Proof of a fundamental result in self-similar traffic modeling

Computer Communication Review

Volumn 27, Issue 2, 1997, Pages 5-23

  Taqqu, Murad S ^a   Willinger, Walter ^b   Sherman, Robert ^c  

^a Boston University   (United States)

^b AT AND T LABS RESEARCH   (United States)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; LOCAL AREA NETWORKS; MATHEMATICAL MODELS; PERFORMANCE;

JOSEPH EFFECT; NOAH EFFECT; TRAFFIC MEASUREMENT;

TELECOMMUNICATION TRAFFIC;

EID: 0031125708     PISSN: 01464833     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/263876.263879     Document Type: Article

References (22)

1. P. Billingsley. Convergence of Probability Measures J. Wiley & Sons, Inc., New York, 1968.
2. N. H. Bingham, C. M. Goldie, and J. L. Teugels. Regular Variation. Cambridge University Press, 1987.
3. K. L. Chung. A Course in Probability Theory. Academic Press, New York, 2nd edition, 1974.
4. D. R. Cox. Renewal Theory. Methuen & Co., London, 1967. Science Paperback Edition.
5. W. Feller. An Introduction to Probability Theory and its Applications, volume 2. Wiley, New York, 2nd edition, 1971.
6. D. Heath, S. Resnick and G. Samorodnitsky. Heavy Tails and Long-Range Dependence in On/Off Processes and Associated Fluid Models. Preprint, School of ORIE, Cornell University, Ithaca, NY, 1996.
7. I. A. Ibragimov and Yu. V. Linnik. Independent and stationary sequences of random variables. Wolters-Nordhoff, The Netherlands, 1971.
8. R. Jain and S. A. Routhier. Packet Trains: Measurements and a New Model for Computer Network Traffic. IEEE Journal on Selected Areas in Communications, Vol. 4, pp. 986-995, 1986.
9. S. Karlin and H. M. Taylor. A First Course in Stochastic Processes. Academic Press, New York, second edition, 1975.
10. T. Konstantopoulos and S-J Lin. High variability versus long-range dependence for network performance. Preprint, 1996.
11. K. R. Krishnan. The Hurst Parameter of non-Markovian On-Off Traffic Sources. Preprint, 1995.
12. W. E. Leland, M. S. Taqqu, W. Willinger, and D. V. Wilson. On the Self-Similar Nature of Ethernet Traffic. ACM/SIGCOMM Computer Communications Review, Vol. 23, pp. 183-193, 1993. Proceedings of the ACM/SIGCOMM'93, San Francisco, September 1993.
13. W. E. Leland, M. S. Taqqu, W. Willinger, and D. V. Wilson. On the Self-Similar Nature of Ethernet Traffic (Extended Version). IEEE/ACM Transactions on Networking, Vol. 2, pp. 1-15, 1994.
14. S. B. Lowen and M. C. Teich. Fractal Renewal Processes Generate 1/f Noise. Physical Review E, 47:992-1001, 1993.
15. B. B. Mandelbrot. Long-Run Linearity, Locally Gaussian Processes, H-Spectra and Infinite Variances. International Economic Review, Vol. 10, pp. 82-113, 1969.
16. G. Samorodnitsky and M. S. Taqqu. Stable Non-Gaussian Processes: Stochastic Models with Infinite Variance. Chapman and Hall, New York, London, 1994.
17. A, V. Skorohod. Limit theorems for stochastic processes with independent increments. Theory of Probability and Its Applications, 2:138-171, 1957.
18. M. S. Taqqu. Weak Convergence to Fractional Brownian Motion and to the Rosenblatt Process. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 31:287-302, 1975.
19. M. S. Taqqu and J. Levy. Using Renewal Processes to Generate Long-Range Dependence and High Variability. In E. Eberlein and M. S. Taqqu, editors, Dependence in Probability and Statistics, pp. 73-89, Boston, 1986. Birkhäuser.
20. J. L. Teugels. Renewal Theorems when the First or the Second Moment is Infinite. The Annals of Mathematical Statistics, 39, pp. 1210-1219, 1968.
21. W. Willinger, M. S. Taqqu, R. Sherman, and D. V. Wilson. Self-similarity through High-Variability: Statistical Analysis of Ethernet LAN Traffic at the Source Level. Computer Communications Review, 25, pp. 100-113, 1995. Proceedings of the ACM/SIGCOMM'95, Cambridge, MA, August 1995.
22. W. Willinger, M. S. Taqqu, R. Sherman, and D. V. Wilson. Self-similarity through High-Variability: Statistical Analysis of Ethernet LAN Traffic at the Source Level. IEEE/ACM Transactions on Networking, Vol. 5, No. 1. pp. 1-16, 1997. Extended version of the preceding paper.