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158
Effective Bandwidths for Multiclass Markov Fluids and Other ATM Sources
, 1993
"... 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 l ..."
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Cited by 187 (14 self)
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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 circuitswitched 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.
Stability, queue length and delay of deterministic and stochastic queueing networks
 IEEE Transactions on Automatic Control
, 1994
"... 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 ..."
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Cited by 173 (20 self)
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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, inputoutput 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 twostate Markov modulated arrival processes, the notion of MER with respect to ` is shown to be
Logarithmic Asymptotics For SteadyState Tail Probabilities In A SingleServer Queue
, 1993
"... We consider the standard singleserver queue with unlimited waiting space and the firstin firstout service discipline, but without any explicit independence conditions on the interarrival and service times. We find conditions for the steadystate waitingtime distribution to have smalltail asympt ..."
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Cited by 150 (14 self)
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We consider the standard singleserver queue with unlimited waiting space and the firstin firstout service discipline, but without any explicit independence conditions on the interarrival and service times. We find conditions for the steadystate waitingtime distribution to have smalltail 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 steadystate 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 multiclass queues based on asymptotic decay rates.
Notes on Effective Bandwidths
, 1996
"... This paper presents a personal view of work to date on effective bandwidths, emphasising the unifying role of the concept: as a summary of the statistical characteristics of sources over different time and space scales; in bounds, limits and approximations for various models of multiplexing unde ..."
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Cited by 131 (4 self)
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This paper presents a personal view of work to date on effective bandwidths, emphasising the unifying role of the concept: as a summary of the statistical characteristics of sources over different time and space scales; in bounds, limits and approximations for various models of multiplexing under quality of service constraints; and as the basis for simple and robust tariffing and connection acceptance control mechanisms for poorly characterized traffic. The framework assumes only stationarity of sources, and illustrative examples include periodic streams, fractional Brownian input, policed and shaped sources, and deterministic multiplexing.
Large Deviations, the Shape of the Loss Curve, and Economies of Scale in Large Multiplexers
, 1995
"... We analyse the queue Q L at a multiplexer with L inputs. We obtain a large deviation result, namely that under very general conditions lim L!1 L \Gamma1 log P[Q L ? Lb] = \GammaI (b) provided the offered load is held constant, where the shape function I is expressed in terms of the cumulant ..."
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Cited by 115 (11 self)
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We analyse the queue Q L at a multiplexer with L inputs. We obtain a large deviation result, namely that under very general conditions lim L!1 L \Gamma1 log P[Q L ? Lb] = \GammaI (b) provided the offered load is held constant, where the shape function I is expressed in terms of the cumulant generating functions of the input traffic. This provides an improvement on the usual effective bandwidth approximation P[Q L ? b] e \Gammaffib , replacing it with P[Q L ? b] e \GammaLI(b=L) . The difference I(b) \Gamma ffi b determines the economies of scale which are to be obtained in large multiplexers. If the limit = \Gamma lim t!1 t t (ffi) exists (here t is the finite time cumulant of the workload process) then lim b!1 (I(b) \Gamma ffi b) = . We apply this idea to a number of examples of arrivals processes: heterogeneous superpositions, Gaussian processes, Markovian additive processes and Poisson processes. We obtain expressions for in these cases. is zero for independent arrivals, but positive for arrivals with positive correlations. Thus economies of scale are obtainable for highly bursty traffic expected in ATM multiplexing.
Probabilistic and Statistical Properties of Words: An Overview
 Journal of Computational Biology
, 2000
"... In the following, an overview is given on statistical and probabilistic properties of words, as occurring in the analysis of biological sequences. Counts of occurrence, counts of clumps, and renewal counts are distinguished, and exact distributions as well as normal approximations, Poisson process a ..."
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Cited by 83 (1 self)
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In the following, an overview is given on statistical and probabilistic properties of words, as occurring in the analysis of biological sequences. Counts of occurrence, counts of clumps, and renewal counts are distinguished, and exact distributions as well as normal approximations, Poisson process approximations, and compound Poisson approximations are derived. Here, a sequence is modelled as a stationary ergodic Markov chain; a test for determining the appropriate order of the Markov chain is described. The convergence results take the error made by estimating the Markovian transition probabilities into account. The main tools involved are moment generating functions, martingales, Stein’s method, and the ChenStein method. Similar results are given for occurrences of multiple patterns, and, as an example, the problem of unique recoverability of a sequence from SBH chip data is discussed. Special emphasis lies on disentangling the complicated dependence structure between word occurrences, due to selfoverlap as well as due to overlap between words. The results can be used to derive approximate, and conservative, con � dence intervals for tests. Key words: word counts, renewal counts, Markov model, exact distribution, normal approximation, Poisson process approximation, compound Poisson approximation, occurrences of multiple words, sequencing by hybridization, martingales, moment generating functions, Stein’s method, ChenStein method. 1.
