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Can self-similar traffic be modeled by Markovian processes?

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Broadband Communications Networks, Services, Applications, Future Directions (IZS 1996)

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Abstract

In this paper, we compare high time resolution local area network (LAN) traffic with three different traffic models: Poisson, ON-OFF and 5-state Markov process. Due to the measured data's extreme variability on time scales ranging from milliseconds to days, it is difficult to find a model for it, especially a Markovian one. Recent studies show that conventional models do not capture the characteristics of the observed traffic. Fractal-based models have already been built to characterize such a traffic but they are not easily tractable tractability of them is not great. Through a new method which integrates different time scales in the model, we have tried to find a quite simple Markovian process having the same behavior as the measured traffic on the LAN. We show in particular that a simple 5-state Markov process integrating different time scales can reasonably model the behavior of measured traffic up to a certain time interval.

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References

  1. Allan T. Andersen, Alex Jensen and Bo Friis Nielsen, “Modelling of apparently self-similar packet arrival processes with Markovian Arrival Processes (MAP)”, COST 242 technical document, Cambridge, 1995

    Google Scholar 

  2. D. Comer, “Internetworking With TCP/IP, Volume 1: Principles, Protocols, and Architecture, Second Edition”, Prentice-Hall, 1991

    Google Scholar 

  3. D. Feldmeier, “Traffic measurements of a Token Ring Network”, Proc. of the IEEE Computer Network symposium, Washington, D. C. (November 1986)

    Google Scholar 

  4. R. Grünenfelder and S. Robert, “Which Arrival Law Parameters Are Decisive for Queueing System Performance”, ITC' 14, Plenary session, Antibes Juan-les-Pins, France, June 6–10, 1994

    Google Scholar 

  5. R. Gusella, “A Measurement Study of Diskless Workstation Traffic on an Ethernet”, IEEE Transactions on Communications, 38(9), Septembre 1990

    Google Scholar 

  6. R. Jain and S. A: Routier, “PAcket Trains: Measurments and a New Model for Computer Network Traffic”, IEEE Journal on Selected Areas in Communications, SAC-4, Number 6 (September 1986)

    Google Scholar 

  7. W. E. Leland and D. V. Wilson, “High Time Resolution Measurements and Analysis of LAN Traffic: Implications for LAN Interconnection”, IEEE Infocomm'91, paper 11D.3.1

    Google Scholar 

  8. P. Lévy, “Systèmes semi-Markoviens à au plus une infinité dénombrable d'états”, Proc. Int. Congr. Math., Amsterdam, vol. 2, 1954

    Google Scholar 

  9. B. B. Mandelbrot and M. S. Taqqu, “Robust R/S analysis of long run serial correlation”, in Proc. 42nd Session ISI, 1979, pp. 69–99

    Google Scholar 

  10. B. B. Mandelbrot and J. W. Van Ness, “Fractional Brownian motions, fractal noises and applications”, SIAM Rev. vol. 5, pp. 228–267, 1969

    Google Scholar 

  11. B. B. Mandelbrot and J. R. Wallis, “Computer experiments with fractional Gaussian noises”, Water Resources Research, vol. 5, pp. 228–267, 1969

    Google Scholar 

  12. S. Manthorpe and X. Garcia, “TCP Performance Over ATM Based LAN Interconnection Services”, Interop'95, Engineers Conference, April 28–30, 1995, Las Vegas, USA

    Google Scholar 

  13. I. Norros, “On the use of fractional Brownian motion in the theory of connectionless networks”, Technical contribution, TD94-33, September 1994

    Google Scholar 

  14. A. Papoulis, “Probability, Random Variables and Stochastic Processes”, Second Edition, Mc Graw-Hill, 1984

    Google Scholar 

  15. W. L. Smith, “Regenerative stochastic processes”, Proc. Roy. Soc. (London), Ser. A, vol. 232, p. 6–31, 1955

    Google Scholar 

  16. W. Willinger, W. E. Leland, M. S. Taqu and D. Wilson, “On the self-similar nature of ethernet traffic (extended version). IEEE/ACM Transactions on Networking, February 1994

    Google Scholar 

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Bernhard Plattner

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© 1996 Springer-Verlag Berlin Heidelberg

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Robert, S., Le Boudec, JY. (1996). Can self-similar traffic be modeled by Markovian processes?. In: Plattner, B. (eds) Broadband Communications Networks, Services, Applications, Future Directions. IZS 1996. Lecture Notes in Computer Science, vol 1044. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022222

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  • DOI: https://doi.org/10.1007/BFb0022222

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60895-0

  • Online ISBN: 978-3-540-49669-4

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