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Mobility increases the capacity of adhoc wireless networks
 IEEE/ACM Transactions on Networking
, 2002
"... The capacity of adhoc wireless networks is constrained by the mutual interference of concurrent transmissions between nodes. We study a model of an adhoc network where n nodes communicate in random sourcedestination pairs. These nodes are assumed to be mobile. We examine the persession throughpu ..."
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Cited by 841 (5 self)
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The capacity of adhoc wireless networks is constrained by the mutual interference of concurrent transmissions between nodes. We study a model of an adhoc network where n nodes communicate in random sourcedestination pairs. These nodes are assumed to be mobile. We examine the persession throughput for applications with loose delay constraints, such that the topology changes over the timescale of packet delivery. Under this assumption, the peruser throughput can increase dramatically when nodes are mobile rather than fixed. This improvement can be achieved by exploiting node mobility as a type of multiuser diversity. 1
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.
Is Network Traffic Approximated By Stable Lévy Motion Or Fractional Brownian Motion?
, 1999
"... Cumulative broadband network traffic is often thought to be well modelled by fractional Brownian motion. However, some traffic measurements do not show an agreement with the Gaussian marginal distribution assumption. We show that if connection rates are modest relative to heavy tailed connection le ..."
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Cited by 68 (9 self)
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Cumulative broadband network traffic is often thought to be well modelled by fractional Brownian motion. However, some traffic measurements do not show an agreement with the Gaussian marginal distribution assumption. We show that if connection rates are modest relative to heavy tailed connection length distribution tails, then stable L'evy motion is a sensible approximation to cumulative traffic over a time period. If connection rates are large relative to heavy tailed connection length distribution tails, then FBM is the appropriate approximation. The results are framed as limit theorems for a sequence of cumulative input processes whose connection rates are varying in such a way as to remove or induce long range dependence.
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 67 (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...
Heavy Tail Modeling And Teletraffic Data
 Annals of Statistics
, 1997
"... . Huge data sets from the teletraffic industry exhibit many nonstandard characteristics such as heavy tails and long range dependence. Various estimation methods for heavy tailed time series with positive innovations are reviewed. These include parameter estimation and model identification methods ..."
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Cited by 54 (4 self)
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. Huge data sets from the teletraffic industry exhibit many nonstandard characteristics such as heavy tails and long range dependence. Various estimation methods for heavy tailed time series with positive innovations are reviewed. These include parameter estimation and model identification methods for autoregressions and moving averages. Parameter estimation methods include those of YuleWalker and the linear programming estimators of Feigin and Resnick as well estimators for tail heaviness such as the Hill estimator and the qqestimator. Examples are given using call holding data and interarrivals between packet transmissions on a computer network. The limit theory makes heavy use of point process techniques and random set theory. 1. Introduction Classical queuing and network stochastic models contain simplifying assumptions guaranteeing the Markov property and insuring analytical tractability. Frequently interarrivals and service times are assumed to be iid and typically underlyi...
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
Random Walks with Strongly Inhomogeneous Rates and Singular Diffusions: Convergence, Localization and Aging in One Dimension
, 2000
"... Let = ( i : i 2 Z) denote i.i.d. positive random variables with common distribution F and (conditional on ) let X = (X t : t 0; X 0 = 0), be a continuoustime simple symmetric random walk on Z with inhomogeneous rates ( \Gamma1 i : i 2 Z). When F is in the domain of attraction of a stable law o ..."
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Cited by 36 (4 self)
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Let = ( i : i 2 Z) denote i.i.d. positive random variables with common distribution F and (conditional on ) let X = (X t : t 0; X 0 = 0), be a continuoustime simple symmetric random walk on Z with inhomogeneous rates ( \Gamma1 i : i 2 Z). When F is in the domain of attraction of a stable law of exponent ff ! 1 (so that E( i ) = 1 and X is subdiffusive), we prove that (X; ), suitably rescaled (in space and time), converges to a natural (singular) diffusion Z = (Z t : t 0; Z 0 = 0) with a random (discrete) speed measure ae. The convergence is such that the "amount of localization", E P i2Z [P(X t = ij )] 2 converges as t ! 1 to E P z2R [P(Z s = zjae)] 2 ? 0, which is independent of s ? 0 because of scaling/selfsimilarity properties of (Z; ae). The scaling properties of (Z; ae) are also closely related to the "aging" of (X; ). Our main technical result is a general convergence criterion for localization and aging functionals of diffusions/walks Y (ffl) with (nonrando...
Heat kernel estimates for Dirichlet fractional Laplacian
 J. European Math. Soc
"... In this paper, we consider the fractional Laplacian −(−∆) α/2 on an open subset in R d with zero exterior condition. We establish sharp twosided estimates for the heat kernel of such Dirichlet fractional Laplacian in C 1,1 open sets. This heat kernel is also the transition density of a rotationally ..."
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Cited by 36 (19 self)
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In this paper, we consider the fractional Laplacian −(−∆) α/2 on an open subset in R d with zero exterior condition. We establish sharp twosided estimates for the heat kernel of such Dirichlet fractional Laplacian in C 1,1 open sets. This heat kernel is also the transition density of a rotationally symmetric stable process killed upon leaving a C 1,1 open set. Our results are the first sharp twosided estimates for the Dirichlet heat kernel of a nonlocal operator on open sets.
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.
Growth and percolation on the uniform infinite planar triangulation
 Geom. Funct. Anal
, 2003
"... A construction as a growth process for sampling of the uniform infinite planar triangulation (UIPT), defined in [4], is given. The construction is algorithmic in nature, and is an efficient method of sampling a portion of the UIPT. By analyzing the progress rate of the growth process we show that a. ..."
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Cited by 27 (2 self)
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A construction as a growth process for sampling of the uniform infinite planar triangulation (UIPT), defined in [4], is given. The construction is algorithmic in nature, and is an efficient method of sampling a portion of the UIPT. By analyzing the progress rate of the growth process we show that a.s. the UIPT has growth rate r 4 up to polylogarithmic factors, confirming heuristic results from the physics literature. Additionally, the boundary component of the ball of radius r separating it from infinity a.s. has growth rate r 2 up to polylogarithmic factors. It is also shown that the properly scaled size of a variant of the free triangulation of an mgon (also defined in [4]) converges in distribution to an asymmetric stable random variable of type 1/2. By combining Bernoulli site percolation with the growth process for the UIPT, it is shown that a.s. the critical probability pc = 1/2 and that at pc percolation does not occur. Subject classification: Primary 05C80; Secondary 05C30, 82B43, 81T40. 1