B. B. Mandelbrot. A fast fractional gaussian noise generator. Water Resources Research, 7(3):543--553, 1971.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....work [2,21] However, none of the tting algorithms developed in these work provide a systematic way for deriving an approximation arbitrarily close to the original distribution. Moreover, the queueing results obtained via these approaches are only numerical. Inspired by a work of Mandelbrot [17], we propose, here, a new methodology for tting hyperexponential distributions to power tail distributions. This Starobinski and Sidi Modeling and Analysis of Power Tail Distributions 3 new approach exhibits several advantages. First, the approximation can be made arbitrarily close to the ....

B. Mandelbrot, A Fast Fractional Gaussian Noise Generator, Water Resources Research, Vol.7, No.3, pp.543-553, 1971.

....of teletra#c is explicitly taken into account, this can also lead to more e#cient tra#c control mechanisms. # Technical Report TR COSC 03 98 1 Several methods for generating pseudo random self similar sequences have been proposed. They include methods based on fast fractional Gaussian noise [15], fractional ARIMA processes [9] the M G # queue model [11] 13] autoregressive processes [3] 8] spatial renewal processes [26] etc. Some of them generate asymptotically self similar sequences and require large amounts of CPU time. For example, Hosking s method [9] based on the ....

....based on the F ARIMA(0,d,0) process, needs many hours to produce a self similar sequence with 131,072 (2 17 ) numbers on a Sun SPARCstation 4 [13] It requires O(n 2 ) computations to generate n numbers. Even though exact methods of generation of self similar sequences exist (for example: [15]) they are only fast enough for short sequences. They are usually inappropriate for generating long sequences because they require multiple passes along generated sequences. To overcome this, approximate methods for generation of self similar sequences in simulation studies of telecommunication ....

Mandelbrot, B. A Fast Fractional Gaussian Noise Generator. Water Resources Research 7 (1971), 543--553.

....if the strongly correlated character of teletra#c is explicitly taken into account, this can also lead to more e#cient tra#c control mechanisms. Several methods for generating pseudo random self similar sequences have been proposed. They include methods based on fast fractional Gaussian noise [18], fractional ARIMA processes [10] the M G # queue model [13] 15] autoregressive processes [4] spatial renewal processes [27] wavelets [1] 12] etc. Some of them generate asymptotically self similar sequences and require large amounts of CPU time. For example, Hosking s method [10] based ....

....[10] based on the F ARIMA(0,d,0) process, needs 1.5 hours to produce a self similar sequence with 131,072 (2 17 ) numbers on a Pentium II [11] 15] It requires O(n 2 ) computations to generate n numbers. Even though exact methods of generation of self similar sequences exist (for example: [18]) they are only fast enough for short sequences. They are usually inappropriate for generating long sequences because they require multiple passes along generated sequences. To overcome this, approximate methods for generation of self similar sequences in simulation studies of computer networks ....

Mandelbrot, B. A Fast Fractional Gaussian Noise Generator. Water Resources Research 7 (1971), 543--553.

....if the strongly correlated character of teletra#c is explicitly taken into account, this can also lead to more e#cient tra#c control mechanisms. Several methods for generating pseudo random self similar sequences have been proposed. They include methods based on fast fractional Gaussian noise [14], fractional ARIMA processes [9] the # Technical Report 1 M G # queue model [10] 12] autoregressive processes [3] 8] spatial renewal processes [23] etc. Some of them generate asymptotically self similar sequences and require large amounts of CPU time. For example, Hosking s method [9] ....

....based on the F ARIMA(0,d,0) process, needs many hours to produce a self similar sequence with 131,072 (2 17 ) numbers on a Sun SPARCstation 4 [12] It requires O(n 2 ) computations to generate n numbers. Even though exact methods of generation of self similar sequences exist (for example: [14]) they are only fast enough for short sequences. They are usually inappropriate for generating long sequences because they require multiple passes along generated sequences. To overcome this, approximate methods for generation of self similar sequences in simulation studies of computer networks ....

