Abstract
In this paper we investigate the characteristics of network traffic via the cluster point process framework. It is found that the exact distributional properties of the arrival process within a flow is not very relevant at large time scales or low frequencies. We also show that heavy-tailed flow duration does not automatically imply long-range dependence at the IP layer. Rather, the number of packets per flow has to be heavy-tailed with infinite variance to give rise to long-range dependent IP traffic. Even then, long-range dependence is not guaranteed if the interarrival times within a flow are much smaller than the interarrival times of flows. In this scenario, the resulting traffic behaves like a short-range dependent heavy-tailed process. We also found that long-range dependent interflow times do not contribute to the spectrum of IP traffic at low frequencies.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ryu, B.K., Lowen, S.B.: Point-process approaches to the modeling and analysis of self-similar traffic. In: IEEE INFOCOM, IEEE Computer Society Press, Los Alamitos (1996)
Lee, I.W.C., Fapojuwo, A.O.: Stochastic processes for computer network traffic. Computer Communications 29(1), 1–23 (2005)
Cox, D., Isham, V.: Point processes - Monographs on applied probability and statistics. Chapman and Hal, Sydney (1980)
Willinger, W., Paxson, V., Taqqu, M.: Self-similarity and heavy-tails: Structural modeling of network traffic. In: Adler, R.J., Feldman, R.E., Taqqu, M. (eds.) A practical guide to heavy-tails: Statistical techniques and applications, pp. 27–54. Birkhäuser, Basel (1998)
Stevens, W.: TCP/IP Illustrated: the protocols. Addison-Wesley, London (1994)
Hohn, N., Veitch, D., Abry, P.: Cluster processes: A natural language for network traffic. IEEE Transactions on Signal Processing, Special Issue on Signal Processing in Networking 51(8), 2229–2244 (2003)
Bartlett, M.: The spectral analysis of point processes. Journal of the Royal Statistical Society. B. 25, 264–296 (1963)
Lewis, P.: A branching Poisson process model for the analysis of computer failure patterns. Journal of the Royal Statistical Society B 26(3), 398–456 (1964)
Park, K., Willinger, W.: Self-similar network traffic and performance evaluation. Wiley-Interscience, New York (2000)
Beran, J.: Statistics for long-memory processes. Chapman and Hall, Sydney (1994)
Goldie, C.M., Kluppelberg, C.: Subexponential distributions. In: Adler, R.J., Feldman, R.E., Taqqu, M. (eds.) A practical guide to heavy-tails: Statistical techniques and applications, pp. 27–54. Birkhäuser, Basel (1998)
Embrechts, P., Hawkes, J.: A limit theorem for the tails of discrete infinitely divisible laws with applications to fluctuation theory. Journal Australian Mathematical Society (Series A) 32, 412–422 (1982)
Baltrunas, A., Daley, D., Kluppelberg, C.: Tail behaviour of the busy period of GI/GI/1 queue with subexponential service times. Stoch. Proc. Appl. 111(2), 237–258 (2004)
Willmot, G., Lin, X.: Lundberg bounds on the tails of compound distributions. Journal of Applied Probability 31(3), 743–756 (1994)
Cox, D.: Renewal theory. Chapman and Hall, Sydney (1962)
Lee, I.W.C., Fapojuwo, A.O.: Network traffic under very heavy-tails. Submitted for review to IEEE Trans. Sig. Proc. (February 2007)
Bingham, N.H., Goldie, C.M., Teugels, J.L.: Regular variation. In: Encyclopedia of mathematics and its applications, Cambridge University press, Cambridge (1987)
Barlow, R., Proschan, F.: Statistical theory of reliability and life testing. Holt, Rinehart and Winston (1975)
Lee, I.W.C., Fapojuwo, A.O.: Wireless TCP/IP traffic: Analysis and modeling. Submitted for review to Computer networks (February 2007)
Daley, D.J.: The Hurst index of long-range dependent renewal processes. The Annals of Probablity 27(4), 2035–2041 (1999)
Abry, P., Veitch, D.: Wavelet analysis of long-range dependent traffic. IEEE Transaction on Info. Theory 44(1), 2–15 (1998)
Mikosch, T., Resnick, S., Rootzen, H., Stegeman, A.: Is network traffic approximated by stable levy motion or fractional brownian motion? Ann. Appl. Probab. 12(1), 23–68 (2002)
Lee, I.W.C., Fapojuwo, A.O.: Modeling wireless TCP connection arrival process. In: IEEE GLOBECOM, IEEE Computer Society Press, Los Alamitos (2006)
Cox, D.R., Lewis, P.A.W.: The statistical analysis of series of events. Methuen (1966)
Li, S., Hwang, C.: Queue response to input correlation functions: Continuous spectral analysis. IEEE/ACM Transactions on Networking 1(6) (1993)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lee, I.W.C., Fapojuwo, A.O. (2007). Understanding IP Traffic Via Cluster Processes. In: Mason, L., Drwiega, T., Yan, J. (eds) Managing Traffic Performance in Converged Networks. ITC 2007. Lecture Notes in Computer Science, vol 4516. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72990-7_25
Download citation
DOI: https://doi.org/10.1007/978-3-540-72990-7_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72989-1
Online ISBN: 978-3-540-72990-7
eBook Packages: Computer ScienceComputer Science (R0)