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51
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.
A multifractal wavelet model with application to TCP network traffic
 IEEE TRANS. INFORM. THEORY
, 1999
"... In this paper, we develop a new multiscale modeling framework for characterizing positivevalued data with longrangedependent correlations (1=f noise). Using the Haar wavelet transform and a special multiplicative structure on the wavelet and scaling coefficients to ensure positive results, the mo ..."
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Cited by 171 (30 self)
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In this paper, we develop a new multiscale modeling framework for characterizing positivevalued data with longrangedependent correlations (1=f noise). Using the Haar wavelet transform and a special multiplicative structure on the wavelet and scaling coefficients to ensure positive results, the model provides a rapid O(N) cascade algorithm for synthesizing Npoint data sets. We study both the secondorder and multifractal properties of the model, the latter after a tutorial overview of multifractal analysis. We derive a scheme for matching the model to real data observations and, to demonstrate its effectiveness, apply the model to network traffic synthesis. The flexibility and accuracy of the model and fitting procedure result in a close fit to the real data statistics (variancetime plots and moment scaling) and queuing behavior. Although for illustrative purposes we focus on applications in network traffic modeling, the multifractal wavelet model could be useful in a number of other areas involving positive data, including image processing, finance, and geophysics.
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.
On Pattern Frequency Occurrences In A Markovian Sequence?
 Algorithmica
, 1997
"... Consider a given pattern H and a random text T generated by a Markovian source. We study the frequency of pattern occurrences in a random text when overlapping copies of the pattern are counted separately. We present exact and asymptotic formulae for all moments (including the variance), and probabi ..."
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Cited by 63 (24 self)
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Consider a given pattern H and a random text T generated by a Markovian source. We study the frequency of pattern occurrences in a random text when overlapping copies of the pattern are counted separately. We present exact and asymptotic formulae for all moments (including the variance), and probability of r pattern occurrences for three different regions of r, namely: (i) r = O(1), (ii) central limit regime, and (iii) large deviations regime. In order to derive these results, we first construct some language expressions that characterize pattern occurrences which are later translated into generating functions. Finally, we use analytical methods to extract asymptotic behaviors of the pattern frequency. Applications of these results include molecular biology, source coding, synchronization, wireless communications, approximate pattern matching, game theory, and stock market analysis. These findings are of particular interest to information theory (e.g., secondorder properties of the re...
Sample Path Large Deviations and Intree Networks
 Queueing Systems
, 1994
"... Using the contraction principle, in this paper we derive a set of closure properties for sample path large deviations. These properties include sum, reduction, composition and reflection mapping. Using these properties, we show that the exponential decay rates of the steady state queue length distri ..."
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Cited by 40 (8 self)
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Using the contraction principle, in this paper we derive a set of closure properties for sample path large deviations. These properties include sum, reduction, composition and reflection mapping. Using these properties, we show that the exponential decay rates of the steady state queue length distributions in an intree network with routing can be derived by a set of recursive equations. The solution of this set of equations is related to the recently developed theory of effective bandwidth for high speed digital networks, especially ATM networks. We also prove a conditional limit theorem that illustrates how a queue builds up in an intree network.
Fractional Brownian motion and data traffic modeling: The other end of the spectrum
 Fractals in Engineering
, 1997
"... Introduction Fractal analysis of computer traffic has received considerable attention since the seminal work of Leland and al. [11] who provided experimental evidence that some traces of data traffic exhibit long range dependence (LRD). This is a typical fractal feature which is not found with the ..."
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Cited by 39 (13 self)
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Introduction Fractal analysis of computer traffic has received considerable attention since the seminal work of Leland and al. [11] who provided experimental evidence that some traces of data traffic exhibit long range dependence (LRD). This is a typical fractal feature which is not found with the classical Poisson models. An important issue since then has been to propose "physical" models that lead to such fractal behavior. A popular model [27] is based on the superposition of simple i.i.d ON/OFF sources which ON and/or OFF periods follow a heavy tailed law (P r(X ? ) ¸ c \Gammaff ; 1 ! ff ! 2). When properly normalized, the resulting traffic is a fractional Brownian motion (fBm) of LRD exponent H = (3 \Gamma ff)=2. Several practical implications of LRD traffic have consequently been investigated, e.g. the queuing behavior [15] (see
Effective Bandwidths of Departure Processes from Queues with Time Varying Capacities
 In Proceedings of IEEE INFOCOM'95
, 1995
"... In this paper, we consider a queue with a time varying capacity and identify the effective bandwidth of the stationary departure process from such a queue. Two important observations are made: (i) the effective bandwidths for the transient departure process and the stationary departure process from ..."
