scholarly journals Long-range dependence ten years of Internet traffic modeling

2004 ◽  
Vol 8 (5) ◽  
pp. 57-64 ◽  
Author(s):  
T. Karagiannis ◽  
M. Molle ◽  
M. Faloutsos
Keyword(s):  
Long Range ◽  
Internet Traffic ◽  
Traffic Modeling ◽  
Long Range Dependence

MODELING NETWORK TRAFFIC USING CAUCHY CORRELATION MODEL WITH LONG-RANGE DEPENDENCE

2005 ◽  
Vol 19 (17) ◽  
pp. 829-840 ◽  
Author(s):  
MING LI ◽  
S. C. LIM
Keyword(s):  
Long Range ◽  
Network Traffic ◽  
Traffic Engineering ◽  
Single Parameter ◽  
Traffic Modeling ◽  
Long Range Dependence ◽  
Correlation Model ◽  
Traffic Time Series ◽  
Fractal Properties

Much attention has been given to the long-range dependence and fractal properties in network traffic engineering, and these properties are also widely observed in many fields of science and technologies. Traffic time series is conventionally characterized by its fractal dimension D, which is a measure for roughness, and by the Hurst parameter H, which is a measure for long-range dependence, see for examples (Refs. 10–12). Each property has been traditionally modeled and explained by self-affine random functions, such as fractional Gaussian noise (FGN)1,10–13,18,22–28 and fractional Brownian motion (FBM),6,7 where a linear relationship between D and H, say D = 2 - H for one-dimensional series, links the two properties. The limitation of single parameter models (e.g., FGN) in long-range dependent (LRD) traffic modeling has been noticed as can be seen from Refs. 1, 18 and 25. Hence, models which can provide good fitting of LRD traffic for both short-term lags and long-term ones are worth studying due to the importance of accurate models of traffic in network communications.13 This letter utilizes a statistical model called the Cauchy correlation model to model LRD traffic. This model characterizes D and H separately, and it allows any combination of two within the constraint of LRD condition. It is a new power-law correlation model for LRD traffic modeling with its local and global behavior decoupling. Its flexibility in data modeling in comparison with a single parameter model of FGN is briefly discussed, and applications to LRD traffic modeling demonstrated.

SIMULATION OF LONG-RANGE DEPENDENT TRAFFIC AND A SIMULATOR OF TCP ARRIVAL TRAFFIC

2001 ◽  
Vol 02 (03) ◽  
pp. 305-315 ◽  
Author(s):  
MING LI ◽  
WEIJIA JIA ◽  
WEI ZHAO
Keyword(s):  
Simulation Model ◽  
White Noise ◽  
Long Range ◽  
Internet Traffic ◽  
Experimental Results ◽  
Long Range Dependence ◽  
Traffic Data ◽  
The Real ◽  
Noise Input

The long-range dependence of Internet traffic has been experimentally observed. One issue in handling long-range dependent traffic is how to simulate random traffic data with long-range dependence. The authors discuss a correlation-based simulator with a white noise input for generating long-range dependent traffic data. With the real TCP traffic traces, a simulation model of TCP arrival traffic is empirically developed and the experimental results are satisfactory.

scholarly journals Long-range dependence in a changing Internet traffic mix

2005 ◽  
Vol 48 (3) ◽  
pp. 401-422 ◽  
Author(s):  
Cheolwoo Park ◽  
Félix Hernández-Campos ◽  
J.S. Marron ◽  
F. Donelson Smith
Keyword(s):  
Long Range ◽  
Internet Traffic ◽  
Long Range Dependence

scholarly journals Long-range dependence analysis of Internet traffic

2010 ◽  
Vol 38 (7) ◽  
pp. 1407-1433 ◽  
Author(s):  
Cheolwoo Park ◽  
Félix Hernández-Campos ◽  
Long Le ◽  
J. S. Marron ◽  
Juhyun Park ◽  
...  
Keyword(s):  
Long Range ◽  
Internet Traffic ◽  
Long Range Dependence ◽  
Dependence Analysis

scholarly journals Representations of hermite processes using local time of intersecting stationary stable regenerative sets

2020 ◽  
Vol 57 (4) ◽  
pp. 1234-1251
Author(s):  
Shuyang Bai
Keyword(s):  
Long Range ◽  
Local Time ◽  
Limit Theorems ◽  
Local Times ◽  
Long Range Dependence ◽  
Random Interval ◽  
Stationary Increments ◽  
Self Similar ◽  
Regenerative Sets

AbstractHermite processes are a class of self-similar processes with stationary increments. They often arise in limit theorems under long-range dependence. We derive new representations of Hermite processes with multiple Wiener–Itô integrals, whose integrands involve the local time of intersecting stationary stable regenerative sets. The proof relies on an approximation of regenerative sets and local times based on a scheme of random interval covering.

scholarly journals On nonparametric regression for bivariate circular long-memory time series

2021 ◽  
Author(s):  
Jan Beran ◽  
Britta Steffens ◽  
Sucharita Ghosh
Keyword(s):  
Time Series ◽  
Nonparametric Regression ◽  
Long Range ◽  
Long Memory ◽  
Regression Function ◽  
Confidence Bands ◽  
Long Range Dependence ◽  
Asymptotic Results ◽  
Memory Time ◽  
Circular Time Series

AbstractWe consider nonparametric regression for bivariate circular time series with long-range dependence. Asymptotic results for circular Nadaraya–Watson estimators are derived. Due to long-range dependence, a range of asymptotically optimal bandwidths can be found where the asymptotic rate of convergence does not depend on the bandwidth. The result can be used for obtaining simple confidence bands for the regression function. The method is illustrated by an application to wind direction data.

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