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Generalized fractional Gaussian noise and its application to traffic modeling

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  • Li, Ming

Abstract

The highlights in this paper are in two aspects. First, we introduce a type of novel fractional noise termed generalized fractional Gaussian noise (gfGn). Its autocorrelation function, power spectrum density function, and the fractal dimension are given. The second aspect is in the case study using gfGn for modeling real traffic traces to exhibit that the gfGn model is more accurate than the conventional fractional Gaussian noise (fGn) one in traffic modeling.

Suggested Citation

  • Li, Ming, 2021. "Generalized fractional Gaussian noise and its application to traffic modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 579(C).
    • Handle: RePEc:eee:phsmap:v:579:y:2021:i:c:s0378437121004118
    DOI: 10.1016/j.physa.2021.126138
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    References listed on IDEAS

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    1. Li, Ming & Li, Jia-Yue, 2017. "Generalized Cauchy model of sea level fluctuations with long-range dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 309-335.
    2. Li, Ming & Lim, S.C., 2008. "Modeling network traffic using generalized Cauchy process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(11), pages 2584-2594.
    3. Markelov, Oleg & Nguyen Duc, Viet & Bogachev, Mikhail, 2017. "Statistical modeling of the Internet traffic dynamics: To which extent do we need long-term correlations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 485(C), pages 48-60.
    4. Li, Ming, 2020. "Multi-fractional generalized Cauchy process and its application to teletraffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    5. Cheolwoo Park & F�lix Hernández-Campos & Long Le & J. S. Marron & Juhyun Park & Vladas Pipiras & F. D. Smith & Richard L. Smith & Michele Trovero & Zhengyuan Zhu, 2011. "Long-range dependence analysis of Internet traffic," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(7), pages 1407-1433, June.
    6. Liu, He & Song, Wanqing & Li, Ming & Kudreyko, Aleksey & Zio, Enrico, 2020. "Fractional Lévy stable motion: Finite difference iterative forecasting model," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    7. Li, Ming, 2017. "Record length requirement of long-range dependent teletraffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 472(C), pages 164-187.
    8. Song, Wanqing & Li, Ming & Li, Yuanyuan & Cattani, Carlo & Chi, Chi-Hung, 2019. "Fractional Brownian motion: Difference iterative forecasting models," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 347-355.
    9. Ming Li, 2013. "Power Spectrum of Generalized Fractional Gaussian Noise," Advances in Mathematical Physics, Hindawi, vol. 2013, pages 1-3, October.
    10. Monika Pinchas, 2014. "Symbol Error Rate for Nonblind Adaptive Equalizers Applicable for the SIMO and FGn Case," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-11, March.
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