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 Time Series Analysis of Computer Network Traffic in a Dedicated Link Aggregation

2021 ◽  
Author(s):  
Ginno Millán ◽  
Gastón Lefranc ◽  
Román Osorio-Comparán ◽  
Víctor Lomas-Berrie
Keyword(s):  
Time Series ◽  
Traffic Flow ◽  
Long Range ◽  
Computer Networks ◽  
Fractal Analysis ◽  
High Speed ◽  
Computer Network ◽  
Time Series Analyses ◽  
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 have fractal behavior when the Hurst exponent is 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 traffic and its impulsiveness during a fractal analysis of temporal scales. Finally, based on the results of the time series analyses, the fact that the traffic flows of current computer networks exhibit fractal behavior with a long-range dependency is reaffirmed.

scholarly journals Time series analysis of computer network traffic in a dedicated link aggregation

2021 ◽  
Author(s):  
Ginno Millán
Keyword(s):  
Time Series ◽  
Traffic Flow ◽  
Long Range ◽  
Computer Networks ◽  
Fractal Analysis ◽  
High Speed ◽  
Computer Network ◽  
Time Series Analyses ◽  
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 have fractal behavior when the Hurst exponent is 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 traffic and its impulsiveness during a fractal analysis of temporal scales. Finally, based on the results of the time series analyses, the fact that the traffic flows of current computer networks exhibit fractal behavior with a long-range dependency is reaffirmed.

scholarly journals Time Series Analysis of Computer Network Traffic in a Dedicated Link Aggregation

2021 ◽  
Author(s):  
Ginno Millán ◽  
Gastón Lefranc ◽  
Román Osorio-Comparán ◽  
Víctor Lomas-Berrie
Keyword(s):  
Time Series ◽  
Traffic Flow ◽  
Long Range ◽  
Computer Networks ◽  
Fractal Analysis ◽  
High Speed ◽  
Computer Network ◽  
Time Series Analyses ◽  
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 have fractal behavior when the Hurst exponent is 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 traffic and its impulsiveness during a fractal analysis of temporal scales. Finally, based on the results of the time series analyses, the fact that the traffic flows of current computer networks exhibit fractal behavior with a long-range dependency is reaffirmed.

scholarly journals Time Series Analysis of Computer Network Traffic in a Dedicated Link Aggregation

2021 ◽  
Author(s):  
Ginno Millán ◽  
Gastón Lefranc ◽  
Román Osorio-Comparán ◽  
Víctor Lomas-Barrie
Keyword(s):  
Time Series ◽  
Traffic Flow ◽  
Long Range ◽  
Computer Networks ◽  
Fractal Analysis ◽  
High Speed ◽  
Computer Network ◽  
Time Series Analyses ◽  
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 have fractal behavior when the Hurst exponent is 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 traffic and its impulsiveness during a fractal analysis of temporal scales. Finally, based on the results of the time series analyses, the fact that the traffic flows of current computer networks exhibit fractal behavior with a long-range dependency is 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 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 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.

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

2021 ◽  
Author(s):  
Ginno Millán
Keyword(s):  
Computer Networks ◽  
Network Flow ◽  
Hurst Exponent ◽  
High Speed ◽  
Second Order ◽  
Traffic Flows ◽  
Temporal Series ◽  
Self Similar ◽  
Speed Computer ◽  
Hurst Exponents

This paper proposes a multifractal model, with the aim of providing a possible explanation for the locality phenomenon that appears in the estimation of the Hurst exponent in stationary second order temporal series representing self-similar traffic flows in current high-speed computer networks. It is shown analytically that this phenomenon occurs if the network flow consists of several components with different Hurst exponents.

scholarly journals A Simple Chaotic Map Model for Fractal Traffic Flows in High-speed Computer Networks

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

An extension of the models used to generate fractal traffic flows is presented 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 by the model, 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.<br>

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