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288
On the Selfsimilar Nature of Ethernet Traffic (Extended Version)
, 1994
"... We demonstrate that Ethernet LAN traffic is statistically selfsimilar, that none of the commonly used traffic models is able to capture this fractallike behavior, that such behavior has serious implications for the design, control, and analysis of highspeed, cellbased networks, and that aggrega ..."
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Cited by 2213 (46 self)
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We demonstrate that Ethernet LAN traffic is statistically selfsimilar, that none of the commonly used traffic models is able to capture this fractallike behavior, that such behavior has serious implications for the design, control, and analysis of highspeed, cellbased networks, and that aggregating streams of such traffic typically intensifies the selfsimilarity (“burstiness”) instead of smoothing it. Our conclusions are supported by a rigorous statistical analysis of hundreds of millions of high quality Ethernet traffic measurements collected between 1989 and 1992, coupled with a discussion of the underlying mathematical and statistical properties of selfsimilarity and their relationship with actual network behavior. We also present traffic models based on selfsimilar stochastic processes that provide simple, accurate, and realistic descriptions of traffic scenarios expected during BISDN deployment.
The iSLIP Scheduling Algorithm for InputQueued Switches
, 1999
"... An increasing number of high performance internetworking protocol routers, LAN and asynchronous transfer mode (ATM) switches use a switched backplane based on a crossbar switch. Most often, these systems use input queues to hold packets waiting to traverse the switching fabric. It is well known th ..."
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Cited by 425 (8 self)
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An increasing number of high performance internetworking protocol routers, LAN and asynchronous transfer mode (ATM) switches use a switched backplane based on a crossbar switch. Most often, these systems use input queues to hold packets waiting to traverse the switching fabric. It is well known that if simple first in first out (FIFO) input queues are used to hold packets then, even under benign conditions, headofline (HOL) blocking limits the achievable bandwidth to approximately 58.6 % of the maximum. HOL blocking can be overcome by the use of virtual output queueing, which is described in this paper. A scheduling algorithm is used to configure the crossbar switch, deciding the order in which packets will be served. Recent results have shown that with a suitable scheduling algorithm, 100 % throughput can be achieved. In this paper, we present a scheduling algorithm called iSLIP. An iterative, roundrobin algorithm, iSLIP can achieve 100% throughput for uniform traffic, yet is simple to implement in hardware. Iterative and noniterative versions of the algorithms are presented, along with modified versions for prioritized traffic. Simulation results are presented to indicate the performance of iSLIP under benign and bursty traffic conditions. Prototype and commercial implementations of iSLIP exist in systems with aggregate bandwidths ranging from 50 to 500 Gb/s. When the traffic is nonuniform, iSLIP quickly adapts to a fair scheduling policy that is guaranteed never to starve an input queue. Finally, we describe the implementation complexity of iSLIP. Based on a twodimensional (2D) array of priority encoders, singlechip schedulers have been built supporting up to 32 ports, and making approximately 100 million scheduling decisions per second.
Hidden Markov processes
 IEEE Trans. Inform. Theory
, 2002
"... Abstract—An overview of statistical and informationtheoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discretetime finitestate homogeneous Markov chain observed through a discretetime memoryless invariant channel. In recent years, the work of Baum and Petrie on finite ..."
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Cited by 264 (5 self)
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Abstract—An overview of statistical and informationtheoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discretetime finitestate homogeneous Markov chain observed through a discretetime memoryless invariant channel. In recent years, the work of Baum and Petrie on finitestate finitealphabet 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 maximumlikelihood (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, finitestate channels, hidden Markov models, identifiability, Kalman filter, maximumlikelihood (ML) estimation, order estimation, recursive parameter estimation, switching autoregressive processes, Ziv inequality. I.
Scheduling Algorithms for Inputqueued Cell Switches
, 1995
"... The algorithms described in this thesis are designed to schedule cells in a very highspeed, parallel, inputqueued crossbar switch. We present several novel scheduling algorithms that we have devised, each aims to match the set of inputs of an inputqueued switch to the set of outputs more effici ..."
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Cited by 174 (5 self)
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The algorithms described in this thesis are designed to schedule cells in a very highspeed, parallel, inputqueued crossbar switch. We present several novel scheduling algorithms that we have devised, each aims to match the set of inputs of an inputqueued 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 ("roundrobin") 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 iSLIP, an iterative algorithm that improves upon SLIP by converging on a maximal size match. The performance of iSLIP improves with up to log 2 N iterations. We show that although it has a longer running time than SLIP, an iSLIP 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...
High timeresolution measurement and analysis of LAN traffic: Implications for LAN interconnection
, 1991
"... 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 network ..."
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Cited by 120 (2 self)
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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 timeresolution 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 shortrange 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 tracedriven simulation of the LANBISDN interface proposed for the SMDS SM service. Our results suggest that the pronounced shortterm traffic correlations, together with the extensive time regime of traffic burstiness, strongly influence the patterns of loss and delay induced by LAN interconnection. 1.
Traffic Models in Broadband Networks
, 1997
"... 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, traff ..."
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Cited by 104 (0 self)
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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 shortrange and nontraditional longrange dependent traffic models are presented. Number of parameters needed, parameter estimation, analytical tractability, and ability of traffic models to capture marginal distribution and autocorrelation 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 NCR9396299. This article is based on Georgia Tech technical report G...
Squeezing the most out of ATM.
 IEEE Transactions on Communications,
, 1996
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Characterizing the Variability of Arrival Processes with Indices of Dispersion
 IEEE Journal on Selected Areas in Communications
, 1990
"... 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 indic ..."
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Cited by 82 (0 self)
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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.
Stochastically Bounded Burstiness for Communication Networks
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1999
"... We develop a network calculus for processes whose burstiness is stochastically bounded by general decreasing functions. This calculus enables us to prove the stability of feedforward networks and obtain statistical upper bounds on interesting performance measures such as delay, at each buffer in the ..."
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Cited by 76 (4 self)
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We develop a network calculus for processes whose burstiness is stochastically bounded by general decreasing functions. This calculus enables us to prove the stability of feedforward networks and obtain statistical upper bounds on interesting performance measures such as delay, at each buffer in the network. Our bounding methodology is useful for a large class of input processes, including important processes exhibiting "subexponentially bounded burstiness" such as fractional Brownian motion. Moreover, it generalizes previous approaches and provides much better bounds for common models of realtime traffic, like Markov modulated processes and other multiple timescale processes. We expect that this new calculus will be of particular interest in the implementation of services providing statistical guarantees.
Multiscale Modeling and Estimation of Poisson Processes with Application to Photonlimited Imaging
 IEEE TRANS. ON INFO. THEORY
, 1999
"... Many important problems in engineering and science are wellmodeled 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 photonlimited imaging problems. This paper studies ..."
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Cited by 72 (10 self)
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Many important problems in engineering and science are wellmodeled 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 photonlimited 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 photonlimited image estimation and its potential to improve nuclear medicine imaging is examined.