Performance impacts of self-similarity in traffic
Authors: Erramilli Ashok 
Published: January 2007

Recent measurement studies in Bellcore and elsewhere have convincingly established the presence of statistical self similarity in high-speed network traffic. What is less clear --- and as such the subject of intense current research --- is the impact of the self-similarity on network performance. Given that traditional queueing models of network performance do not model self-similarity, the validity of traditional models to predict network performance would be supported if it is shown that self-similarity does not have measurable impacts on performance. On the other hand, if the converse of this assertion were true, it would have significant impacts on the way networks are designed and analyzed, as well as open up new areas of research in mathematical modeling, queueing analysis, network design and control. The issues addressed in this session are therefore of fundamental importance in high-speed network research.Given that queueing behavior is dominated by traffic characteristics over the time scales of busy periods, it has been argued that phenomena that span many time scales, such as self-similarity, should not be relevant for queueing performance. However, the paper by Narayan, Erramilli and Willinger presents evidence that for data traffic, the long range dependence (which is related to the self-similarity in traffic) can dominate queueing behavior under a variety of conditions. Specifically, it is shown based on a series of carefully designed simulation experiments with actual traffic traces, that the queueing behavior with actual traces is considerably heavier than that predicted by traditional theory, and that these differences are attributable to long range dependence. The paper by Heyman and Lakshman investigates modeling of video traffic to predict cell loss performance with finite buffer systems, and they conclude that long-range dependence is not a crucial property in determining the finite buffer behavior of video conferences. In particular, a Markov chain model that does not model long-range dependence is nevertheless able to reproduce various operating characteristics over a wide range of loadings obtained with the actual video trace. Mukherjee, Adas, Klivansky and Song investigate the performance impacts of short-range and long-range correlation components using simulations with a fractional ARIMA model. They also discuss a strategy to provide quality of service guarantees with long range dependent traffic, as well as recent results on NSFNET traffic. Finally, the paper by Li describes a frequency-domain based analytical tool that matches a special class of Markov chains with traces exhibiting a variety of characteristics, including long-range dependence. Good agreement is reported between analytical queueing solutions of the matched Markov chains, and simulation results obtained video and data traffic traces.This session therefore brings together a wide range of viewpoints on this issue. Resolution of such seemingly conflicting conclusions lies in the fact that in performance analysis, answers sensitively depend on the specific details of a problem. Thus the proper question to ask is not whether or not self-similarity matters in queueing; but under what conditions it matters. Likewise, the question to ask is not whether a class of models is invalid; but to identify the conditions under which traditional Markov or self-similar traffic models are expected to be valid. Finally, given an understanding of statistical features that are relevant to a given problem, the challenge is to model these accurately and parsimoniously so that the model is useful in practical performance analysis. The work outlined in the abstracts below adds significantly to our understanding of these issues.