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14
Loss Probability Calculations and Asymptotic Analysis for Finite Buffer Multiplexers
, 2001
"... In this paper, we propose an approximation for the loss probability, @ A, in a finite buffer system with buffer size. Our study is motivated by the case of a highspeed network where a large number of sources are expected to be multiplexed. Hence, by appealing to Central Limit Theorem type of argum ..."
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Cited by 47 (4 self)
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In this paper, we propose an approximation for the loss probability, @ A, in a finite buffer system with buffer size. Our study is motivated by the case of a highspeed network where a large number of sources are expected to be multiplexed. Hence, by appealing to Central Limit Theorem type of arguments, we model the input process as a general Gaussian process. Our result is obtained by making a simple mapping from the tail probability in an infinite buffer system to the loss probability in a finite buffer system. We also provide a strong asymptotic relationship between our approximation and the actual loss probability for a fairly large class of Gaussian input processes. We derive some interesting asymptotic properties of our approximation and illustrate its effectiveness via a detailed numerical investigation.
A Central Limit Theorem Based Approach for Analyzing Queue Behavior in HighSpeed Networks
, 1998
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A centrallimittheorembased approach for analyzing queue behavior in highspeed networks
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1998
"... In this paper, we study P(Q > x), the tail of the steadystate queue length distribution at a highspeed multiplexer. In particular, we focus on the case when the aggregate traffic to the multiplexer can be characterized by a stationary Gaussian process. We provide two asymptotic upper bounds for ..."
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Cited by 35 (0 self)
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In this paper, we study P(Q > x), the tail of the steadystate queue length distribution at a highspeed multiplexer. In particular, we focus on the case when the aggregate traffic to the multiplexer can be characterized by a stationary Gaussian process. We provide two asymptotic upper bounds for the tail probability and an asymptotic result that emphasizes the importance of the dominant time scale and the maximum variance. One of our bounds is in a singleexponential form and can be used to calculate an upper bound to the asymptotic constant. However, we show that this bound, being of a singleexponential form, may not accurately capture the tail probability. Our asymptotic result on the importance of the maximum variance and our extensive numerical study on a known lower bound motivate the development of our second asymptotic upper bound. This bound is expressed in terms of the maximum variance of a Gaussian process, and enables the accurate estimation of the tail probability over a wide range of queue lengths. We apply our results to Gaussian as well as multiplexed nonGaussian input sources, and validate their performance via simulations. Wherever possible, we have conducted our simulation study using importance sampling in order to improve its reliability and to effectively capture rare events. Our analytical study is based on extreme value theory, and therefore different from the approaches using traditional Markovian and Large Deviations techniques.
Modeling Heterogeneous Network Traffic in Wavelet Domain: Part II  NonGaussian Traffic
 IEEE/ACM Transactions on Networking
, 1999
"... Following our work described in Part I of this paper that modeled various correlation structures of Gaussian traffic in wavelet domain, we extend our previous models to heterogeneous network traffic with either a nonGaussian distribution or a periodic structure. To include a nonGaussian distributi ..."
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Cited by 25 (1 self)
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Following our work described in Part I of this paper that modeled various correlation structures of Gaussian traffic in wavelet domain, we extend our previous models to heterogeneous network traffic with either a nonGaussian distribution or a periodic structure. To include a nonGaussian distribution, we first investigate what higherorder statistics are pertinent by exploring a relationship between timescale analysis of wavelets and cumulative traffic. We then develop a novel algorithm in the wavelet domain to capture the important statistics. By utilizing local properties of wavelet basis in both space and time, we further extend such wavelet models to periodic MPEG traffic. As wavelets provide a natural fit to higherorder statistics as well as localized spatial and temporal dependence of periodic traffic at different time scales, the resulting wavelet models for both nonGaussian and periodic traffic are simple and accurate with the lowest computational complexity attainable. 1 I...
