Recent 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, which is marked by the presence of correlations that can extend over many time scales. In this paper, 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. 1...

A fundamental problem in text data mining is to extract meaningful structure from document streams that arrive continuously over time. E-mail and news articles are two natural examples of such streams, each characterized by topics that appear, grow in intensity for a period of time, and then fade away. The published literature in a particular research field can be seen to exhibit similar phenomena over a much longer time scale. Underlying much of the text mining work in this area is the following intuitive premise --- that the appearance of a topic in a document stream is signaled by a "burst of activity," with certain features rising sharply in frequency as the topic emerges.

We show the existence of effective bandwidths for multiclass Markov fluids and other types of sources that are used to model ATM traffic. More precisely,we show that when such sources share a buffer with deterministic service rate, a constraint on the tail of the buffer occupancy distribution is a linear constraint on the number of sources. That is, for a small loss probability one can assume that each source transmits at a fixed rate called its effective bandwidth. When traffic parameters are known, effective bandwidths can be calculated and may be used to obtain a circuit-switched style call acceptance and routing algorithm for ATM networks. The important feature of the effective bandwidth of a source is that it is a characteristic of that source and the acceptable loss probability only.Thus, the effective bandwidth of a source does not depend on the number of sources sharing the buffer nor on the model parameters of other types of sources sharing the buffer.

Motivated by recent development in high speed networks, in this paper we study two types of stability problems: (i) conditions for queueing networks that render bounded queue lengths and bounded delay for customers, and (ii) conditions for queueing networks in which the queue length distribution of a queue has an exponential tail with rate `. To answer these two types of stability problems, we introduce two new notions of traffic characterization: minimum envelope rate (MER) and minimum envelope rate with respect to `. Based on these two new notions of traffic characterization, we develop a set of rules for network operations such as superposition, input-output relation of a single queue, and routing. Specifically, we show that (i) the MER of a superposition process is less than or equal to the sum of the MER of each process, (ii) a queue is stable in the sense of bounded queue length if the MER of the input traffic is smaller than the capacity, (iii) the MER of a departure process from a stable queue is less than or equal to that of the input process (iv) the MER of a routed process from a departure process is less than or equal to the MER of the departure process multiplied by the MER of the routing process. Similar results hold for MER with respect to ` under a further assumption of independence. These rules provide a natural way to analyze feedforward networks with multiple classes of customers. For single class networks with nonfeedforward routing, we provide a new method to show that similar stability results hold for such networks under the FCFS policy. Moreover, when restricting to the family of two-state Markov modulated arrival processes, the notion of MER with respect to ` is shown to be

Variable bit-rate (VBR) compressed video traffic is expected to be a significant component of the traffic mix in integrated services networks. This traffic is hard to manage because it has strict delay and loss requirements while simultaneously exhibiting burstiness at multiple time scales. We show that burstiness over long time scales, in conjunction with resource reservation using one-shot traffic descriptors, can substantially degrade the loss rate, end-to-end delay, and statistical multiplexing gain of a connection. We use large-deviation theory to model the performance of multiple time-scale traffic and to motivate the design of renegotiated constant bit rate (RCBR) service. Sources using

Abstract-A new approach to determining the admissibility of variable bit rate (VBR) traffic in buffered digital networks is developed. In this approach all traffic presented to the network is assumed to have been subjected to leaky-bucket regulation, and extremal, periodic, on-off regulated traffic is considered; the analysis is based on fluid models. Each regulated traffic stream is allocated bandwidth and buffer resources which are independent of other traffic. Bandwidth and buffer allocations are traded off in a manner optimal for an adversarial situation involving minimal knowledge of other traffic. This leads to a single-resource statistical-multiplexing problem which is solved using techniques previously used for unbuffered traffic. VBR traffic is found to be divisible into two classes, one for which statistical multiplexing is effective and one for which statistical multiplexing is ineffective in the sense that accepting small losses provides no advantage over requiring lossless performance. The boundary of the set of admissible traffic sources is examined, and is found to be sufficiently linear that an effective bandwidth can be meaningfully assigned to each VBR source, so long as only statistically-multiplexable sources are considered, or only nonstatistically-multiplexable sources are considered. If these two types of sources are intermixed, then nonlinear interactions occur and fewer sources can be admitted than a linear theory would predict. A qualitative characterization of the nonlinearities is presented. The complete analysis involves conservative approx-imations; however, admission decisions based on this work are expected to be less overly conservative than decisions based on alternative approaches. I.

We consider the standard single-server queue with unlimited waiting space and the first-in first-out service discipline, but without any explicit independence conditions on the interarrival and service times. We find conditions for the steady-state waiting-time distribution to have small-tail asymptotics of the form x - 1 logP(W > x) - q * as x for q * > 0. We require only stationarity of the basic sequence of service times minus interarrival times and a Ga .. rtnerEllis condition for the cumulant generating function of the associated partial sums, i.e., n - 1 log Ee qS n y(q) as n , plus regularity conditions on the decay rate function y. The asymptotic decay rate q * is the root of the equation y(q) = 0. This result in turn implies a corresponding asymptotic result for the steady-state workload in a queue with general nondecreasing input. This asymptotic result covers the case of multiple independent sources, so that it provides additional theoretical support for a concept of effective bandwidths for admission control in multi-class queues based on asymptotic decay rates.

The algorithms described in this thesis are designed to schedule cells in a very high-speed, parallel, input-queued crossbar switch. We present several novel scheduling algorithms that we have devised, each aims to match the set of inputs of an input-queued switch to the set of outputs more efficiently, fairly and quickly than existing techniques. In Chapter 2 we present the simplest and fastest of these algorithms: SLIP --- a parallel algorithm that uses rotating priority ("round-robin") arbitration. SLIP is simple: it is readily implemented in hardware and can operate at high speed. SLIP has high performance: for uniform i.i.d. Bernoulli arrivals, SLIP is stable for any admissible load, because the arbiters tend to desynchronize. We present analytical results to model this behavior. However, SLIP is not always stable and is not always monotonic: adding more traffic can actually make the algorithm operate more efficiently. We present an approximate analytical model of this behavior. SLIP prevents starvation: all contending inputs are eventually served. We present simulation results, indicating SLIP's performance. We argue that SLIP can be readily implemented for a 32x32 switch on a single chip. In Chapter 3 we present i-SLIP, an iterative algorithm that improves upon SLIP by converging on a maximal size match. The performance of i-SLIP improves with up to log 2 N iterations. We show that although it has a longer running time than SLIP, an i-SLIP scheduler is little more complex to implement. In Chapter 4 we describe maximum or maximal weight matching algorithms based on the occupancy of queues, or waiting times of cells. These algorithms are stabl...

In this paper we identify the challenges and open issues involved in providing quality-of-service (QOS) guarantees to sessions in a high-speed wide area network and briefly survey research in this area. Four approaches towards providing QOS guarantees are described and discussed: the tightly controlled approach, the approximate approach, the bounding approach, and the observation-based approach.

The dramatically increased bandwidths and processing capabilities of future high-speed networks make possible many distributed real-time applications, such as sensor-based applications and multimedia services. Since these applications will have traffic characteristics and performance requirements that differ dramatically from those of current data-oriented applications, new communication network architectures and protocols will be required. In this paper we discuss the performance requirements and traffic characteristics of various real-time applications, survey recent developments in the areas of network architecture and protocols for supporting real-time services, and develop frameworks in which these, and future, research efforts can be considered.