Can self-similar traffic be modeled by Markovian processes?
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.
KeywordsLAN Traffic self-similar Markovian models long range dependences
Unable to display preview. Download preview PDF.
- [Andersen 95]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, 1995Google Scholar
- [Comer 91]D. Comer, “Internetworking With TCP/IP, Volume 1: Principles, Protocols, and Architecture, Second Edition”, Prentice-Hall, 1991Google Scholar
- [Feldmeier 86]D. Feldmeier, “Traffic measurements of a Token Ring Network”, Proc. of the IEEE Computer Network symposium, Washington, D. C. (November 1986)Google Scholar
- [Grünenfelder 94]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, 1994Google Scholar
- [Gusella 90]R. Gusella, “A Measurement Study of Diskless Workstation Traffic on an Ethernet”, IEEE Transactions on Communications, 38(9), Septembre 1990Google Scholar
- [Jain 86]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
- [Leland 91]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.3.1Google Scholar
- [Lévy 54]P. Lévy, “Systèmes semi-Markoviens à au plus une infinité dénombrable d'états”, Proc. Int. Congr. Math., Amsterdam, vol. 2, 1954Google Scholar
- [Mandelbrot 68]B. B. Mandelbrot and M. S. Taqqu, “Robust R/S analysis of long run serial correlation”, in Proc. 42nd Session ISI, 1979, pp. 69–99Google Scholar
- [Mandelbrot 69]B. B. Mandelbrot and J. W. Van Ness, “Fractional Brownian motions, fractal noises and applications”, SIAM Rev. vol. 5, pp. 228–267, 1969Google Scholar
- [Mandelbrot 79]B. B. Mandelbrot and J. R. Wallis, “Computer experiments with fractional Gaussian noises”, Water Resources Research, vol. 5, pp. 228–267, 1969Google Scholar
- [Manthorpe 94]S. Manthorpe and X. Garcia, “TCP Performance Over ATM Based LAN Interconnection Services”, Interop'95, Engineers Conference, April 28–30, 1995, Las Vegas, USAGoogle Scholar
- [Norros 94]I. Norros, “On the use of fractional Brownian motion in the theory of connectionless networks”, Technical contribution, TD94-33, September 1994Google Scholar
- [Papoulis 84]A. Papoulis, “Probability, Random Variables and Stochastic Processes”, Second Edition, Mc Graw-Hill, 1984Google Scholar
- [Smith 55]W. L. Smith, “Regenerative stochastic processes”, Proc. Roy. Soc. (London), Ser. A, vol. 232, p. 6–31, 1955Google Scholar
- [Willinger 94]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 1994Google Scholar