IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v579y2021ics0378437121004118.html
   My bibliography  Save this article

Generalized fractional Gaussian noise and its application to traffic modeling

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437121004118
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2021.126138?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Ming & Wang, Anqi, 2020. "Fractal teletraffic delay bounds in computer networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    2. Li, Ming, 2020. "Multi-fractional generalized Cauchy process and its application to teletraffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    3. 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).
    4. 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.
    5. 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.
    6. 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.
    7. Bhagaban Behera, 2013. "Drug Trafficking as a Non-Traditional Security Threat to Central Asian States," Jadavpur Journal of International Relations, , vol. 17(2), pages 229-251, December.
    8. Zeinali, Narges & Pourdarvish, Ahmad, 2022. "An entropy-based estimator of the Hurst exponent in fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 591(C).
    9. Heydari, M.H. & Razzaghi, M., 2021. "A numerical approach for a class of nonlinear optimal control problems with piecewise fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    10. Bigsten, Arne & Tengstam, Sven, 2015. "International Coordination and the Effectiveness of Aid," World Development, Elsevier, vol. 69(C), pages 75-85.
    11. Li, Wei-Zhen & Zhai, Jin-Rui & Jiang, Zhi-Qiang & Wang, Gang-Jin & Zhou, Wei-Xing, 2022. "Predicting tail events in a RIA-EVT-Copula framework," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    12. Tajmirriahi, Mahnoosh & Amini, Zahra, 2021. "Modeling of seizure and seizure-free EEG signals based on stochastic differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    13. Li, Ming & Zhang, Peidong & Leng, Jianxing, 2016. "Improving autocorrelation regression for the Hurst parameter estimation of long-range dependent time series based on golden section search," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 189-199.
    14. Liudvikas Kaklauskas & Leonidas Sakalauskas, 2013. "Study of on-line measurement of traffic self-similarity," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(1), pages 63-84, January.
    15. Hosseininia, M. & Heydari, M.H. & Avazzadeh, Z., 2022. "Orthonormal shifted discrete Legendre polynomials for the variable-order fractional extended Fisher–Kolmogorov equation," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    16. Tarr, G. & Weber, N.C. & Müller, S., 2015. "The difference of symmetric quantiles under long range dependence," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 144-150.
    17. Heydari, M.H. & Razzaghi, M. & Rouzegar, J., 2022. "Chebyshev cardinal polynomials for delay distributed-order fractional fourth-order sub-diffusion equation," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    18. Song, Wanqing & Cattani, Carlo & Chi, Chi-Hung, 2020. "Multifractional Brownian motion and quantum-behaved particle swarm optimization for short term power load forecasting: An integrated approach," Energy, Elsevier, vol. 194(C).
    19. Bogachev, Mikhail I. & Kuzmenko, Alexander V. & Markelov, Oleg A. & Pyko, Nikita S. & Pyko, Svetlana A., 2023. "Approximate waiting times for queuing systems with variable long-term correlated arrival rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 614(C).
    20. Pyko, Nikita S. & Pyko, Svetlana A. & Markelov, Oleg A. & Karimov, Artur I. & Butusov, Denis N. & Zolotukhin, Yaroslav V. & Uljanitski, Yuri D. & Bogachev, Mikhail I., 2018. "Assessment of cooperativity in complex systems with non-periodical dynamics: Comparison of five mutual information metrics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1054-1072.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:579:y:2021:i:c:s0378437121004118. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.