scholarly journals Self-Similar Markovian Sources

2020 ◽  
Vol 10 (11) ◽  
pp. 3727 ◽  
Author(s):  
Adam Domański ◽  
Joanna Domańska ◽  
Katarzyna Filus ◽  
Jakub Szyguła ◽  
Tadeusz Czachórski
Keyword(s):  
Long Range ◽  
Computer Networks ◽  
Markov Models ◽  
Internet Traffic ◽  
Similar Process ◽  
Queueing Models ◽  
Network Structures ◽  
Self Similarity ◽  
Self Similar

Markov queueing models are a powerful tool to evaluate the performance of computer networks and have been used in telecommunication studies for over 100 years. To apply them to the evaluation of the modern Internet, we should not only adapt them to the contemporary network structures but also include a description of the complex stochastic patterns (self-similarity and long-range dependance) of transmitted flows. We examine the features of two Markov models of an almost self-similar process, keeping in mind the modeling of Internet traffic. We have found that the obtained results are comparable with those achieved using a well-known generator of self-similar traffic.

scholarly journals Proposal of an estimator of the Hurst parameter for a self-similar process representative of the degree of randomness of the recorded traffic in IEEE 802.3-2005 networks

2021 ◽  
Author(s):  
Ginno Millán
Keyword(s):  
Computer Networks ◽  
Memory Structure ◽  
Similar Process ◽  
Hurst Parameter ◽  
Long Term Memory ◽  
Term Memory ◽  
Traffic Stream ◽  
Self Similar

An hypothesis for the existence of a process with long term memory structure, that represents the independence between the degree of randomness of the traffic generated by the sources and the pattern of traffic stream exhibited by the network is presented, discussed and developed. This methodology is offered as a new and alternative way of approaching the estimation of performance and the design of computer networks ruled by the standard IEEE 802.3-2005.

scholarly journals Abstract Description of Internet Traffic of Generalized Cauchy Type

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Ming Li ◽  
Wei Zhao
Keyword(s):  
Fractal Dimension ◽  
Fundamental Problem ◽  
Internet Traffic ◽  
Similar Process ◽  
Hurst Parameter ◽  
Cauchy Type ◽  
Self Similarity ◽  
Abstract Description ◽  
The One ◽  
Traffic Theory

Self-similar process with long-range dependence (LRD), that is, fractional Gaussian noise (fGn) with LRD is a widely used model of Internet traffic. It is indexed by its Hurst parameterHfGnthat linearly relates to its fractal dimensionDfGn. Note that, on the one hand, the fractal dimensionDof traffic measures local self-similarity. On the other hand, LRD is a global property of traffic, which is characterized by its Hurst parameterH. However, by using fGn, both the self-similarity and the LRD of traffic are measured byHfGn. Therefore, there is a limitation for fGn to accurately model traffic. Recently, the generalized Cauchy (GC) process was introduced to model traffic with the flexibility to separately measure the fractal dimensionDGCand the Hurst parameterHGCof traffic. However, there is a fundamental problem whether or not there exists the generality that the GC model is more conformable with real traffic than single parameter models, such as fGn,irrelevant of traffic traces used in experimental verification. The solution to that problem remains unknown but is desired for model evaluation in traffic theory or for model selection against specific issues, such as queuing analysis relating to the autocorrelation function (ACF) of arrival traffic. The key contribution of this paper is our solution to that fundamental problem (see Theorem 3.17) with the following features in analysis. (i) Set-valued analysis of the traffic of the fGn type. (ii) Set-valued analysis of the traffic of the GC type. (iii) Revealing the generality previously mentioned by comparing metrics of the traffic of the fGn type to that of the GC type.

scholarly journals Self-similar processes in collective risk theory

1998 ◽  
Vol 11 (4) ◽  
pp. 429-448 ◽  
Author(s):  
Zbigniew Michna
Keyword(s):  
Long Range ◽  
Risk Model ◽  
Queueing Systems ◽  
Risk Process ◽  
Risk Theory ◽  
Similar Process ◽  
Long Range Dependence ◽  
Insurance Company ◽  
Collective Risk ◽  
Self Similar

