The modelling of ethernet data and of signals that are heavy-tailed with infinite variance

Scandinavian Journal of Statistics

Volumn 29, Issue 2, 2002, Pages 273-295

  Taqqu, Murad S ^a,b  

^a BOSTON UNIVERSITY   (United States)

^b Boston University   (United States)

Author keywords

Computer networks; Fractional Brownian motion; Heavy tails; Renewal reward processes; Self similar processes; Stable processes

Indexed keywords

EID: 0036014592     PISSN: 03036898     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9469.00283     Document Type: Conference Paper

References (34)

1. Abry, P. & Veitch, D. (1998). Wavelet analysis of long range dependent traffic. IEEE Trans. Information Theory 44, 2-15.
2. Abry, P., Flandrin, P., Taqqu, M.S. & Veitch, D. (2001). Self-similarity and tong-range dependence through the wavelet lens. In Long-range dependence: theory and applications (eds P. Doukhan, G. Oppenheim & M.S. Taqqu), Birkhänser, Boston. Preprint.
3. Beran, J., Sherman, R., Taqqu, M.S. & Willinger, W. (1995). Long-range dependence in variable-bit-rate video traffic. IEEE Trans. Comm. 43, 1566-1579.
4. Bingham, N.H., Goldie, C.M. & Teugels, J.L. (1987). Regular variation. Cambridge University Press, Cambridge.
5. Feldmann, A., Gilbert, A. & Willinger, W. (1998). Data networks as cascades: investigating the multifractal nature of Internet WAN traffic. In Proceedings of the ACM/SIGCOMM'98, 28, 42-55. Vancouver, Canada.
6. Feldmann, A., Gilbert, A., Huang, P. & Willinger, W. (1999). Dynamics of IP traffic: a study of the role of variability and the impact of control. Proceedings of the ACM/SIGCOMM'99, Cambridge, MA. Comput. Comm. Rev. 29, 301-313.
7. Garrett, M.W. & Willinger, W. (1994). Analysis, modeling and generation of self-similar VBR video traffic. In Proceedings of the ACM Sigcomm '94, London, UK, 269-280.
8. Kolmogorov, A.N. (1941). Local structure of turbulence in an incompressible liquid for very large Reynolds numbers. C.R. (Dokl.) Acad. Sci. URSS (N.S.) 30, 299-303. Reprinted in Friedlander, G.K. & Topper, L. (1961). Turbulence: classic papers on statistical theory. Interscience, New York.
9. Levy, J. & Taqqu, M.S. (1987). On renewal processes having stable inter-renewal intervals and stable rewards. Ann. Sci. Math. Québec 11, 95-110.
10. Levy, J.B. & Taqqu, M.S. (2000). Renewal reward processes with heavy-tailed interrenewal times and heavy-tailed rewards. Bernoulli 6, 23-44.
11. Leland, W.E., Taqqu, M.S., Willinger, W. & Wilson, D.V. (1994). On the self-similar nature of Ethernet traffic (Extended version). IEEE/ACM Trans. Networking 2, 1-15.
12. Leland, W.E. & Wilson, D.V. (1991). High time-resolution measurement and analysis of LAN traffic: implications for LAN interconnection. In Proceedings of the Infocom '91, Bal Harbour, FL, 1360-1366.
13. Mandelbrot, B.B. (1969). Long-run linearity, locally Gaussian processes, H-spectra and infinite variances. Internat. Econom. Rev. 10, 82-113.
14. Mannersalo, P. & Norros, I. (1997). Multifractal analysis of real ATM traffic: a first look. Technical report, COST257TD, VTT Information Technology.
15. Mikosch, T., Resnick, S., Rootzén, H. & Stegeman, A. (1999). Is network traffic approximated by stable Lévy motion or fractional Brownian motion? Preprint.
16. Park, K. & Willinger, W. (eds) (2000). Self-similar network traffice and performance evaluation. Wiley, New York.
17. Pipiras, V. & Taqqu, M.S. (2000). The limit of a renewal-reward process with heavy-tailed rewards is not a linear fractional stable motion. Bernoulli 6, 607-614.
