| Peer-Reviewed

Engineering Approach to Calculating QoS of Server with Self-Similar Incoming Traffic Based on Recursive Scalable Poisson Model

Received: 21 November 2017     Accepted: 27 November 2017     Published: 2 January 2018
Views:       Downloads:
Abstract

To date the prospects for using the accumulated over many years mathematical and software for the modeling of telecommunications with the Poisson input flow are under a big question. The matter is that a new fractal queuing theory is already on the threshhold. This article formulates and solves the problem of application of a queuing system model with a Poisson incoming flow for the purposes of server modeling described by QS with self-similar incoming traffic of the "fractal Brownian motion" type (according to Norros). Based on the results of the morphological analysis, the Norros model was decomposed into Poisson components connected by a scalable recurrence scheme. The variance of the number of packets in the server, raised to the power determined by the Hurst parameter acts as the similarity coefficient of fractal and Poisson QSs. The method for rescaling Poisson solutions into fractal solutions was constructed on the basis of the similarity coefficient. According to this method in order to find the fractal delay of access, the Poisson delay should be multiplied by the similarity coefficient, and to estimate the probability of packet loss, it is necessary to extract a root of degree equal to the similarity coefficient from classical exponential losses. The scope of the re-scaling method focuses on the pre-project stages of creating telecommunications, where there is no need for high accuracy of simulation results.

Published in American Journal of Networks and Communications (Volume 6, Issue 6)
DOI 10.11648/j.ajnc.20170606.11
Page(s) 79-86
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Self-Similarity, Norros Model, Hurst Parameter, Similarity Coefficient, Recurrence Model, Two-Parameter Exponential Distribution, Access Delay, Loss Probability

References
[1] O. I. Sheluhin, S. M. Smolskiy, A. V. Osin, “Self-Similar Processes in Telecommunications,” Wiley, Chichester, England, 2007, 314 pp.
[2] “Self-similar process - Wikipedia“, 2017, Available: https://en.wikipedia.org/wiki/. [Accessed: 8 November, 2017].
[3] I. Norros, “A storage model with self-similar input“, Queuing Systems, vol. 16, no. 3, pp. 387–396, 1994.
[4] L. Kleinrok, “Queueing Systems“, Volume II: “Computer Applications“, John Willey and Sons Inc, 1976, 549 pp.
[5] S. Sh. Kuthbitdinov, "A model for estimating the guaranteed bit rate of multiservice self- similar traffic" / S. Sh. Kutbitdinov, V. V. Lokhmotko, S. R. Rudinskaya // Infocommunications. Network-Technologies-Solutions, no. 1, pp. 5-11, 2016 (in russian).
[6] A. I. Kostromitsky, V. S. Volotka, “Approaches to simulating self-similar traffic“, 2010. Available: http://selfsimilar.narod.ru/kostromitsky1.pdf [Accessed: 20 Оctober, 2017] (in Russian).
[7] S. R. Rudinskaya, S. Sh. Kutbitdinov, V. V. Lokhmotko, “Recurrent analogue of the Norros delay model“, Modern means of communication, ХХII ISTC, Minsk, RB, 2017, pp. 55-57.
[8] C. Forbes, M. Evans, N. Hastings, B. Peacock, “Statistical Distributions“, Fourth Edition, John Wiley & Sons, Inc, 212 р.
[9] M. A. Shneps, “Erlang's first formula as the basis for computing communication networks“/ Collection of scientific papers "Digital communication networks"// Riga, LatvSU named after P. Stuchki, 1989, pp. 21-33 (in Russian).
[10] G. J. Klir, "Architecture of Systems Problem Solving", Plenum Press, New York, 1985, 544 p.
[11] S. Sh. Kutbitdinov, V. V. Lokhmotko, S. R. Rudinskaya, "Estimation of QoS-parameters in the environment of a double stochastic Poisson process // Proceedings of the XVII International Scientific and Technical Conference "Modern Means of Communication", Minsk, 16-18 October 2012, p. 65 (in Russian).
[12] S. Sh. Kutbitdinov, V. V. Lokhmotko, “A model of the queuing system in the environment of a double stochastic Poisson process” // Collected papers of the Fourteenth International Scientific and Practical Conference "Fundamental and Applied Research, Development and Application of High Technologies in Industry and Economics", Volume 1, December 4-5, 2012, Saint- Petersburg, Russia, pp. 52-55 (in Russian).
Cite This Article
  • APA Style

    Vladimir Lokhmotko, Sabina Rudinskaya. (2018). Engineering Approach to Calculating QoS of Server with Self-Similar Incoming Traffic Based on Recursive Scalable Poisson Model. American Journal of Networks and Communications, 6(6), 79-86. https://doi.org/10.11648/j.ajnc.20170606.11