Collective risk theory is concerned with random fluctuations of the total assets and the risk reserve of an insurance company. In this paper we consider self-similar, continuous processes with stationary increments for the renewal model in risk theory. We construct a risk model which shows a mechanism of long range dependence of claims. We approximate the risk process by a self similar process with drift. The ruin probability within finite time is estimated for fractional Brownian motion with drift. A similar model is applicable in queueing systems, describing long range dependence in on/off processes and associated fluid models. The obtained results are useful in communication network models, as well as storage and inventory models.

scholarly journals Estimation of the self-similarity parameter in long memory processes

1970 ◽  
Vol 38 ◽  
pp. 32-37 ◽  
Author(s):  
MMA Sarker
Keyword(s):  
Long Memory ◽  
The Self ◽  
Similar Process ◽  
Long Range Dependence ◽  
Self Similarity ◽  
Similarity Parameter ◽  
Data Set ◽  
Memory Processes ◽  
Long Memory Processes ◽  
Self Similar

Long memory processes, where positive correlations between observations far apart in time and space decay very slowly to zero with increasing time lag, occur quite frequently in fields such as hydrology and economics. Stochastic processes that are invariant in distribution under judicious scaling of time and space, called self-similar process, can parsimoniously model the long-run properties of phenomena exhibiting long-range dependence. Four of the heuristic estimation approaches have been presented in this study so that the self-similarity parameter, H that gives the correlation structure in long memory processes, can be effectively estimated. Finally, the methods presented in this paper were applied to two observed time series, namely Nile River Data set and the VBR (Variable- Bit-Rate) data set. The estimated values of H for two data sets found from different methods suggest that all methods are not equally good for estimation. Keywords: Long memory process, long-range dependence, Self-similar process, Hurst Parameter, Gaussian noise. DOI: 10.3329/jme.v38i0.898 Journal of Mechanical Engineering Vol.38 Dec. 2007 pp.32-37  

scholarly journals Un modelo multifractal simplificado para flujos de tráfico autosimilares

2018 ◽  
pp. 20-25
Keyword(s):  
Computer Networks ◽  
Network Flow ◽  
Hurst Exponent ◽  
High Speed ◽  
The Self ◽  
Traffic Flows ◽  
Self Similarity ◽  
Temporal Series ◽  
Self Similar ◽  
Speed Computer

Un modelo multifractal simplificado para flujos de tráfico autosimilares A simplified multifractal model for self-similar traffic flows Ginno Millán Universidad Católica del Norte, Larrondo 1281, Coquimbo, Chile DOI: https://doi.org/10.33017/RevECIPeru2014.0003/ Resumen Este artículo propone un nuevo modelo multifractal, con el ánimo de proveer una posible explicación al fenómeno de localidad que aparece en la estimación del exponente de Hurst en series temporales estacionarias de segundo orden, representativas de los flujos de tráfico autosimilares en las actuales redes de computadoras de alta velocidad. Analíticamente se demuestra que este fenómeno se presenta cuando los flujos se componen de diversos tipos de tráficos con diferentes exponentes de Hurst. Descriptores: Autosimilitud, exponente de Hurst (H), fenómeno de localidad, multifractales. Abstract This paper proposes a new multifractal model, with the aim to provide a possible explanation to the locality phenomena to appear in the estimation of 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 flow consists of several components whit different Hurst exponents. Keywords: Self-similarity, Hurst exponent (H), locality phenomena, multifractals.

ANALYSIS OF THE PROCESS OF SELFSIMILARITY OF NETWORK TRAFFIC AS AN APPROACH TO DETECTING CYBER ATTACKS ON COMPUTER NETWORKS

2020 ◽  
Author(s):  
И.В. КОТЕНКО ◽  
А.М. КРИБЕЛЬ ◽  
О.С. ЛАУТА ◽  
И.Б. САЕНКО
Keyword(s):  
Brownian Motion ◽  
Computer Networks ◽  
Network Traffic ◽  
Telecommunication Network ◽  
Cyber Attacks ◽  
Self Similarity ◽  
Data Set ◽  
Fractal Brownian Motion ◽  
Self Similar

