• Title/Summary/Keyword: Self-Similar

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ON A SELF-SIMILAR MEASURE ON A SELF-SIMILAR CANTOR SET

  • Baek, In-Soo
    • Journal of the Chungcheong Mathematical Society
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    • v.16 no.2
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    • pp.1-10
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    • 2003
  • We compare a self-similar measure on a self-similar Cantor set with a quasi-self-similar measure on a deranged Cantor set. Further we study some properties of a self-similar measure on a self-similar Cantor set.

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SIMPLE APPROACH TO MULTIFRACTAL SPECTRUM OF A SELF-SIMILAR CANTOR SET

  • BAEK, IN-Soo
    • Communications of the Korean Mathematical Society
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    • v.20 no.4
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    • pp.695-702
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    • 2005
  • We study the transformed measures with respect to the real parameters of a self-similar measure on a self-similar Can­tor set to give a simple proof for some result of its multifractal spectrum. A transformed measure with respect to a real parameter of a self-similar measure on a self-similar Cantor set is also a self­similar measure on the self-similar Cantor set and it gives a better information for multifractals than the original self-similar measure. A transformed measure with respect to an optimal parameter deter­mines Hausdorff and packing dimensions of a set of the points which has same local dimension for a self-similar measure. We compute the values of the transformed measures with respect to the real parameters for a set of the points which has same local dimension for a self-similar measure. Finally we investigate the magnitude of the local dimensions of a self-similar measure and give some correlation between the local dimensions.

A Comparison of Three Fixed-Length Sequence Generators of Synthetic Self-Similar Network Traffic (Synthetic Self-Similar 네트워크 Traffic의 세 가지 고정길이 Sequence 생성기에 대한 비교)

  • Jeong, Hae-Duck J.;Lee, Jong-Suk R.
    • The KIPS Transactions:PartC
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    • v.10C no.7
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    • pp.899-914
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    • 2003
  • It is generally accepted that self-similar (or fractal) processes may provide better models for teletraffic in modern telecommunication networks than Poisson Processes. If this is not taken into account, it can lead to inaccurate conclusions about performance of telecommunication networks. Thus, an important requirement for conducting simulation studies of telecommunication networks is the ability to generate long synthetic stochastic self-similar sequences. Three generators of pseudo-random self-similar sequences, based on the FFT〔20〕, RMD〔12〕 and SRA methods〔5, 10〕, are compared and analysed in this paper. Properties of these generators were experimentally studied in the sense of their statistical accuracy and times required to produce sequences of a given (long) length. While all three generators show similar levels of accuracy of the output data (in the sense of relative accuracy of the Horst parameter), the RMD- and SRA-based generators appear to be much faster than the generator based on FFT. Our results also show that a robust method for comparative studies of self-similarity in pseudo-random sequences is needed.

ON A QUASI-SELF-SIMILAR MEASURE ON A SELF-SIMILAR SET ON THE WAY TO A PERTURBED CANTOR SET

  • Baek, In-Soo
    • The Pure and Applied Mathematics
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    • v.11 no.1
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    • pp.51-61
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    • 2004
  • We find an easier formula to compute Hausdorff and packing dimensions of a subset composing a spectral class by local dimension of a self-similar measure on a self-similar Cantor set than that of Olsen. While we cannot apply this formula to computing the dimensions of a subset composing a spectral class by local dimension of a quasi-self-similar measure on a self-similar set on the way to a perturbed Cantor set, we have a set theoretical relationship between some distribution sets. Finally we compare the behaviour of a quasi-self-similar measure on a self-similar Cantor set with that on a self-similar set on the way to a perturbed Cantor set.

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Algorithmic Generation of Self-Similar Network Traffic Based on SRA (SRA 알고리즘을 이용한 Self-Similar 네트워크 Traffic의 생성)

  • Jeong HaeDuck J.;Lee JongSuk R.
    • The KIPS Transactions:PartC
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    • v.12C no.2 s.98
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    • pp.281-288
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    • 2005
  • It is generally accepted that self-similar (or fractal) Processes may provide better models for teletraffic in modem computer networks than Poisson processes. f this is not taken into account, it can lead to inaccurate conclusions about performance of computer networks. Thus, an important requirement for conducting simulation studies of telecommunication networks is the ability to generate long synthetic stochastic self-similar sequences. A generator of pseudo-random self similar sequences, based on the SRA (successive random addition) method, is implemented and analysed in this paper. Properties of this generator were experimentally studied in the sense of its statistical accuracy and the time required to produce sequences of a given (long) length. This generator shows acceptable level of accuracy of the output data (in the sense of relative accuracy of the Hurst parameter) and is fast. The theoretical algorithmic complexity is O(n).