Mandelbrot, B. A Fast Fractional Gaussian Noise Generator. Water Resources Research 7 (1971), 543--553. 8

....work [2,21] However, none of the fitting algorithms developed in these work provide a systematic way for deriving an approximation arbitrarily close to the original distribution. Moreover, the queueing results obtained via these approaches are only numerical. Inspired by a work of Mandelbrot [17], we propose, here, a new methodology for fitting hyperexponential distributions to power tail distributions. This Starobinski and Sidi Modeling and Analysis of Power Tail Distributions 3 new approach exhibits several advantages. First, the approximation can be made arbitrarily close to the ....

B. Mandelbrot, A Fast Fractional Gaussian Noise Generator, Water Resources Research, Vol.7, No.3, pp.543-553, 1971.

....become desirable, especially for generating long traces for the purpose of network performance testing, simulation and analysis. Several approximation algorithms have been proposed, which include: ffl a fast but ad hoc method suggested by Mandelbrot that is based on short memory approximation [11]; ffl queuing based methods such as a method based on the M G 1 queue length with Poisson arrivals and heavy tailed service time [4] ffl transform methods based on inversely transforming known FBM coeOEcients in the transformed domain, these include methods based on the fast Fourier transform ....

B.B. Mandelbrot. A fast fractional Gaussian noise generator. Water Resources Research, 7:543553, 1971.

....work [AnN98] However, none of the fitting algorithms developed in these works provide a systematic way for deriving an approximation arbitrarily close to the original distribution. Moreover, the queueing results obtained via these approaches are only numerical. Inspired by a work of Mandelbrot [Man71], we develop, here, a new analytical methodology 15 for fitting hyperexponential distributions to heavy tailed distributions. This new approach exhibits several advantages. First, the approximation can be made arbitrarily close to the exact distribution and bounds on the approximation error are ....

B. Mandelbrot, "A Fast Fractional Gaussian Noise Generator," Water Resources Research, Vol.7, No.3, pp.543-553, 1971.

....work [AnN98] However, none of the fitting algorithms developed in these works provide a systematic way for deriving an approximation arbitrarily close to the original distribution. Moreover, the queueing results obtained via these approaches are only numerical. Inspired by a work of Mandelbrot [Man71], we propose, here, a new methodology for fitting hyperexponential distributions to heavy tailed distributions. This new approach exhibits several advantages. First, the approximation can be made arbitrarily close to the exact distribution and bounds on the approximation error are easily obtained. ....

B. Mandelbrot, "A Fast Fractional Gaussian Noise Generator," Water Resources Research, Vol.7, No.3, pp.543-553, 1971.

....practice. There exist numerous methods to date for generating self similar traffic traces. Exact methods, which are based on the Durbin Levinson algorithm [37, 394] are discussed in [24, 146, 196, 198, 394] They are generally impractical for long time series. Approximate methods are described in [30, 74, 120, 215, 245, 252, 258, 285, 290, 331, 334, 337, 356, 374, 376, 404,412]; some of these methods rely on earlier results reported in [77, 165,391] derived for a different purpose and re interpreted here in the context of synthetic traffic generation. These methods are generally very fast and feasible for even A Bibliographical Guide 7 very long time series. However, ....

B. B. Mandelbrot. A fast fractional Gaussian noise generator. Water Resources Research, 7:543--553, 1971.

.... the fact that fBm is the limit of a fractional Poisson field [Nor94, Man83] ffl Pareto distribution: aggregate several on off sources where the on off periods are Pareto (heavy tailed) distributed [Geo94] ffl Markov process: use a Markov processes to produce the high and low frequency spectra [Man71, Rob95]. ffl Random Midpoint Displacement: sum up properly scaled Gaussian numbers in a recursive manner [Pei92, Fou82] This paper focuses on random midpoint displacement. Compared to the recursive implementation in the original paper [Fou82] the algorithm is transformed into an iterative one. An ....

Benoit B. Mandelbrot. A fast Fractional Gaussian Noise Generator. Water Resource Research, 7(3), June 1971.

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B. B. Mandelbrot. A fast fractional gaussian noise generator. Water Resources Research, 7(3):543--553, 1971.

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Benoit B. Mandelbrot. A fast fractional Gaussian noise generator. Water Resources Research, 7:543--53, 1971.

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B. B. Mandelbrot, "A Fast Fractional Gaussian Noise Generator", Water Resources Research 7, 543-553, 1971.

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