Tutorial on Variational Approximation Methods
 In Advanced Mean Field Methods: Theory and Practice
, 2000
"... We provide an introduction to the theory and use of variational methods for inference and estimation in the context of graphical models. Variational methods become useful as ecient approximate methods when the structure of the graph model no longer admits feasible exact probabilistic calculations. T ..."
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Cited by 74 (1 self)
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We provide an introduction to the theory and use of variational methods for inference and estimation in the context of graphical models. Variational methods become useful as ecient approximate methods when the structure of the graph model no longer admits feasible exact probabilistic calculations. The emphasis of this tutorial is on illustrating how inference and estimation problems can be transformed into variational form along with describing the resulting approximation algorithms and their properties insofar as these are currently known. 1 Introduction The term variational methods refers to a large collection of optimization techniques. The classical context for these methods involves nding the extremum of an integral depending on an unknown function and its derivatives. This classical de nition, however, and the accompanying calculus of variation no longer adequately characterizes modern variational methods. Modern variational approaches have become indispensable tools in...
Modeling and simulation of selfsimilar variable bit rate compressed video: A unified approach
 in Proc. ACM SIGCOMM
, 1995
"... Variable bit rate (VBR) compressed video is expected to become one of the major loading factors in highspeed packet networks such asATMbased BISDN. However, recent measurements based on long empirical traces (complete movies) revealed that VBR video tra c possesses selfsimilar (or fractal) chara ..."
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Cited by 68 (2 self)
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Variable bit rate (VBR) compressed video is expected to become one of the major loading factors in highspeed packet networks such asATMbased BISDN. However, recent measurements based on long empirical traces (complete movies) revealed that VBR video tra c possesses selfsimilar (or fractal) characteristics, meaning that the dependence in the tra c stream lasts much longer than traditional models can capture. In this paper, we present a uni ed approach which, in addition to accurately modeling the marginal distribution of empirical video records, also models directly both the short and the longterm empirical autocorrelation structures. We also present simulation results using synthetic data and compare with results based on empirical video traces. Furthermore, we extend the application of e cient estimation techniques based on importance sampling that we had used before only for simple fractal processes. We use importance sampling techniques to e ciently estimate low probabilities of packet losses that occur when a multiplexer is fed with synthetic tra c from our selfsimilar VBR video model. 1
Effective bandwidths: call admission, traffic policing, and filtering for ATM networks
, 1994
"... In this paper we review and extend the effective bandwidth results of Kelly [28], and Kesidis, Walrand and Chang [29, 6]. These results provide a framework for call admission schemes which are sensitive to constraints on the mean delay or the tail distribution of the workload in buffered queues. We ..."
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Cited by 60 (9 self)
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In this paper we review and extend the effective bandwidth results of Kelly [28], and Kesidis, Walrand and Chang [29, 6]. These results provide a framework for call admission schemes which are sensitive to constraints on the mean delay or the tail distribution of the workload in buffered queues. We present results which are valid for a wide variety of traffic streams and discuss their applicability for traffic management in ATM networks. We discuss the impact of traffic policing schemes, such as thresholding and ltering, on the effective bandwidth of sources. Finally we discuss effective bandwidth results for Brownian traffic models for which explicit results reveal the interaction arising in finite buffers.
Variational Methods for Inference and Estimation in Graphical Models
, 1997
"... Graphical models enhance the representational power of probability models through qualitative characterization of their properties. This also leads to greater efficiency in terms of the computational algorithms that empower such representations. The increasing complexity of these models, however, qu ..."
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Cited by 57 (3 self)
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Graphical models enhance the representational power of probability models through qualitative characterization of their properties. This also leads to greater efficiency in terms of the computational algorithms that empower such representations. The increasing complexity of these models, however, quickly renders exact probabilistic calculations infeasible. We propose a principled framework for approximating graphical models based on variational methods. We develop variational techniques from the perspective that unifies and expands their applicability to graphical models. These methods allow the (recursive) computation of upper and lower bounds on the quantities of interest. Such bounds yield considerably more information than mere approximations and provide an inherent error metric for tailoring the approximations individually to the cases considered. These desirable properties, concomitant to the variational methods, are unlikely to arise as a result of other deterministic or stochas...