The changing nature of network traffic: scaling phenomena

ABSTRACT

In this paper, we report on some preliminary results from an in-depth, wavelet-based analysis of a set of high-quality, packet-level traffic measurements, collected over the last 6-7 years from a number of different wide-area networks (WANs). We first validate and confirm an earlier finding, originally due to Paxson and Floyd [14], that actual WAN traffic is consistent with statistical self-similarity for sufficiently large time scales. We then relate this large-time scaling phenomenon to the empirically observed characteristics of WAN traffic at the level of individual connections or applications. In particular, we present here original results about a detailed statistical analysis of Web-session characteristics, and report on an intriguing scaling property of measured WAN traffic at the transport layer (i.e., number of TCP connection arrivals per time unit). This scaling property of WAN traffic at the TCP layer was absent in the pre-Web period but has become ubiquitous in today's WWW-dominated WANs and is a direct consequence of the ever-increasing popularity of the Web (WWW) and its emergence as the major contributor to WAN traffic. Moreover, we show that this changing nature of WAN traffic can be naturally accounted for by self-similar traffic models, primarily because of their ability to provide physical explanations for empirically observed traffic phenomena in a networking context. Finally, we provide empirical evidence that actual WAN traffic traces also exhibit scaling properties over small time scales, but that the small-time scaling phenomenon is distinctly different from the observed large-time scaling property. We relate this newly observed characteristic of WAN traffic to the effects that the dominant network protocols (e.g., TCP) and controls have on the flow of packets across the network and discuss the potential that multifractals have in this context for providing a structural modeling approach for WAN traffic and for capturing in a compact and parsimonious manner the observed scaling phenomena at large as well as small time scales.

REFERENCES

• 1: [1] P. Abry and D. Veitch. Wavelet analysis of long-range dependent traffic. IEEE Transactions on Information Theory 44, pp. 2-15, 1998.
• 2: Mark E. Crovella , Azer Bestavros, Self-similarity in World Wide Web traffic: evidence and possible causes, Proceedings of the 1996 ACM SIGMETRICS international conference on Measurement and modeling of computer systems, p.160-169, May 23-26, 1996, Philadelphia, Pennsylvania, United States
• 3: [3] D. R. Cox. Long-range dependence: A review. In H. A. David and H. T. David, editors, Statistics: An Appraisal, pages 55-74. Iowa State University Press, Ames, Iowa, 1984.
• 4: Ingrid Daubechies, Ten lectures on wavelets, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992
• 5: [5] C. J. G. Evertsz and B. B. Mandelbrot. Multifractal measures. In H. -O. Peitgen, H. Jurgens and D. Saupe, editors, Chaos and Fractals: New Frontiers in Science, Springer-Verlag, New York, 1992.
• 6: Anja Feldmann, On-line call admission for high-speed networks, Carnegie Mellon University, Pittsburgh, PA, 1996
• 7: [7] A. Feldmann. Modelling characteristics of TCP connections. Preprint, 1996.
• 8: [8] V. K. Gupta and E. C. Waymire. A statistical analysis of mesoscale rainfall as a random cascade. Journal of Applied Meteorology 32, pp. 251-267, 1993.
• 9: [9] R. Holley and E. C. Waymire. Multifractal dimensions and scaling exponents for strongly bounded random cascades. Annals of Applied Probability 2, pp. 819-845, 1992.
• 10: Gerald Kaiser, A friendly guide to wavelets, Birkhauser Boston Inc., Cambridge, MA, 1994
• 11: [11] T. G. Kurtz. Limit theorems for workload input models. In F. P. Kelly, S. Zachary, and I. Ziedins, editors, Stochastic Networks: Theory and Applications. Clarendon Press, Oxford, 1996.
• 12: Will E. Leland , Murad S. Taqqu , Walter Willinger , Daniel V. Wilson, On the self-similar nature of Ethernet traffic (extended version), IEEE/ACM Transactions on Networking (TON), v.2 n.1, p.1-15, Feb. 1994 [doi>10.1109/90.282603]
• 13: [13] Y. Meyer. Wavelets and operators, Cambridge University Press, Cambridge, UK, 1993.
• 14: Vern Paxson , Sally Floyd, Wide area traffic: the failure of Poisson modeling, IEEE/ACM Transactions on Networking (TON), v.3 n.3, p.226-244, June 1995 [doi>10.1109/90.392383]
• 15: [15] R. H. Riedi and J. Levy Vehel. Multifractal properties of TCP traffic: A numerical study. Preprint, 1997.
• 16: W. Richard Stevens, TCP/IP illustrated (vol. 1): the protocols, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1993
• 17: [17] M. S. Taqqu, V. Teverovsky and W. Willinger. Is network traffic self-similar or multifractal? Fractals 5, pp. 63-73, 1997.
• 18: [18] W. Willinger, M. S. Taqqu, and A. Erramilli. A bibliographical guide to self-similar traffic and performance modeling for modern high-speed networks. In F. P. Kelly, S. Zachary, and I. Ziedins, editors, Stochastic Networks: Theory and Applications, pages 339-366. Clarendon Press, Oxford, 1996.
• 19: Walter Willinger , Vern Paxson , Murad S. Taqqu, Self-similarity and heavy tails: structural modeling of network traffic, A practical guide to heavy tails: statistical techniques and applications, Birkhauser Boston Inc., Cambridge, MA, 1998
• 20: Walter Willinger , Murad S. Taqqu , Robert Sherman , Daniel V. Wilson, Self-similarity through high-variability: statistical analysis of Ethernet LAN traffic at the source level, IEEE/ACM Transactions on Networking (TON), v.5 n.1, p.71-86, Feb. 1997 [doi>10.1109/90.554723]

INDEX TERMS

Primary Classification:
  C. Computer Systems Organization
  C.2 COMPUTER-COMMUNICATION NETWORKS

Additional Classification:
  D. Software
  D.4 OPERATING SYSTEMS

General Terms:
Documentation, Management, Measurement