Предложен подход кобнаружению кибератак на компьютерные сети, основанный на выявлениианомалий в сетевом трафике путем оценки свойства самоподобия. Рассмотрены методы выявления долговременной зависимости в фрактальном броуновском движении и реальном сетевом трафике компьютерных сетей. Показано, что трафик телекоммуникационной сети является самоподобной структурой и его поведение близко к фрактальному броуновскому движению. В качестве инструментов при разработке данного подхода были использованы фрактальный анализ и математическая статистика. Анализируются вопросы программной реализации предлагаемого подхода и формирования набора данных, содержащего сетевые пакеты компьютерных сетей. Экспериментальные результаты, полученные с использованием сгенерированного набораданных, продемонстрировали наличие самоподобия у сетевого трафика компьютерных сетей и подтвердили высокую эффективность предлагаемого подхода: он позволяет обнаруживать кибератаки в реальном или близком к реальному масштабе времени. The paper discusses an approach to detecting cyber attacks on computer networks, based on identifying anomalies in network traffic by assessing its self-similarity property. Methods for identifying long-term dependence in fractal Brownian motion and real network traffic of computer networks are considered. It is shown that the traffic of a telecommunication network is a self-similar structure and its behavior is close to fractal Brownian motion. Fractal analysis and mathematical statistics were used as tools in the development of this approach. The issues of the software implementation of the proposed approach and the formation of a data set containing network packets of computer networks are considered. The experimental results obtained using the generated dataset demonstrated the existence of selfsimilarity in the network traffic of computer networks and confirmed the fair efficiency of the proposed approach. The proposed can be used to quickly detect cyber attacks in real or near real time.

scholarly journals Presentation of an Estimator for the Hurst Parameter for a Self-Similar Process Representing the Traffic in IEEE 802.3 Networks

2009 ◽  
Vol 4 (2) ◽  
pp. 137 ◽  
Author(s):  
Ginno Millán ◽  
Gastón Lefranc
Keyword(s):  
Computer Networks ◽  
Memory Structure ◽  
Similar Process ◽  
Hurst Parameter ◽  
Long Term Memory ◽  
Term Memory ◽  
Traffic Stream ◽  
Self Similar

The hypothesis for the existence of a process with long term memory structure, that represents the independence between the degree of randomness of the traffic generated by the sources and the pattern of traffic stream exhibited by the network is presented, discussed and developed. This methodology is offered as a new and alternative way of approaching the estimation of performance and the design of computer networks ruled by the standard IEEE 802.3-2005.

scholarly journals SELF-SIMILARITY IN THE TAXONOMIC CLASSIFICATION OF HUMAN LANGUAGES

2001 ◽  
Vol 04 (02n03) ◽  
pp. 281-286 ◽  
Author(s):  
DAMIAN H. ZANETTE
Keyword(s):  
Long Range ◽  
Power Law ◽  
Biological Species ◽  
Statistical Properties ◽  
Taxonomic Classification ◽  
Self Similarity ◽  
Self Similar ◽  
Evolutionary Foundation ◽  
Language Classification

Statistical properties of the taxonomic classification of human languages are studied. It is shown that, at the highest levels of the taxonomic hierarchy, the frequency of taxon members as a function of the number of languages belonging to each member decays as a power law. This feature reveals that a self-similar structure underlies the taxonomy of languages, exactly as observed in the taxonomic classification of biological species. Such an analogy is a clue to the evolutionary foundation of language classification based on long-range comparison.

GENERATION AND PREDICTION OF SELF-SIMILAR PROCESSES BY SURROGATES

Fractals ◽  
2006 ◽  
Vol 14 (01) ◽  
pp. 17-26 ◽  
Author(s):  
D. CHAKRABORTY ◽  
T. K. ROY
Keyword(s):  
Time Series ◽  
Power Spectrum ◽  
Power Law ◽  
Rank Order ◽  
Surrogate Data ◽  
Similar Process ◽  
Self Similarity ◽  
Random Data ◽  
Similarity Parameter ◽  
Self Similar

A self-similar process has power spectrum with power law depending on its self-similarity parameter H and we use this property for its generation by the method of surrogate data. The surrogates are a set of random data with the same distribution as that of the increments of the process. These are iteratively rearranged according to the rank order of a time series obtained with the same power law spectrum. The method is fast, and reliable as shown by the characteristics reproduced. It is also possible to extend this method to prediction of a self-similar process, the success of which will depend on the number of available data.

Sign in / Sign up

Export Citation Format

Share Document