Ashok Erramilli

Experimental queueing analysis with long-range dependent packet 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.

Self-similar traffic and network dynamics

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 todays 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.

An application of deterministic chaotic maps to model packet traffic

We investigate the application of deterministic chaotic maps to model traffic sources in packet based networks, motivated in part by recent measurement studies which indicate the presence of significant statistical features in packet traffic more characteristic of fractal processes than conventional stochastic processes. We describe one approach whereby traffic sources can be modeled by chaotic maps, and illustrate the traffic characteristics that can be generated by analyzing several classes of maps. We outline a potential performance analysis approach based on chaotic maps that can be used to assess the traffic significance of fractal properties. We show that low order nonlinear maps can capture several of the fractal properties observed in actual data, and show that the source characteristics observed in actual traffic can lead to heavy-tailed queue length distributions. It is our conclusion that while there are considerable analytical difficulties, chaotic maps may allow accurate, yet concise, models of packet traffic, with some potential for transient and steady state analysis.

Performance impacts of multi-scaling in wide area TCP/IP traffic

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.

Chaotic Maps As Models of Packet Traffic

Recent packet traffic measurement studies have indicated the presence of significant statistical features which are more characteristic of fractal processes than conventional stochastic processes. We demonstrate the feasibility of modeling these features efficiently using deterministic chaotic maps. We pr esent results fr om several maps to i llustrate the traf fic characteristics that can be modeled, including a two parameter nonlinear map that captures several fractal properties. We further outline a performance analysis method based on chaotic maps that can be used to assess the t raffic significance of fractal propert ies. It is our conclusion that while there are considerable analytical dif ficulties, chaotic maps may allow accurate, yet concise, models of packet traffic, with some potential for transient and steady state analysis.

Oscillations and chaos in a flow model of a switching system

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 systems 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 systems 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. >

Network performance for TCP networks Part I: Persistent sources

A method is presented which can form the basis for capacity planning for TCP traffic from persistent sources. The method estimates the rates of flows across an arbitrary network as determined by the TCP flow control, and can therefore estimate the performance of a TCP network. The method is simple, fast and provides good 1st order estimates with significant robustness. The method is extendible to a-persistent sources.

A reliable and efficient multicast for broadband broadcast networks

A reliable and efficient data transfer protocol is proposed for multicast applications in broadband broadcast networks. The protocol is based on negative acknowledgements, with several enhancements so that it matches most of the functionality of a positive acknowledgement based protocol. The protocol makes the best use of resources in the broadband network environment by conserving processing and trading off transmission and storage resources. The performance of this protocol is compared with the positive acknowledgement based protocol on the basis of maximum throughput as a function of group size for lecture and conference applications.

Multi-scaling models of TCP/IP and sub-frame VBR video traffic

Recent measurement and simulation studies have revealed that wide area network traffic displays complex statistical characteristics-possibly multifractal scaling-on fine timescales, in addition to the well-known property of self-similar scaling on coarser timescales. In this paper we investigate the performance and network engineering significance of these fine timescale features using measured TCP and MPEG2 video traces, queueing simulations and analytical arguments. We demonstrate that the fine timescale features can affect performance substantially at low and intermediate utilizations, while the longer timescale self-similarity is important at intermediate and high utilizations. We relate the fine timescale structure in the measured TCP traces to flow controls, and show that UDP traffic — which is not flow controlled-lacks such fine timescale structure. Likewise we relate the fine timescale structure in video MPEG2 traces to sub-frame encoding. We show that it is possibly to construct a relatively parsimonious multi-fractal cascade model of fine timescale features that matches the queueing performance of both the TCP and video traces. We outline an analytical method to estimate 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 controls can be significantly influenced by fine timescale fluctuations in network traffic. The work reported here can be used to model the relevant characteristics of wide area traffic across a full range of engineering timescales, and can be the basis of more accurate network performance analysis and engineering.

Fast and physically-based generation of self-similar network traffic with applications to ATM performance evaluation

Self-similarity concepts relate statistical properties of processes observed at different time scales through judicious scaling of time and space. They have recently been shown to be ideally suited to account for the surprising scaling properties that measured network traffic (e.g., number of packets/bytes per time unit) exhibits over a wide range of time scales, from milliseconds to seconds to minutes and beyond. The observed self-similar property in measurements from working packet networks is in sharp contrast to commonly made assumptions about the bursty nature of network traffic and challenges many of the traditional approaches to traffic and performance modeling. In this paper, we illustrate how the self-similar finding gives rise to new mathematical results that (i) clear the way for physically-based approaches to network traffic modeling, (ii) can be combined with high-performance computing capabilities to yield new and fast (i.e., linear in the number of observations) methods for generating self-similar traces, and (iii) provide new insights into the potential performance implications that self-similar traffic can have on the design of network equipment and on the perceived quality-of-service experienced by some of the dominant applications and services. In particular, studying the cell loss dynamics (rather than the traditional long-term cell loss rate) observed at an ATM switch that is fed by self-similar traffic, we discuss the impact of network traffic self-similarity on broadband services such as VBR video and on popular network protocols such as TCP/IP. ample evidence that actual network traffic is fractal in nature in that it exhibits statistical features over many timescales. In particular, these studies have demonstrated that measured traffic rates (i.e., number of packets or cells or bytes per time unit) in LAN/MAN/WAN environments, where data transfer rates typically vary between 1.5 - 155 Mbps, exhibit surprising scaling properties over a wide range of time scales; that is, actual network traffic looks statistically the same in the small (i.e., at small time scales, on the order of imilliseconds or seconds) and in the large (i.e., at time scales on the order of seconds and beyond) , and rto natural length of a “burst” is discernible: at every time scale ranging from milliseconds to seconds to minutes and beyond, bursts have the same qualitative appearance and cause the resulting traffic to exhibit fractal-like characteristics. The observed self-similarity properties in measurements from working packet networks is in sharp contrast to commonly made modeling choices in today’s traffic theory and practice (where the focus remains on reproducing the bursty behavior of network traffic time scale by time scalle) and challenges traditional approaches to traffic and performance modeling. At the same time, it provides new insights into the dynamic nature of actual network traffic, gives rise to novel modeling approaclies that take into account the specific features of the underlying networking structure and hence allows for plausible physical explanations of observed traEic characteristics in the networking context. For example, not only can the observed self-similar natuire of Ethernet LAN traffic at the aggregate level (Le., aggregated over all active hosts on the network; see Leland, Taqqu, Willinger,