We perform an extensive wavelet analysis of Internet backbone traffic traces to observe and understand the causes of small-time scaling phenomena present in them. We observe that for a majority of the traces, the second-order scaling exponents at small time scales (1-100 ms) are fairly close to 0.5, indicating that traffic fluctuations at these time scales are nearly uncorrelated. Some traces, however, do exhibit moderately large scaling exponents (≈0.7) at small time scales. In addition, the traces manifest mostly monofractal behaviors at small time scales. To identify the network causes of the observed scaling behavior, we analyze the flow composition of the traffic along two dimensions-flow byte contribution and flow density. Our study points to the dense flows (i.e., flows with densely clustered packets) as the correlation-causing factor in small time scales, and reveals that the traffic composition in terms of proportions of dense vs. sparse flows plays a major role in influencing the small-time scalings of aggregate traffic. Since queuing inside routers is influenced by traffic fluctuations at small time-scales, our observations and results have important implications for networking modeling, service provisioning and traffic engineering.
Bibliographical noteFunding Information:
Zhi-Li Zhang was supported in part by NSF grants ITR-0085824 and CAREER Award NCR-9734428, and by the University of Minnesota McKnight Land-grant professorship. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the funding agencies.
Zhi-Li Zhang received the B.S. degree in computer science from Nanjing University, China, in 1986 and his M.S. and Ph.D. degrees in computer science from the University of Massachusetts in 1992 and 1997. In 1997 he joined the Computer Science and Engineering faculty at the University of Minnesota, where he is currently an Associate Professor. From 1987 to 1990, he conducted research in Computer Science Department at Aarhus University, Denmark, under a fellowship from the Chinese National Committee for Education. He has held visiting positions at Sprint Advanced Technology Labs; IBM T.J. Watson Research Center; Fujitsu Labs of America, Microsoft Research China, and INRIA, Sophia-Antipolis, France. His research interests include computer communication and networks, especially the QoS guarantee issues in high-speed networks, multimedia and real-time systems, and modeling and performance evaluation of computer and communication systems.
- Long range dependence