Abstract
A self-similar point process is developed by embedding a process with bursty behavior over timescales. This embedding is not arbitrary, but achieved through a model which itself has fractal patterns. This model decomposes the self-similar point process over its timescales in a manner that may be tractable for accurate characterization and control of packet traffic. The limiting behavior of the model is shown to possess the properties of a self-similar point process, namely, bursts of arrivals which have no (intrinsic) timescale. Furthermore, this model leads to efficient synthesis of such a process.
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References
B. B. Mandelbrot, “Self-similar error clusters in communication systems and the concept of conditional stationarity,” IEEE Transactions on Communication Technology, vol. COM-13, pp. 71–90, March 1965.
J. Beran, Statistics for Long-Memory Process. New York: Chapman and Hall, 1994.
M. E. Crovella and M. S. Taqqu, “Estimating the heavy tail index from scaling properties,” Methodology and Computing in Applied Probability, vol. 1, no. 1, 1999 to appear.
S. B. Lowen and M. C. Teich, “Fractal renewal processes generate 1/f noise,” Physics Review, vol. E, no. 47, pp. 992–1001, 1993.
B. K. Ryu and S. B. Lowen, “Point Process Approaches to the Modeling and Analysis of Self-Similar Traffic — Part I: Model Construction,” in Proc. IEEE INFOCOM’96, pp. 1468–1475, March 1996.
B. Tsybakov and N. D. Georganas, “Self-similar processes in Communications Networks,” IEEE Transactions on Information Theory, vol. 44, pp. 1713–1725, September 1998.
W. Leland, M. Taqqu, W. Willinger, and D. Wilson, “On the self-similar nature of Ethernet traffic.,” IEEE/ACM transactions on Networking, vol. 2, pp. 1–15, February 1994.
V. Paxson and S. Floyd, “Wide-area traffic: the failure of Poisson Modeling,” in Proc. Sigcomm’94, pp. 257–268, October 1994.
M. Parulekar and A. Makowski, “Tail Probabilities for a multiplexer with self-similar traffic,” in Proc. IEEE INFOCOM’96, pp. 1452–1459, March 1996.
A. T. Andersen and B. F. Nielsen, “An application of superposition of two state Markovian sources to the modelling of self-similar behavior,” in Proc. IEEE INFOCOM’97, 1997.
A. Feldmann and W. Whitt, “Fitting Mixture of Exponentials to Long-Tail Distributions to Analyze Network Performance Models,” Performance Evaluation, vol. 31, pp. 245–279, January 1998.
N. Likhanov, B. Tsybakov, and N. D. Georganas, “Analysis of an ATM buffer with self-similar (“fractal”) input traffic,” in Proc. IEEE INFOCOM’95, 1995.
P. R. Jelenkovic and A. A. Lazar, “Asymptotic Results for Multiplexing Subexponential On-Off Processes,” Advances in Applied Probability, vol. 31, no. 2, 1999 to appear.
A. Erramilli, R. P. Singh, and P. Pruthi, “Modeling Packet Traffic with Chaotic Maps,” Royal Institute of Technology, ISRN, KTH/IT/R-94/18, August 1994.
W. M. Lam and G. W. Wornell, “Multiscale Representation and Estimation of Fractal Point Processes,” IEEE Transactions on Signal Processing, vol. 43, pp. 2606–2617, November 1995.
W. Rudin, Priniciples of Mathematical Analysis. McGraw Hill, 1976.
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Krishnam, M.A., Venkatachalam, A., Capone, J.M. (2000). A Self-Similar Point Process Through Fractal Construction. In: Pujolle, G., Perros, H., Fdida, S., Körner, U., Stavrakakis, I. (eds) Networking 2000 Broadband Communications, High Performance Networking, and Performance of Communication Networks. NETWORKING 2000. Lecture Notes in Computer Science, vol 1815. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45551-5_22
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DOI: https://doi.org/10.1007/3-540-45551-5_22
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