Modelling the self-similar behaviour of network traffic

2000 ◽  
Vol 34 (1) ◽  
pp. 37-47 ◽  
Author(s):  
Christos Stathis ◽  
Basil Maglaris
Keyword(s):  
Network Traffic ◽  
The Self ◽  
Self Similar

scholarly journals Statistical research and modeling network traffic

2021 ◽  
Vol 244 ◽  
pp. 07002
Author(s):  
Tatiana Tatarnikova ◽  
Igor Sikarev ◽  
Vladimir Karetnikov ◽  
Artem Butsanets
Keyword(s):  
Network Traffic ◽  
Least Squares Method ◽  
Regression Line ◽  
The Self ◽  
Logarithmic Scale ◽  
Self Similarity ◽  
Statistical Research ◽  
Similarity Parameter ◽  
Real Network ◽  
Self Similar

The self-similarity properties of the considered traffic were checked on different time scales obtained on the available daily traffic data. An estimate of the tail severity of the distribution self-similar traffic was obtained by constructing a regression line for the additional distribution function on a logarithmic scale. The self-similarity parameter value, determined by the severity of the distribution “tail”, made it possible to confirm the assumption of traffic self-similarity. A review of models simulating real network traffic with a self-similar structure was made. Implemented tools for generating artificial traffic in accordance with the considered models. Made comparison of artificial network traffic generators according to the least squares method criterion for approximating the artificial traffic point values by the approximation function of traffic. Qualitative assessments traffic generators in the form of the software implementation complexity were taken into account, which, however, can be a subjective assessment. Comparative characteristics allow you to choose some generators that most faithfully simulate real network traffic. The proposed sequence of methods to study the network traffic properties is necessary to understand its nature and to develop appropriate models that simulate real network traffic.

scholarly journals Statistical models of network traffic

Connectivity ◽  
2021 ◽  
Vol 149 (1) ◽  
Author(s):  
N. M. Yakymchuk ◽  
Keyword(s):  
Network Traffic ◽  
High Speed ◽  
Packet Switching ◽  
Telecommunication Networks ◽  
The Self ◽  
Statistical Characteristics ◽  
Similar Process ◽  
Data Traffic ◽  
Similarity Parameter ◽  
Self Similar

The article considers the issues of statistical modeling of traffic in telecommunication networks with packet switching. The simulation results are used in the development of network technical condition management systems, in particular, diagnostics, troubleshooting and network configuration management. The peculiarities of congestion control of separate network segments are emphasized. With improper analysis the overload condition can be mistaken for equipment failure. Therefore, control and elimination of congestion is a statistical task. The concept of end-to-end network diagnostics is considered. This concept provides for effective assessment of the quality of functioning of all network components taking into account their interrelationships. The main issues are the interaction of equipment, inefficient configuration, improper network organization and user operation. Methods of traffic statistical control characteristics based on perforated and marker bucket algorithms are analyzed. A feature of these algorithms is the formation of a strict output stream at a rate that does not depend on the non-uniformity of the input stream. The possibility of improving the token bucket algorithm by adapting to changes in the statistical characteristics of traffic is shown. To solve this problem, statistical mathematical models of network traffic are built. Data traffic circulating in telecommunication networks by packet switching has self-similar (fractal) properties. The self-similar process retains its properties when considered at different time scales (invariance to scale changes). The degree of statistical stability of the process with multiple scaling is determined by the Hirst parameter (the self-similarity parameter). Graphs of statistical characteristics of low-speed and high-speed data traffic are obtained. Their comparative analysis is carried out.

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

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

This paper proposes a new multifractal model with the aim to provide a possible explanation for the locality phenomena to appear in the estimation of the Hurst exponent in stationary second order temporal series, representing the self-similar traffic flows in high-speed computer networks. Analytically it is shown that this phenomenon occurs if the network traffic flows consists of several components whit different Hurst exponents.

scholarly journals Basic characteristics of networks with self-similar traffic simulation

2019 ◽  
Vol 20 (1-2) ◽  
pp. 137-141
Author(s):  
Marek Aleksander ◽  
Roman Odarchenko ◽  
Sergiy Gnatyuk ◽  
Tadeusz Kantor
Keyword(s):  
Stochastic Process ◽  
Real Time ◽  
Experimental Research ◽  
Network Traffic ◽  
Network Performance ◽  
The Self ◽  
Self Similarity ◽  
Complex Models ◽  
Self Similar ◽  
Basic Characteristics

This paper is devoted to simulations the networks with self-similar traffic. The self-similarity in the stochastic process is identified by calculation of the Herst parameter value. Based on the results, received from the experimental research of network performance, we may conclude that the observed traffic in real-time mode is self-similar by its nature. Given results may be used for the further investigation of network traffic and work on the existing models of network traffic (particularly for new networks concepts like IoT, WSN, BYOD etc) from viewpoint of its cybersecurity. Furthermore, the adequacy of the description of real is achieved by complexifying the models, combining several models and integration of new parameters. Accordingly, for more complex models, there are higher computing abilities needed or longer time for the generation of traffic realization..

scholarly journals Hausdorff measure and Assouad dimension of generic self-conformal IFS on the line

2020 ◽  
pp. 1-31
Author(s):  
Balázs Bárány ◽  
Károly Simon ◽  
István Kolossváry ◽  
Michał Rams
Keyword(s):  
Hausdorff Measure ◽  
Similar Case ◽  
Iterated Function Systems ◽  
The Self ◽  
Dimensional Hausdorff Measure ◽  
Assouad Dimension ◽  
Iterated Function ◽  
Self Similar ◽  
Weak Separation ◽  
Topological Sense

This paper considers self-conformal iterated function systems (IFSs) on the real line whose first level cylinders overlap. In the space of self-conformal IFSs, we show that generically (in topological sense) if the attractor of such a system has Hausdorff dimension less than 1 then it has zero appropriate dimensional Hausdorff measure and its Assouad dimension is equal to 1. Our main contribution is in showing that if the cylinders intersect then the IFS generically does not satisfy the weak separation property and hence, we may apply a recent result of Angelevska, Käenmäki and Troscheit. This phenomenon holds for transversal families (in particular for the translation family) typically, in the self-similar case, in both topological and in measure theoretical sense, and in the more general self-conformal case in the topological sense.

scholarly journals Onset of the Mach Reflection of Zel’dovich–von Neumann–Döring Detonations

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 314
Author(s):  
Tianyu Jing ◽  
Huilan Ren ◽  
Jian Li
Keyword(s):  
Hot Spot ◽  
Mach Reflection ◽  
Near Field ◽  
The Self ◽  
Small Scale ◽  
Mach Stem ◽  
Self Similarity ◽  
Von Neumann ◽  
Similarity Problem ◽  
Self Similar

The present study investigates the similarity problem associated with the onset of the Mach reflection of Zel’dovich–von Neumann–Döring (ZND) detonations in the near field. The results reveal that the self-similarity in the frozen-limit regime is strictly valid only within a small scale, i.e., of the order of the induction length. The Mach reflection becomes non-self-similar during the transition of the Mach stem from “frozen” to “reactive” by coupling with the reaction zone. The triple-point trajectory first rises from the self-similar result due to compressive waves generated by the “hot spot”, and then decays after establishment of the reactive Mach stem. It is also found, by removing the restriction, that the frozen limit can be extended to a much larger distance than expected. The obtained results elucidate the physical origin of the onset of Mach reflection with chemical reactions, which has previously been observed in both experiments and numerical simulations.

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