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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 1218 (6 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.
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 213 (34 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 112 (12 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 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...
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 74 (26 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.
Limit Theorems For Continuous Time Random Walks With Infinite Mean Waiting Times
 JOURNAL OF APPLIED PROBABILITY
, 2003
"... A continuous time random walk is a simple random walk subordinated to a renewal process, used in physics to model anomalous diffusion. In this paper we show that, when the time between renewals has infinite mean, the scaling limit is an operator Levy motion subordinated to the hitting time process o ..."
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Cited by 72 (33 self)
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A continuous time random walk is a simple random walk subordinated to a renewal process, used in physics to model anomalous diffusion. In this paper we show that, when the time between renewals has infinite mean, the scaling limit is an operator Levy motion subordinated to the hitting time process of a classical stable subordinator. Density functions for the limit process solve a fractional Cauchy problem, the generalization of a fractional partial differential equation for Hamiltonian chaos. We also establish a functional limit theorem for random walks with jumps in the strict generalized domain of attraction of a full operator stable law, which is of some independent interest.
Stochastic Solutions for Fractional Cauchy Problems
 Calc. Appl. Anal
, 2001
"... Every infinitely divisible law defines a convolution semigroup that solves an abstract Cauchy problem. In the fractional Cauchy problem, we replace the first order time derivative by a fractional derivative. Solutions to fractional Cauchy problems are obtained by subordinating the solution to the or ..."
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Cited by 69 (25 self)
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Every infinitely divisible law defines a convolution semigroup that solves an abstract Cauchy problem. In the fractional Cauchy problem, we replace the first order time derivative by a fractional derivative. Solutions to fractional Cauchy problems are obtained by subordinating the solution to the original Cauchy problem. Fractional Cauchy problems are useful in physics to model anomalous di#usion.
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 67 (5 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...