An efficient method for simulating fractional stable motion

An efficient methodology for simulating paths of fractional stable motion is presented. The proposed approach is based on invariance principles for linear processes. A detailed analysis of the error terms involved is given and the performance of the method is assessed through an extensive simulation study.

[1]  Sally Floyd,et al.  Wide area traffic: the failure of Poisson modeling , 1995, TNET.

[2]  Ilkka Norros,et al.  Simulation of fractional Brownian motion with conditionalized random midpoint displacement , 1999 .

[3]  C. R. Dietrich,et al.  Fast and Exact Simulation of Stationary Gaussian Processes through Circulant Embedding of the Covariance Matrix , 1997, SIAM J. Sci. Comput..

[4]  José R. Gallardo,et al.  Use of alpha-stable self-similar stochastic processes for modeling traffic in broadband networks , 2000, Perform. Evaluation.

[5]  Vern Paxson,et al.  Fast, approximate synthesis of fractional Gaussian noise for generating self-similar network traffic , 1997, CCRV.

[6]  Jan Beran,et al.  Statistics for long-memory processes , 1994 .

[7]  Ilkka Nomos.  On the Use of Fractional Brownian Motion in the Theory of Connectionless Networks , 1995 .

[8]  Dimitrios Hatzinakos,et al.  Network heavy traffic modeling using α-stable self-similar processes , 2001, IEEE Trans. Commun..

[9]  Gabriel Lang,et al.  Quadratic variations and estimation of the local Hölder index of a gaussian process , 1997 .

[10]  D. Applebaum.  Stable non-Gaussian random processes , 1995, The Mathematical Gazette.

[11]  Walter Willinger,et al.  Self-Similarity in High-Speed Packet Traffic: Analysis and Modeling of Ethernet Traffic Measurements , 1995 .

[12]  John T. Kent,et al.  Estimating the Fractal Dimension of a Locally Self-similar Gaussian Process by using Increments , 1997 .

[13]  B. Mandelbrot,et al.  Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[14]  Ilkka Norros,et al.  On the Use of Fractional Brownian Motion in the Theory of Connectionless Networks , 1995, IEEE J. Sel. Areas Commun..

[15]  Patrick Flandrin,et al.  Wavelet analysis and synthesis of fractional Brownian motion , 1992, IEEE Trans. Inf. Theory.

[16]  D. Nualart.  Variations quadratiques et inégalités pour les martingales a deux indices , 1985 .

[17]  P. Abry,et al.  The wavelet based synthesis for fractional Brownian motion , 1996 .

[18]  Stefano Giordano,et al.  Testing /spl alpha/-stable processes in modelling broadband teletraffic , 2000, 2000 IEEE International Conference on Communications. ICC 2000. Global Convergence Through Communications. Conference Record.

[19]  Walter Willinger,et al.  On the self-similar nature of Ethernet traffic , 1993, SIGCOMM '93.

[20]  J. Coeurjolly,et al.  Simulation and identification of the fractional Brownian motion: a bibliographical and comparative study , 2000 .

[21]  K. S. Vastolaz.  Workload Generation for ns Simulations of Wide AreaNetworks and the Internet , 2022 .

[22]  Florin Avram,et al.  Weak Convergence of Moving Averages with Infinite Variance , 1986 .

[23]  C. Mallows,et al.  A Method for Simulating Stable Random Variables , 1976 .

[24]  A. Wood,et al.  Simulation of Stationary Gaussian Processes in [0, 1] d , 1994 .

[25]  A. Astrauskas.  Limit theorems for sums of linearly generated random variables , 1983 .

[26]  Walter Willinger,et al.  Is Network Traffic Self-Similar or Multifractal? , 1997 .

[27]  Fotios C. Harmantzis,et al.  Tail probabilities for the multiplexing of fractional /spl alpha/-stable broadband traffic , 2001, ICC 2001. IEEE International Conference on Communications. Conference Record (Cat. No.01CH37240).

[28]  Patrice Abry,et al.  Wavelet Analysis of Long-Range-Dependent Traffic , 1998, IEEE Trans. Inf. Theory.

[29]  J..  Estimating the Fractal Dimension of Chaotic Time Series , 1990 .

[30]  Walter Willinger,et al.  On the Self-Similar Nature of Ethernet Traffic ( extended version ) , 1995 .

[31]  Yu. A. Davydov,et al.  The Invariance Principle for Stationary Processes , 1970 .

[32]  Walter Willinger,et al.  Self-Similar Network Traffic and Performance Evaluation , 2000 .

[33]  Sally Floyd,et al.  Wide-Area Traffic: The Failure of Poisson Modeling , 1994, SIGCOMM.

[34]  Takis Konstantopoulos,et al.  Macroscopic models for long-range dependent network traffic , 1998, Queueing Syst. Theory Appl..