18. Pipiras, V., Taqqu, M.S. & Levy, J.B. (2000). Slow, fast and arbitrary growth conditions for renewal reward processes when the renewals and the rewards are heavy-tailed. Preprint.
19. Resnick, S.I. & Rootzén, H. (1998). Self-similar communication models and very heavy tails. ORIE Technical Report 1228, Cornell University.
20. Resnick, S.I. & Samorodnitsky, G. (2000). Fluid queues, leaky buckets, on-off processes and teletraffic modeling with highly variable and correlated inputs. In Self-similar network traffic and performance evaluation (eds K. Park & W. Willinger), Wiley Interscience, New York.
21. Riedi, R.H. & Véhel J.L. (1997). Multifractal properties of TCP traffic: a numerical study. INRIA Research Report 3129. See also: Lévy Véhel, J. & Riedi, R. (1997) Fractional Brownian motion and data traffic modeling. In Fractals in engineering, from theory and industrial applications, 185-202. Springer, New York.
22. Riedi, R.H. & Véhel J.L. (1997). Multifractal properties of TCP traffic: a numerical study. INRIA Research Report 3129. See also: Lévy Véhel, J. & Riedi, R. (1997) Fractional Brownian motion and data traffic modeling. In Fractals in engineering, from theory and industrial applications, 185-202. Springer, New York.
23. Samorodnitsky, G. & Taqqu, M.S. (1994). Stable non-Gaussian processes: stochastic models with infinite variance. Chapman & Hall, New York, London.
24. Schoch, J.F. & Hupp, J.A. (1980). Measured performance of an ethernet local network. Comm. ACM 23, 711-721.
25. Taqqu, M.S. & Levy, J. (1986). Using renewal processes to generate long-range dependence and high variability. In Dependence in probability and statistics (eds E. Eberlein & M.S. Taqqu), 73-89, Birkhäuser, Boston.
26. Taqqu, M.S. & Teverovsky, V. (1997). Robustness of Whittle-type estimates for time series with long-range dependence. Stoch. Models 13, 723-757.
27. Taqqu, M.S. & Teverovsky, V. (1998). On estimating the intensity of long-range dependence in finite and infinite variance series. In A practical guide to heavy tails: statistical techniques and applications (eds R. Adler, R. Feldman & M.S. Taqqu), 177-217, Birkhäuser, Boston.
28. Taqqu, M.S., Teverovsky, V. & Willinger, W. (1995). Estimators for long-range dependence: an empirical study. Fractals 3, 785-798. Reprinted in Fractal geometry and analysis (eds C.J.G. Evertsz, H.-O. Peitgens & R.F. Voss) World Scientific Publishing, Singapore, 1996.
29. Taqqu, M.S., Teverovsky, V. & Willinger, W. (1997a). Is network traffic self-similar or multifractal? Fractals 5, 63-74.
30. Taqqu, M.S., Willinger, W. & Sherman, R. (1997b). Proof of a fundamental result in self-similar traffic modelling. Comput. Comm. Rev. 27, 5-23.
31. Willinger, W., Taqqu, M.S., Leland, W.E. & Wilson, V. (1995). Self-similarity in high-speed packet traffic: analysis and modeling of Ethernet traffic measurements. Statist. Sci. 10, 67-85.
32. Willinger, W., Taqqu, M.S. & Erramilli, A. (1996). A bibliographical guide to self-similar traffic and performance modeling for modern high-speed networks. In Stochastic networks: theory and applications (eds F.P. Kelly, S. Zachary & I. Ziedins), 339-366, Clarendon Press, Oxford.
33. Willinger, W., Taqqu, M.S., Sherman, R. & Wilson, D.V. (1997). Self-similarity through high-variability: statistical analysis of Ethernet LAN traffic at the source level. IEEE/ACM Trans. Networking 5, 71-86. An extended version of the paper with the same title that appeared in Comput. Comm. Rev. 25 (1995) 100-113.
34. Willinger, W., Paxson, V., Riedi, R.H. & Taqqu, M.S. (2001). Long-range dependence and data network traffic. In Long-range dependence: theory and applications (eds P. Doukhan, G. Oppenheim & M.S. Taqqu), Birkhäuser, Boston. Preprint.