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...

Abstract—An overview of statistical and information-theoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discrete-time finite-state homogeneous Markov chain observed through a discrete-time memoryless invariant channel. In recent years, the work of Baum and Petrie on finite-state finite-alphabet HMPs was expanded to HMPs with finite as well as continuous state spaces and a general alphabet. In particular, statistical properties and ergodic theorems for relative entropy densities of HMPs were developed. Consistency and asymptotic normality of the maximum-likelihood (ML) parameter estimator were proved under some mild conditions. Similar results were established for switching autoregressive processes. These processes generalize HMPs. New algorithms were developed for estimating the state, parameter, and order of an HMP, for universal coding and classification of HMPs, and for universal decoding of hidden Markov channels. These and other related topics are reviewed in this paper. Index Terms—Baum–Petrie algorithm, entropy ergodic theorems, finite-state channels, hidden Markov models, identifiability, Kalman filter, maximum-likelihood (ML) estimation, order estimation, recursive parameter estimation, switching autoregressive processes, Ziv inequality. I.

The interconnection of local area networks is increasingly important, but little data are available on the characteristics of the aggregate traffic that LANs will be submitting to the interconnection media. In order to understand the interactions between LANs and the proposed interconnection networks (MANs, WANs, and BISDN networks), it is necessary to study the behavior of this external LAN traffic over many time scales – from milliseconds to hundreds of seconds. We present a high time-resolution hardware monitor for Ethernet LANs that avoids the shortcomings of previous monitoring tools, such as traffic burst clipping and timestamp jitter. Using data recorded by our monitor for several hundred million Ethernet packets, we present an overview of the short-range time correlations in external LAN traffic. Our analysis shows that LAN traffic is extremely bursty across time domains spanning six orders of magnitude. We compare this behavior with simple formal traffic models and employ the data in a trace-driven simulation of the LAN-BISDN interface proposed for the SMDS SM service. Our results suggest that the pronounced short-term traffic correlations, together with the extensive time regime of traffic burstiness, strongly influence the patterns of loss and delay induced by LAN interconnection. 1.

Even though ATM seems to be clearly the wave of the future, one performance analysis indicates that the combination of stringent performance requirements (e.g., 10 - 9 cell blocking probabilities), moderate-size buffers and highly bursty traffic will require that the utilization of the network be quite low. That performance analysis is based on asymptotic decay rates of steady-state distributions used to develop a concept of effective bandwidths for connection admission control. However, we have developed an exact numerical algorithm that shows that the effective-bandwidth approximation can overestimate the target small blocking probabilities by several orders of magnitude when there are many sources that are more bursty than Poisson. The bad news is that the appealing simple connection-admissioncontrol algorithm using effective bandwidths based solely on tailprobability asymptotic decay rates may actually not be as effective as many have hoped. The good news is that the statistical multiplexing gain on ATM networks may actually be higher than some have feared. For one example, thought to be realistic, our analysis indicates that the network actually can support twice as many sources as predicted by the effectivebandwidth approximation. That discrepancy occurs because for a large number of bursty sources the asymptotic constant in the tail probability exponential asymptote is extremely small. That in turn can be explained by the observation that the asymptotic constant decays exponentially in the number of sources when the sources are scaled to keep the total arrival rate fixed. We also show that the effective-bandwidth approximation is not always conservative. Specifically, for sources less bursty than Poisson, the asymptotic constant grows exponentially in the numbe...

Traffic models are at the heart of any performance evaluation of telecommunications networks. An accurate estimation of network performance is critical for the success of broadband networks. Such networks need to guarantee an acceptable quality of service (QoS) level to the users. Therefore, traffic models need to be accurate and able to capture the statistical characteristics of the actual traffic. In this article we survey and examine traffic models that are currently used in the literature. Traditional short-range and non-traditional long-range dependent traffic models are presented. Number of parameters needed, parameter estimation, analytical tractability, and ability of traffic models to capture marginal distribution and auto-correlation structure of actual traffic are discussed. n Figure 1. Finite state model for voice. This research was supported in part by the National Science Foundation under grant NCR-9396299. This article is based on Georgia Tech technical report G...

This paper is principally concerned with resource allocation for connections tolerating statistical qualityof service #QoS# guarantees in a public wide-area ATM network. Our aim is to sketch a framework, based on e#ective bandwidths, for call admission schemes that are sensitivetoindividual QoS requirements and account for statistical multiplexing. We begin by describing recent results approximating the e#ective bandwidth required by heterogeneous streams sharing bu#ered links, including results for the packetized generalized processor sharing service discipline. Extensions to networks follow via the concept of decoupling bandwidths - motivated by a study of the input-output properties of queues. Based on these results we claim that networks with su#cient routing diversity will inherently satisfy nodal decoupling. We then discuss on-line methods for estimating the e#ective bandwidth of a connection. Using this type of tra#c monitoring we propose an approach to usage parameter ...

We propose to characterize the burstiness of packet arrival processes with indices of dispersion for intervals and for counts. These indices, which are functions of the variance of intervals and counts, are relatively straightforward to estimate and convey much more information than simpler indices, such as the coefficient of variation, that are often used to describe burstiness quantitatively.

: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : xii 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 1. The problem : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 2. Overview of thesis : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 3. Contribution of our work : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 2 Taxonomy of traffic characteristics : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 1. Aggregation granularity : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 2. Host versus network centric perspective : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 3. Host centric perspective : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 1. Delay and jitter : : : : : ...

Multicast applications, including audio and video, are expected to consume a large fraction of resources in forthcoming high speed networks. Because of this, new services are needed to provide the quality of service (QoS) required by these applications. In this paper we take a step in this direction by presenting a general framework for admission control and resource reservation for multicast sessions. Within this framework, efficient and practical algorithms that aim to efficiently utilize network resources are developed. The problem of admission control is decomposed into several subproblems that include: the division of end-to-end QoS requirements into local QoS requirements, the mapping of local QoS requirements into resource allocation, and the optimization of the resulting resource allocation for a multicast session. These are solved independently of each other yielding a set of mechanisms and policies that can be used to provide admission control and resource reservation for mul...

Many important problems in engineering and science are well-modeled by Poisson processes. In many applications it is of great interest to accurately estimate the intensities underlying observed Poisson data. In particular, this work is motivated by photon-limited imaging problems. This paper studies a new Bayesian approach to Poisson intensity estimation based on the Haar wavelet transform. It is shown that the Haar transform provides a very natural and powerful framework for this problem. Using this framework, a novel multiscale Bayesian prior to model intensity functions is devised. The new prior leads to a simple, Bayesian intensity estimation procedure. Furthermore, we characterize the correlation behavior of the new prior and show that it has 1/f spectral characteristics. The new framework is applied to photon-limited image estimation and its potential to improve nuclear medicine imaging is examined.