Fast Self-Similar Network Traffic Generation Based on FGN and Daubechies Wavelets (FGN과 Daubechies Wavelets을 이용한 빠른 Self-Similar 네트워크 Traffic의 생성)

  • Jeong, Hae-Duck;Lee, Jong-Suk
    • The KIPS Transactions:PartC
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    • v.11C no.5
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    • pp.621-632
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    • 2004
  • Recent measurement studies of real teletraffic data in modern telecommunication networks have shown that self-similar (or fractal) processes may provide better models of teletraffic in modern telecommunication networks than Poisson processes. If this is not taken into account, it can lead to inaccurate conclusions about performance of telecommunication networks. Thus, an important requirement for conducting simulation studies of telecommunication networks is the ability to generate long synthetic stochastic self-similar sequences. A new generator of pseu-do-random self-similar sequences, based on the fractional Gaussian nois and a wavelet transform, is proposed and analysed in this paper. Specifically, this generator uses Daubechies wavelets. The motivation behind this selection of wavelets is that Daubechies wavelets lead to more accurate results by better matching the self-similar structure of long range dependent processes, than other types of wavelets. The statistical accuracy and time required to produce sequences of a given (long) length are experimentally studied. This generator shows a high level of accuracy of the output data (in the sense of the Hurst parameter) and is fast. Its theoretical algorithmic complexity is 0(n).

Self-Similarity Characteristic in Data traffic (데이터 트래픽 Self-Similar 특성에 관한 연구)

  • 장우현;오행석
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • 2000.10a
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    • pp.272-277
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    • 2000
  • The classical queuing analysis has been tremendously useful in doing capacity planning and performance prediction, However, in many real-world cases. it has found that the predicted results form a queuing analysis differ substantially hem the actual observed performance. Specially, in recent years, a number of studies have demonstrated that for some environments, the traffic pattern is self-similar rather than Poisson. In this paper, we study these self-similar traffic characteristics and the definition of self-similar stochastic processes. Then, we consider the examples of self-similar data traffic, which is reported from recent measurement studies. Finally, we wish you that it makes out about the characteristics of actual data traffic more easily.

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Mobile Communications Data traffic using Self-Similarity Characteristic (Self-Similar 특성을 이용한 이동전화 데이터 트래픽 특성)

  • 이동철;양성현;김기문
    • Journal of the Korea Computer Industry Society
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    • v.3 no.7
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    • pp.915-920
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    • 2002
  • The classical queuing analysis has been tremendously useful in doing capacity planning and performance prediction. However, in many real-world cases. it has found that the predicted results form a queuing analysis differ substantially from the actual observed performance. Specially, in recent years, a number of studies have demonstrated that for some environments, the traffic pattern is self-similar rather than Poisson. In this paper, we study these self-similar traffic characteristics and the definition of self-similar stochastic processes. Then, we consider the examples of self-similar data traffic, which is reported from recent measurement studies. Finally, we wish yon that it makes out about the characteristics of actual data traffic more easily.

  • PDF

Self-Similarity Characteristic in Data traffic (Self-Similar특성을 이용한 데이터 트래픽 특성에 관한 연구)

  • 이동철;김기문;김동일
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • 2001.05a
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    • pp.173-178
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    • 2001
  • The classical queuing analysis has been tremendously useful in doing capacity planning and performance prediction. However, in many real-world cases. it has found that the predicted results form a queuing analysis differ substantially from the actual observed performance. Specially, in recent years, a number of studies have demonstrated that for some environments, the traffic pattern is self-similar rather than Poisson. In this paper, we study these self-similar traffic characteristics and the definition of self-similar stochastic processes. Then, we consider the examples of self-similar data traffic, which is reported from recent measurement studies. Finally, we wish you that it makes out about the characteristics of actual data traffic more easily.

  • PDF

Self-Similarity Characteristic in Data traffic (Self-Similar특성을 이용한 데이터 트래픽 특성에 관한 연구)

  • 이동철;김기문;김동일
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • 2001.10a
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    • pp.454-459
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    • 2001
  • The classical queuing analysis has been tremendously useful in doing capacity planning and performance prediction. However, in many real-world cases. it has found that the predicted results form a queuing analysis differ substantially from the actual observed performance. Specially, in recent years, a number of studies have demonstrated that for some environments, the traffic pattern is self-similar rather than Poisson. In this paper, we study these self-similar traffic characteristics and the definition of self-similar stochastic processes. Then, we consider the examples of self-similar data traffic, which is reported from recent measurement studies. Finally, we wish you that it makes out about the characteristics of actual data traffic more easily.

  • PDF