    Copy | Download

    ACS Style

    Vladimir Lokhmotko; Sabina Rudinskaya. Engineering Approach to Calculating QoS of Server with Self-Similar Incoming Traffic Based on Recursive Scalable Poisson Model. Am. J. Netw. Commun. 2018, 6(6), 79-86. doi: 10.11648/j.ajnc.20170606.11

    Copy | Download

    AMA Style

    Vladimir Lokhmotko, Sabina Rudinskaya. Engineering Approach to Calculating QoS of Server with Self-Similar Incoming Traffic Based on Recursive Scalable Poisson Model. Am J Netw Commun. 2018;6(6):79-86. doi: 10.11648/j.ajnc.20170606.11

    Copy | Download

  • @article{10.11648/j.ajnc.20170606.11,
      author = {Vladimir Lokhmotko and Sabina Rudinskaya},
      title = {Engineering Approach to Calculating QoS of Server with Self-Similar Incoming Traffic Based on Recursive Scalable Poisson Model},
      journal = {American Journal of Networks and Communications},
      volume = {6},
      number = {6},
      pages = {79-86},
      doi = {10.11648/j.ajnc.20170606.11},
      url = {https://doi.org/10.11648/j.ajnc.20170606.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajnc.20170606.11},
      abstract = {To date the prospects for using the accumulated over many years mathematical and software for the modeling of telecommunications with the Poisson input flow are under a big question. The matter is that a new fractal queuing theory is already on the threshhold. This article formulates and solves the problem of application of a queuing system model with a Poisson incoming flow for the purposes of server modeling described by QS with self-similar incoming traffic of the "fractal Brownian motion" type (according to Norros). Based on the results of the morphological analysis, the Norros model was decomposed into Poisson components connected by a scalable recurrence scheme. The variance of the number of packets in the server, raised to the power determined by the Hurst parameter acts as the similarity coefficient of fractal and Poisson QSs. The method for rescaling Poisson solutions into fractal solutions was constructed on the basis of the similarity coefficient. According to this method in order to find the fractal delay of access, the Poisson delay should be multiplied by the similarity coefficient, and to estimate the probability of packet loss, it is necessary to extract a root of degree equal to the similarity coefficient from classical exponential losses. The scope of the re-scaling method focuses on the pre-project stages of creating telecommunications, where there is no need for high accuracy of simulation results.},
     year = {2018}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Engineering Approach to Calculating QoS of Server with Self-Similar Incoming Traffic Based on Recursive Scalable Poisson Model
    AU  - Vladimir Lokhmotko
    AU  - Sabina Rudinskaya
    Y1  - 2018/01/02
    PY  - 2018
    N1  - https://doi.org/10.11648/j.ajnc.20170606.11
    DO  - 10.11648/j.ajnc.20170606.11
    T2  - American Journal of Networks and Communications
    JF  - American Journal of Networks and Communications
    JO  - American Journal of Networks and Communications
    SP  - 79
    EP  - 86
    PB  - Science Publishing Group
    SN  - 2326-8964
    UR  - https://doi.org/10.11648/j.ajnc.20170606.11
    AB  - To date the prospects for using the accumulated over many years mathematical and software for the modeling of telecommunications with the Poisson input flow are under a big question. The matter is that a new fractal queuing theory is already on the threshhold. This article formulates and solves the problem of application of a queuing system model with a Poisson incoming flow for the purposes of server modeling described by QS with self-similar incoming traffic of the "fractal Brownian motion" type (according to Norros). Based on the results of the morphological analysis, the Norros model was decomposed into Poisson components connected by a scalable recurrence scheme. The variance of the number of packets in the server, raised to the power determined by the Hurst parameter acts as the similarity coefficient of fractal and Poisson QSs. The method for rescaling Poisson solutions into fractal solutions was constructed on the basis of the similarity coefficient. According to this method in order to find the fractal delay of access, the Poisson delay should be multiplied by the similarity coefficient, and to estimate the probability of packet loss, it is necessary to extract a root of degree equal to the similarity coefficient from classical exponential losses. The scope of the re-scaling method focuses on the pre-project stages of creating telecommunications, where there is no need for high accuracy of simulation results.
    VL  - 6
    IS  - 6
    ER  - 

    Copy | Download

Author Information
  • Federal Communications Agency (Rossvyaz), The Bonch-Bruevich Saint-Petersburg State University of Telecommunications, Saint-Petersburg, Russian Federation

  • Department of Education, Belarusian State Academy of Telecommunications, Minsk, The Republic of Belarus

  • Sections