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435
SelfSimilarity Through HighVariability: Statistical Analysis of Ethernet LAN Traffic at the Source Level
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1997
"... A number of recent empirical studies of traffic measurements from a variety of working packet networks have convincingly demonstrated that actual network traffic is selfsimilar or longrange dependent in nature (i.e., bursty over a wide range of time scales)  in sharp contrast to commonly made tr ..."
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Cited by 714 (24 self)
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A number of recent empirical studies of traffic measurements from a variety of working packet networks have convincingly demonstrated that actual network traffic is selfsimilar or longrange dependent in nature (i.e., bursty over a wide range of time scales)  in sharp contrast to commonly made traffic modeling assumptions. In this paper, we provide a plausible physical explanation for the occurrence of selfsimilarity in LAN traffic. Our explanation is based on new convergence results for processes that exhibit high variability (i.e., infinite variance) and is supported by detailed statistical analyses of realtime traffic measurements from Ethernet LAN's at the level of individual sources. This paper is an extended version of [53] and differs from it in significant ways. In particular, we develop here the mathematical results concerning the superposition of strictly alternating ON/OFF sources. Our key mathematical result states that the superposition of many ON/OFF sources (also k...
Excitatory and inhibitory interactions in localized populations of model
 Biophysics
, 1972
"... ABSMAcr Coupled nonlinear differential equations are derived for the dynamics of spatially localized populations containing both excitatory and inhibitory model neurons. Phase plane methods and numerical solutions are then used to investigate population responses to various types of stimuli. The res ..."
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Cited by 468 (15 self)
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ABSMAcr Coupled nonlinear differential equations are derived for the dynamics of spatially localized populations containing both excitatory and inhibitory model neurons. Phase plane methods and numerical solutions are then used to investigate population responses to various types of stimuli. The results obtained show simple and multiple hysteresis phenomena and limit cycle activity. The latter is particularly interesting since the frequency ofthe limit cycle oscillationis found to be a monotonic function of stimulus intensity. Finally, it is proved that the existence of limit cycle dynamics in response to one class of stimuli implies the existence of multiple stable states and hysteresis in response to a different class of stimuli. The relation between these findings and a number of experiments is discussed.
Proof of a Fundamental Result in SelfSimilar Traffic Modeling
 COMPUTER COMMUNICATION REVIEW
, 1997
"... We state and prove the following key mathematical result in selfsimilar traffic modeling: the superposition of many ON/OFF sources (also known as packet trains) with strictly alternating ON and OFFperiods and whose ONperiods or OFFperiods exhibit the Noah Effect (i.e., have high variability or ..."
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Cited by 276 (9 self)
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We state and prove the following key mathematical result in selfsimilar traffic modeling: the superposition of many ON/OFF sources (also known as packet trains) with strictly alternating ON and OFFperiods and whose ONperiods or OFFperiods exhibit the Noah Effect (i.e., have high variability or infinite variance) can produce aggregate network traffic that exhibits the Joseph Effect (i.e., is selfsimilar or longrange dependent). There is, moreover, a simple relation between the parameters describing the intensities of the Noah Effect (high variability) and the Joseph Effect (selfsimilarity). This provides a simple physical explanation for the presence of selfsimilar traffic patterns in modern highspeed network traffic that is consistent with traffic measurements at the source level. We illustrate how this mathematical result can be combined with modern highperformance computing capabilities to yield a simple and efficient lineartime algorithm for generating selfsimilar traf...
The FourierSeries Method For Inverting Transforms Of Probability Distributions
, 1991
"... This paper reviews the Fourierseries method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourierseries method are remar ..."
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Cited by 203 (52 self)
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This paper reviews the Fourierseries method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourierseries method are remarkably easy to use, requiring programs of less than fifty lines. The Fourierseries method can be interpreted as numerically integrating a standard inversion integral by means of the trapezoidal rule. The same formula is obtained by using the Fourier series of an associated periodic function constructed by aliasing; this explains the name of the method. This Fourier analysis applies to the inversion problem because the Fourier coefficients are just values of the transform. The mathematical centerpiece of the Fourierseries method is the Poisson summation formula, which identifies the discretization error associated with the trapezoidal rule and thus helps bound it. The greatest difficulty is approximately calculating the infinite series obtained from the inversion integral. Within this framework, lattice cdf's can be calculated from generating functions by finite sums without truncation. For other cdf's, an appropriate truncation of the infinite series can be determined from the transform based on estimates or bounds. For Laplace transforms, the numerical integration can be made to produce a nearly alternating series, so that the convergence can be accelerated by techniques such as Euler summation. Alternatively, the cdf can be perturbed slightly by convolution smoothing or windowing to produce a truncation error bound independent of the original cdf. Although error bounds can be determined, an effective approach is to use two different methods without elaborate error analysis. For this...
Neuronal spike trains and stochastic point processes. II. Simultaneous spike trains
 Biophys. J
, 1967
"... AsTRAcT The statistical analysis oftwo simultaneously observed trainsofneuronal spikes is described, using as a conceptual framework the theory of stochastic point processes. The first statistical question that arises is whether the observed trains are independent; statistical techniques for testing ..."
