novel constructive mathematical model based on the multifractal formalism in order to accurately characterizing the localized fluctuations present in the course of traffic flows today high-speed computer networks is presented. The proposed model has the target to analyze self-similar second-order time series representative of traffic flows in terms of their roughness and impulsivity.

scholarly journals Discussion of the Analysis of Self-similar Teletraffic with Long-range Dependence (LRD) at the Network Layer Level

2010 ◽  
Vol 5 (5) ◽  
pp. 799
Author(s):  
Ginno Millán ◽  
Héctor Kaschel ◽  
Gastón Lefranc
Keyword(s):  
Long Range ◽  
High Speed ◽  
Computer Network ◽  
Specific Task ◽  
Traffic Flows ◽  
Network Layer ◽  
Traffic Models ◽  
Self Similar ◽  
Speed Computer ◽  
Theoretical Foundations

Traffic streams, sources as well as aggregated traffic flows, often exhibit long-range-dependent (LRD) properties. This paper presents the theoretical foundations to justify that the behavior of traffic in a high-speed computer network can be modeled from a self-similar perspective by limiting its scope of analysis to the network layer, since the most relevant properties of self-similar processes are consistent for use in the formulation of traffic models when performing this specific task.

scholarly journals Self-similar Traffic Analysis at Network Layer Level. Part II: Application

2021 ◽  
Author(s):  
Ginno Millán
Keyword(s):  
High Speed ◽  
Computer Network ◽  
The Self ◽  
Long Range Dependence ◽  
Traffic Flows ◽  
Efficient Tool ◽  
Network Layer ◽  
Self Similar ◽  
Novel Concept ◽  
Speed Computer

In previous work has been proposed, and theoretically confirmed, that the self-similar whit long-range dependence traffic flows may be limited to the network layer. In this paper applies this novel concept to the study of traffic recorded in an IEEE 802.3u network environment whit the aim to prove their validity as a simply and efficient tool for high speed computer network traffic flows analysis.

scholarly journals Self-similar Traffic Analysis at Network Layer Level. Part I: Fundamentals

2021 ◽  
Author(s):  
Ginno Millán
Keyword(s):  
Long Range ◽  
High Speed ◽  
Computer Network ◽  
Specific Task ◽  
Traffic Flows ◽  
Network Layer ◽  
Traffic Models ◽  
Self Similar ◽  
Speed Computer ◽  
Theoretical Foundations

Traffic streams, sources as well as aggregated traffic flows, often exhibit long-range-dependent (LRD) properties. This paper presents the theoretical foundations to justify that the behavior of traffic in a high-speed computer network can be modeled from a self-similar perspective by limiting its scope of analysis at the network layer, given that the most relevant properties of self-similar processes are consistent for use in the formulation of traffic models when performing this specific task.

scholarly journals Preliminaries on the Accurate Estimation of the Hurst Exponent Using Time Series

2021 ◽  
Author(s):  
Ginno Millán ◽  
Román Osorio-Comparán ◽  
Gastón Lefranc
Keyword(s):  
Time Series ◽  
Hurst Exponent ◽  
High Speed ◽  
Mean Squared Error ◽  
Computer Network ◽  
Accurate Estimation ◽  
Minimum Length ◽  
Squared Error ◽  
In Series ◽  
Speed Computer

<div>This article explores the required amount of time series points from a high-speed computer network to accurately estimate the Hurst exponent. The methodology consists in designing an experiment using estimators that are applied to time series addresses resulting from the capture of high-speed network traffic, followed by addressing the minimum amount of point required to obtain in accurate estimates of the Hurst exponent. The methodology addresses the exhaustive analysis of the Hurst exponent considering bias behaviour, standard deviation, and Mean Squared Error using fractional Gaussian noise signals with stationary increases. Our results show that the Whittle estimator successfully estimates the Hurst exponent in series with few</div><div>points. Based on the results obtained, a minimum length for the time series is empirically proposed. Finally, to validate the results, the methodology is applied to real traffic captures in a high-speed computer network.</div>