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Cited by 29 (1 self)
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In this paper, we consider a queue with a time varying capacity and identify the effective bandwidth of the stationary departure process from such a queue. Two important observations are made: (i) the effective bandwidths for the transient departure process and the stationary departure process from such a queue are in general different, and (ii) sometimes it is necessary to build up the queue first in order to have a large excursion of the stationary departure process. The new result on the effective bandwidth of the stationary departure process is applied to intree networks with time varying capacities and priority tandem queues. Algorithms for approximating the tail distributions of queue lengths in such networks are derived.
On the Approximate Pattern Occurrences in a Text
 In IEEE Computer Society, editor, Compression and Complexity of SEQUENCES 1997
, 1997
"... Consider a given pattern H and a random text T generated randomly according to the Bernoulli model. We study the frequency of approximate occurrences of the pattern a random text when overlapping copies of the approximate pattern are counted separately. We provide exact and asymptotic formul# for ..."
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Cited by 28 (13 self)
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Consider a given pattern H and a random text T generated randomly according to the Bernoulli model. We study the frequency of approximate occurrences of the pattern a random text when overlapping copies of the approximate pattern are counted separately. We provide exact and asymptotic formul# for mean, variance and probability of occurrence as well as asymptotic results including the central limit theorem and large deviations. Our approach is combinatorial: we #rst construct some language expressions that characterize pattern occurrences which are translated into generating functions, and #nally we use analytical methods to extract asymptotic behaviors of the pattern frequency. Applications of these results include molecular biology, source coding, synchronization, wireless communications, approximate pattern matching, games, and stock market analysis. These #ndings are of particular interest to information theory #e.g., secondorder properties of the relative frequency#, and molecular biology problems #e.g., #nding patterns with unexpected high or low frequencies, and gene recognition#.
Multifractal Processes
, 1999
"... This paper has two main objectives. First, it develops the multifractal formalism in a context suitable for both, measures and functions, deterministic as well as random, thereby emphasizing an intuitive approach. Second, it carefully discusses several examples, such as the binomial cascades and sel ..."
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Cited by 28 (6 self)
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This paper has two main objectives. First, it develops the multifractal formalism in a context suitable for both, measures and functions, deterministic as well as random, thereby emphasizing an intuitive approach. Second, it carefully discusses several examples, such as the binomial cascades and selfsimilar processes with a special eye on the use of wavelets. Particular attention is given to a novel class of multifractal processes which combine the attractive features of cascades and selfsimilar processes. Statistical properties of estimators as well as modelling issues are addressed.
Asymptotic Buffer Overflow Probabilities in Multiclass Multiplexers: An Optimal Control Approach
 IEEE Trans. Automatic Control
, 1997
"... We consider a multiclass multiplexer with support for multiple service classes, and dedicated buffers for each service class. Under specific scheduling policies for sharing bandwidth among these classes, we seek the asymptotic (as the buffer size goes to infinity) tail of the buffer overflow probabi ..."
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Cited by 26 (1 self)
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We consider a multiclass multiplexer with support for multiple service classes, and dedicated buffers for each service class. Under specific scheduling policies for sharing bandwidth among these classes, we seek the asymptotic (as the buffer size goes to infinity) tail of the buffer overflow probability for each dedicated buffer. We assume dependent arrival and service processes as is usually the case in models of bursty traffic. In the standard large deviations methodology, we provide a lower and a matching (up to first degree in the exponent) upper bound on the buffer overflow probabilities. We introduce a novel optimal control approach to address these problems. In particular, we relate the lower bound derivation to a deterministic optimal control problem, which we explicitly solve. Optimal state trajectories of the control problem correspond to typical congestion scenarios. We explicitly and in detail characterize the most likely modes of overflow. We specialize our results to the ...