One of the most significant findings of traffic measurement studies over the last decade has been the observed self-similarity in packet network traffic. Subsequent research has focused on the origins of this self-similarity, and the network engineering significance of this phenomenon. This paper reviews what is currently known about network traffic self-similarity and its significance. We then consider a matter of current research, namely, the manner in which network dynamics (specifically, the dynamics of transmission control protocol (TCP), the predominant transport protocol used in today's Internet) can affect the observed self-similarity. To this end, we first discuss some of the pitfalls associated with applying traditional performance evaluation techniques to highly-interacting, large-scale networks such as the Internet. We then present one promising approach based on chaotic maps to capture and model the dynamics of TCP-type feedback control in such networks. Not only can appropriately chosen chaotic map models capture a range of realistic source characteristics, but by coupling these to network state equations, one can study the effects of network dynamics on the observed scaling behavior We consider several aspects of TCP feedback, and illustrate by examples that while TCP-type feedback can modify the self-similar scaling behavior of network traffic, it neither generates it nor eliminates it.

Recent measurement and simulation studies have revealed that wide area network traffic has complex statistical, possibly multifractal, characteristics on short timescales, and is self-similar on long timescales. In this paper, using measured TCP traces and queueing simulations, we show that the fine timescale features can affect performance substantially at low and intermediate utilizations, while the coarse timescale self-similarity is important at intermediate and high utilizations. We outline an analytical method for estimating performance for traffic that is self-similar on coarse timescales and multi-fractal on fine timescales, and show that the engineering problem of setting safe operating points for planning or admission control can be significantly affected by fine timescale fluctuations in network traffic.

Traffic measurement studies from a wide range of working packet networks have convincingly established the presence of significant statistical features that are characteristic of fractal traffic processes, in the sense that these features span many time scales. Of particular interest in packet traffic modeling is a property called long-range dependence (LRD), which is marked by the presence of correlations that can extend over many time scales. We demonstrate empirically that, beyond its statistical significance in traffic measurements, long-range dependence has considerable impact on queueing performance, and is a dominant characteristic for a number of packet traffic engineering problems. In addition, we give conditions under which the use of compact and simple traffic models that incorporate long-range dependence in a parsimonious manner (e.g., fractional Brownian motion) is justified and can lead to new insights into the traffic management of high speed networks.

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.

Field data from digital switching systems in an access tandem environment indicate unexpectedly large queuing delays at moderate occupancies. It is shown that these delays are caused by an effect called traffic synchronization, which is the batching of a system's workload caused by interactions between the system and incident traffic. The authors develop a flow model to study this effect and show that a momentary overload can cause sustained oscillations in the system's queues. There are several steady-state modes of operation, and it is shown that for certain parameter ranges the system is chaotic. Such oscillatory behavior can significantly lower the real-time capacity of the switching system, and controls to limit the synchronization effect are suggested. These controls are incorporated into the flow model and analyzed. The results described are validated by numerical studies, simulations, and field data.>

Random sensor motion is one source of error in source location using a passive array. This paper attempts to determine whether correlations in the sensor motion can be exploited to remove such errors. A travelling wave perturbation is considered, because it is representative of a class of practical problems where the motion of nearby sensors is highly correlated. Cramer-Rao bounds on source location parameters are derived in the cases of arrays of two sensors andM (\gg 1)sensors. It is shown that the incremental errors due to sensor motion are more strongly dependent on the observation time and the signal to noise ratio than in the independent sensor motion case. Heuristic insights are provided into the results with discussions of processing schemes that approach the Cramer-Rao bounds.

A fundamental limitation in underwater source localization procedures using arrays of spatially distributed sensors is the uncertainty in sensor positions. This paper examines delay estimation in the presence of background noise, random array perturbations and an auxiliary source at a known location. Cramer-Rao bounds on the delay estimate are given, and the behavior of the bound as a function of the auxiliary source strength is examined. It is shown that the auxiliary source can be used to reduce estimation errors due to sensor displacements; at the same time it may add to the errors due to the background noise. It is concluded that under some conditions the auxiliary source can be used to reduce the total error in the delay estimate.

The effect of random sensor motion on source localization is considered. A lower bound on the error due to sensor motion in the estimate of time delay between a pair of sensors is derived assuming a first-order Markov spectrum for the sensor motion. The dependence of the lower bound on the fluctuation error is studied, and the implications of the bound on processing schemes are examined. The analysis is extended to (M-1) delays and M sensors, and the problem of correlated sensor motion is discussed.