ON THE SUPREMUM DISTRIBUTION OF INTEGRATED STATIONARY GAUSSIAN PROCESSES WITH NEGATIVE LINEAR DRIFT
 ADVANCES IN APPLIED PROBABILITY
, 1999
"... In this paper we study the supremum distribution of a class of Gaussian processes having stationary increments and negative drift using key results from Extreme Value Theory. We focus on deriving an asymptotic upper bound to the tail of the supremum distribution of such processes. Our bound is valid ..."
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Cited by 19 (5 self)
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In this paper we study the supremum distribution of a class of Gaussian processes having stationary increments and negative drift using key results from Extreme Value Theory. We focus on deriving an asymptotic upper bound to the tail of the supremum distribution of such processes. Our bound is valid for both discrete and continuoustime processes. We discuss the importance of the bound, its applicability to queueing problems, and show numerical examples to illustrate
Queueing Analysis of HighSpeed Multiplexers including LongRange Dependent Arrival Processes.
 Proc. IEEE INFOCOM
, 1999
"... With the advent of highspeed networks, a single link will carry hundreds or even thousands of applications. This results in a very natural application of the Central Limit Theorem, to model the network traffic by Gaussian stochastic processes. In this paper we study the tail probability P({Q>x}) ..."
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Cited by 18 (2 self)
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With the advent of highspeed networks, a single link will carry hundreds or even thousands of applications. This results in a very natural application of the Central Limit Theorem, to model the network traffic by Gaussian stochastic processes. In this paper we study the tail probability P({Q>x})of a queueing system when the input process is assumed to be a very general class of Gaussian processes which includes a large class of selfsimilar or other types of longrange dependent Gaussian processes. For example, past work on Fractional Brownian Motion, and variations therein, are but a small subset of the work presented in this paper. Our study is based on Extreme Value Theory and we show that log P({Q>x})+m x/2grows at most on the order of log x,wherem x corresponds to the reciprocal of the maximum (normalized) variance of a Gaussian process directly related to the aggregate input process. Our result is considerably stronger than the existing results in the literature based on Large D...
New Bounds and Approximations using Extreme Value Theory for the Queue Length Distribution in HighSpeed Networks.
, 1998
"... In this paper we study P({Q>x}), the tail of the steady state queue length distribution at a highspeed multiplexer. The tail probability distribution P({Q>x}) is a fundamental measure of network congestion and thus important for the efficient design and control of networks. In particular, we ..."
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Cited by 7 (0 self)
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In this paper we study P({Q>x}), the tail of the steady state queue length distribution at a highspeed multiplexer. The tail probability distribution P({Q>x}) is a fundamental measure of network congestion and thus important for the efficient design and control of networks. In particular, we focus on the case when the aggregate traffic to the multiplexer can be characterized by a stationary Gaussian process. In our approach, a multiplexer is modeled by a fluid queue serving a large number of input processes. We propose two asymptotic upper bounds for P({Q>x}), and provide several numerical examples to illustrate the tightness of these bounds. We also use these bounds to study important properties of the tail probability. Further, we apply these bounds for a large number of nonGaussian input sources, and validate their performance via simulations. We have conducted our simulation study using Importance Sampling in order to improve its reliability and to effectively capture rare events. Our...
MeasurementBased Admission Control in IntegratedServices Networks
, 1998
"... To satisfy the quality of service requirements of realtime multimedia applications, networks must employ resource reservation and admission control. In this paper, we describe a new MeasurementBased Admission Control (MBAC) algorithm that uses empirical traffic envelopes of the aggregate traffic f ..."
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Cited by 2 (2 self)
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To satisfy the quality of service requirements of realtime multimedia applications, networks must employ resource reservation and admission control. In this paper, we describe a new MeasurementBased Admission Control (MBAC) algorithm that uses empirical traffic envelopes of the aggregate traffic flow to allocate network resources. Our framework of traffic envelopes provides a robust and accurate characterization of the aggregate flow, capturing the extent to which flows statistically multiplex as well as the temporal correlation structure of the aggregate flow. In estimating applications' future performance, we introduce the notion of a schedulability confidence level which describes the uncertainty of the measurementbased "prediction", based on which we devise techniques to accurately estimate packet loss probability for a buffered multiplexer servicing heterogeneous and bursty traffic flows.