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

Vladimir Lokhmotko; Sabina Rudinskaya

doi:doi:10.11648/j.ajnc.20170606.11

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

Vladimir Lokhmotko, Sabina Rudinskaya

Published in American Journal of Networks and Communications (Volume 6, Issue 6)

Received: 21 November 2017 Accepted: 27 November 2017 Published: 2 January 2018

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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).

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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

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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

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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

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@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}
}

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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
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PB  - Science Publishing Group
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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  -

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Author Information

Vladimir Lokhmotko

Federal Communications Agency (Rossvyaz), The Bonch-Bruevich Saint-Petersburg State University of Telecommunications, Saint-Petersburg, Russian Federation
Sabina Rudinskaya

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

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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

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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

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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