• 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.

• 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.

• 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.

• 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.

• 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).

• 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).

• 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.

• 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.

• 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.

• 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.