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Statistical modeling of the Internet traffic dynamics: To which extent do we need long-term correlations?

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  • Markelov, Oleg
  • Nguyen Duc, Viet
  • Bogachev, Mikhail

Abstract

Recently we have suggested a universal superstatistical model of user access patterns and aggregated network traffic. The model takes into account the irregular character of end user access patterns on the web via the non-exponential distributions of the local access rates, but neglects the long-term correlations between these rates. While the model is accurate for quasi-stationary traffic records, its performance under highly variable and especially non-stationary access dynamics remains questionable. In this paper, using an example of the traffic patterns from a highly loaded network cluster hosting the website of the 1998 FIFA World Cup, we suggest a generalization of the previously suggested superstatistical model by introducing long-term correlations between access rates. Using queueing system simulations, we show explicitly that this generalization is essential for modeling network nodes with highly non-stationary access patterns, where neglecting long-term correlations leads to the underestimation of the empirical average sojourn time by several decades under high throughput utilization.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:485:y:2017:i:c:p:48-60
    DOI: 10.1016/j.physa.2017.05.023
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    Cited by:

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    2. Butusov, Denis N. & Karimov, Artur I. & Pyko, Nikita S. & Pyko, Svetlana A. & Bogachev, Mikhail I., 2018. "Discrete chaotic maps obtained by symmetric integration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 955-970.
    3. 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.
    4. Li, Ming, 2021. "Generalized fractional Gaussian noise and its application to traffic modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 579(C).
    5. 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).
    6. Zhou, Hanchu & Chang, Fangrong, 2022. "The long-memory temporal dependence of traffic crash fatality for different types of road users," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    7. Li, Ming & Wang, Anqi, 2020. "Fractal teletraffic delay bounds in computer networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).

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