Representative Time Series Fractal Analysis of the Traffic Flows of a Dedicated High-Speed Link

2021 ◽  
Author(s):  
Ginno Millan ◽  
manuel vargas ◽  
Guillermo Fuertes
Keyword(s):  
Time Series ◽  
Traffic Flow ◽  
Long Range ◽  
Computer Networks ◽  
Fractal Analysis ◽  
High Speed ◽  
Long Range Dependence ◽  
Traffic Flows ◽  
Speed Computer

Fractal behavior and long-range dependence are widely observed in measurements and characterization of traffic flow in high-speed computer networks of different technologies and coverage levels. This paper presents the results obtained when applying fractal analysis techniques on a time series obtained from traffic captures coming from an application server connected to the internet through a high-speed link. The results obtained show that traffic flow in the dedicated high-speed network link exhibited fractal behavior since the Hurst exponent was in the range of 0.5, 1, the fractal dimension between 1, 1.5, and the correlation coefficient between -0.5, 0. Based on these results, it is ideal to characterize both the singularities of the fractal traffic and its impulsiveness during a fractal analysis of temporal scales. Finally, based on the results of the time series analyzes, the fact that the traffic flows of current computer networks exhibited fractal behavior with a long-range dependence was reaffirmed.

scholarly journals A Simple Chaotic Map Model for Fractal Traffic Flows in High-speed Computer Networks (Extended and Renewed Version)

2021 ◽  
Author(s):  
Ginno Millán
Keyword(s):  
Computer Networks ◽  
Hurst Exponent ◽  
High Speed ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Traffic Flows ◽  
One Dimensional ◽  
Temporal Series ◽  
Proposed Model ◽  
Speed Computer

This paper presents an extension of the models used to generate fractal traffic flows in high-speed computer networks by means of the formulation of a model that considers the use of one-dimensional chaotic maps. Based on the disaggregation of the temporal series generated, a valid explanation of behavior of the values of Hurst exponent is proposed and the feasibility of their control from the parameters of the proposed model is shown.

scholarly journals A simple multifractal model for self-similar traffic flows in high-speed computer networks

2021 ◽  
Author(s):  
Ginno Millán
Keyword(s):  
High Speed ◽  
Process Models ◽  
Traffic Modeling ◽  
Traffic Flows ◽  
Markov Modulated Poisson Process ◽  
Traffic Trace ◽  
Self Similar ◽  
Markov Modulated ◽  
Speed Computer ◽  
Fitting Model

This paper presents a simple and fast technique of multifractal traffic modeling. It proposes a method of fitting model to a given traffic trace. A comparison of simulation results obtained for an exemplary trace, multifractal model and Markov Modulated Poisson Process models has been performed.

scholarly journals Traffic flows analysis in high-speed computer networks using time series (Draft 2)

2021 ◽  
Author(s):  
Ginno Millán
Keyword(s):  
Time Series ◽  
Hurst Exponent ◽  
High Speed ◽  
Minimum Length ◽  
Traffic Network ◽  
Traffic Flows ◽  
High Speed Network ◽  
In Series ◽  
Speed Computer ◽  
Real Traffic

This article explores the required amount of time series points from a high-speed traffic network to accurately estimate the Hurst exponent. The methodology consists in designing an experiment using estimators that are applied to time series, followed by addressing the minimum amount of points required to obtain accurate estimates of the Hurst exponent in real-time. The methodology addresses the exhaustive analysis of the Hurst exponent considering bias behavior, standard deviation, mean square error, and convergence using fractional gaussian noise signals with stationary increases. Our results show that the Whittle estimator successfully estimates the Hurst exponent in series with few points. Based on the results obtained, a minimum length for the time series is empirically proposed. Finally, to validate the results, the methodology is applied to real traffic captures in a high-speed network based on the IEEE 802.3ab standard.

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