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Minimization of Packet Loss Probability in Network with Fractal Traffic

  • Vladimir N. Zadorozhnyi
  • Tatiana R. ZakharenkovaEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 800)

Abstract

Methods for radical reduction of packet loss probability in telecommunication networks with fractal traffic are developed. We investigate ways of preventing the losses within the framework of queueing theory; relevant simulation experiments are carried out. It is determined that strategy for the channel number increase in the network nodes has principally higher efficiency than that for the buffer increasing and/or channel performance increasing. Approximation methods for loss probability in the nodes of multiserver queueing system without buffers are investigated. The paper offers to approximate the loss probability in the node with n channels by steady-state probability in the state n of relating infinite-server queueing systems. We develop an analytical-statistical technique of optimal channel distribution over the nodes in networks with fractal traffic which is based on such approximation. The example of the method application is provided. The developed method could be used by engineers designing the telecommunication networks.

Keywords

Telecommunication networks Analytical-statistical techniques Fractal traffic Queueing theory 

References

  1. 1.
    Leland, W.E., Taqqu, M.S., Willinger, W., Wilson, D.V.: On the self-similar nature of ethernet traffic. ACM/SIGCOMM Comput. Commun. Rev. 23, 146–155 (1993)Google Scholar
  2. 2.
    Crovella, M.E., Taqqu, M., Bestavros, A.: Heavy tailed-probability distributions in the world wide web. IEEE/ACM Trans. Netw. 5(6), 835–846 (1997)CrossRefzbMATHGoogle Scholar
  3. 3.
    Czachórski, T., Domańska, J., Pagano, M.: On stochastic models of internet traffic. In: Dudin, A., Nazarov, A., Yakupov, R. (eds.) ITMM 2015. CCIS, vol. 564, pp. 289–303. Springer, Cham (2015). doi: 10.1007/978-3-319-25861-4_25 CrossRefGoogle Scholar
  4. 4.
    Kleinrock, L.: Queueing Systems: Computer Applications, vol. 2. Wiley Interscience, New York (1976). 576 pageszbMATHGoogle Scholar
  5. 5.
    Zwart, A.P.: Queueing Systems with Heavy Tails. Eindhoven University of Technology (2001). 227 pagesGoogle Scholar
  6. 6.
    Asmussen, S., Binswanger, K., Hojgaard, B.: Rare events simulation for heavy-tailed distributions. Bernoulli 6(2), 303–322 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Boots, N.K., Shahabuddin, P.: Simulating GI/GI/1 queues and insurance risk processes with subexponential distributions. In: Proceedings of the 2000 Winter Simulation Conference, pp. 656–665 (2000). Unpublished manuscript, Free University, Amsterdam. Shortened versionGoogle Scholar
  8. 8.
    Zadorozhnyi, V.: Fractal queues simulation peculiarities. In: Dudin, A., Nazarov, A., Yakupov, R. (eds.) ITMM 2015. CCIS, vol. 564, pp. 415–432. Springer, Cham (2015). doi: 10.1007/978-3-319-25861-4_35 CrossRefGoogle Scholar
  9. 9.
    Zadorozhnyi, V.N.: Peculiarities and methods of fractal queues simulation. In: 2016 International Siberian Conference on Control and Communications (SIBCON), Fundamental Problems of Communications, Moscow, Russia, 12–14 May 2016Google Scholar
  10. 10.
    Zadorozhnyi, V.N., Zakharenkova, T.R.: Methods of simulation queueing systems with heavy tails. In: Dudin, A., Gortsev, A., Nazarov, A., Yakupov, R. (eds.) ITMM 2016. CCIS, vol. 638, pp. 382–396. Springer, Cham (2016). doi: 10.1007/978-3-319-44615-8_33 CrossRefGoogle Scholar
  11. 11.
    Zadorozhnyi, V.N. Simulation modeling of fractal queues. In: Dynamics of Systems, Mechanisms and Machines (Dynamics), pp. 1–4 (2014). doi: 10.1109/Dynamics.2014.7005703
  12. 12.
    Moiseev, A.N., Nazarov, A.A.: Beskonechnolinejnye sistemy i seti-massovogo obsluzhivaniya [Infinite-linear queueing systems and networks]. NTL Publ., Tomsk (2015). 240 pagesGoogle Scholar
  13. 13.
    Korn, G.A., Korn, T.M.: Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review. General Publishing Company (2000). 1151 pagesGoogle Scholar
  14. 14.
    Zadorozhnyi, V.N., Zakharenkova, T.R.: Optimization of channel distribution over nodes in networks with fractal traffic. In: 2016 Dynamics of Systems, Mechanisms and Machines, Dynamics, Omsk, Russia, 14–16 November (2016). doi: 10.1109/Dynamics.2016.7819112
  15. 15.
    Li, A., Whitt, W.: Approximate blocking probabilities in loss models with independence and distribution assumptions relaxed. Perform. Eval. 80, 82–101 (2014)CrossRefGoogle Scholar
  16. 16.
    Zakharenkova, T.R.: On loss probability in fractal multiserver queueing systems. Omsk Sci. Bull. 3(153), 110–114 (2017)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Vladimir N. Zadorozhnyi
    • 1
  • Tatiana R. Zakharenkova
    • 1
    Email author
  1. 1.Omsk State Technical UniversityOmskRussia

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