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Cited by 180 (1 self)
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AsTRAcT The statistical analysis oftwo simultaneously observed trainsofneuronal spikes is described, using as a conceptual framework the theory of stochastic point processes. The first statistical question that arises is whether the observed trains are independent; statistical techniques for testing independence are developed around the notion that, under the null hypothesis, the times of spike occurrence in one train represent random instants in time with respect to the other. Ifthe null hypothesis is rejectedif dependence is attributed to the trainsthe problem then becomes that of characterizing the nature and source of the observed dependencies. Statistical signs of various classes of dependencies, including direct interaction and shared input, are discussed and illustrated through computer simulations of interacting neurons. The effects ofnonstationarities on the statistical measures for simultaneous spike trains are also discussed. For twotrain comparisons of irregularly discharging nerve cells, moderate nonstationarities areshown tohave little effecton the detection of interactions. Combining repetitive stimulation and simultaneous recording of spike trains from two (or more) neurons yields additional clues as to possible modes of interaction among the monitored neurons; the theory presented is illustrated by an application to experimentally obtained data from auditory neurons. Acompanion paper covers the analysis ofsingle spike trains.
Population Dynamics of Spiking Neurons: Fast Transients, Asynchronous States, and Locking
 NEURAL COMPUTATION
, 2000
"... An integral equation describing the time evolution of the population activity in a homogeneous pool of spiking neurons of the integrateandfire type is discussed. It is analytically shown that transients from a state of incoherent firing can be immediate. The stability of incoherent firing is analy ..."
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Cited by 154 (24 self)
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An integral equation describing the time evolution of the population activity in a homogeneous pool of spiking neurons of the integrateandfire type is discussed. It is analytically shown that transients from a state of incoherent firing can be immediate. The stability of incoherent firing is analyzed in terms of the noise level and transmission delay and a bifurcation diagram is derived. The response of a population of noisy integrateandfire neurons to an input current of small amplitude is calculated and characterized by a linear filter L. The stability of perfectly synchronized `locked' solutions is analyzed.
Sound Mobility Models
 in ACM MobiCom
, 2003
"... and evaluation of mobile systems. By using mobility models that describe constituent movement, one can explore large systems, producing repeatable results for comparison between alternatives. Unfortunately, the vast majority of mobility modelsincluding all those in which nodal speed and distance ..."
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Cited by 143 (2 self)
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and evaluation of mobile systems. By using mobility models that describe constituent movement, one can explore large systems, producing repeatable results for comparison between alternatives. Unfortunately, the vast majority of mobility modelsincluding all those in which nodal speed and distance or destination are chosen independently su#er from decay ; average speed decreases until converging to some longterm average. Such decay provides an unsound basis for simulation studies that collect results averaged over time, complicating the experimental process.
One hundred years of forgetting: A quantitative description of retention
 Psychological Review
, 1996
"... A sample of 210 published data sets were assembled that (a) plotted amount remembered versus time, (b) had 5 or more points, and (c) were smooth enough to fit at least 1 of the functions tested with a correlation coefficient of.90 or greater. Each was fit to 105 different 2parameter functions. The ..."
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Cited by 133 (3 self)
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A sample of 210 published data sets were assembled that (a) plotted amount remembered versus time, (b) had 5 or more points, and (c) were smooth enough to fit at least 1 of the functions tested with a correlation coefficient of.90 or greater. Each was fit to 105 different 2parameter functions. The best fits were to the logarithmic function, the power function, the exponential in the square root of time, and the hyperbola in the square root of time. It is difficult to distinguish among these 4 functions with the available data, but the same set of 4 functions fit most data sets, with autobiographical memory being the exception. Theoretical motivations for the best fitting functions are offered. The methodological problems of evaluating functions and the advantages of searching existing data for regularities before formulating theories are considered. At the simplest level, this article is a search for regularities. We ask whether there is one retention function that can describe all of memory, or perhaps a different function for each of a small number of different kinds of memory. At a more abstract level, it is about the role of theory and data in psychological research. Can we most rapidly advance psychology as a science by developing theories at the level that commonly fills psychological journals such as this one, or should we first try to describe phenomena that could constrain theories by establishing robust, preferably quantitative, regularities (Rubin, 1985, 1989, 1995)? A balance between these alternatives is needed, and here we argue that to obtain such a balance more description is needed. Retention offers the ideal topic to make this abstract, philo
Network Coverage Using Low DutyCycled Sensors: Random & Coordinated Sleep Algorithms
, 2004
"... This paper investigates the problem of providing network coverage using wireless sensors that operate on low duty cycles (measured by the percentage time a sensor is on or active), i.e., each sensor alternates between active and sleep states to conserve energy with an average sleep period (much) lon ..."
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Cited by 112 (0 self)
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This paper investigates the problem of providing network coverage using wireless sensors that operate on low duty cycles (measured by the percentage time a sensor is on or active), i.e., each sensor alternates between active and sleep states to conserve energy with an average sleep period (much) longer than the active period. The dynamic change in topology as a result of such dutycycling has potentially disruptive effect on the operation and performance of the network. This is compensated by adding redundancy in the sensor deployment. In this paper we examine the fundamental relationship between the reduction in sensor duty cycle and the required level of redundancy for a fixed performance measure, and explore the design of good sensor sleep schedules. In particular, we consider two types of mechanisms, the random sleep type where each sensor keeps an activesleep schedule independent of another, and the coordinated sleep type where sensors coordinate with each other in reaching an activesleep schedule. Both types are studied within the context of providing network coverage. We present specific scheduling algorithms within each type, and illustrate their coverage and duty cycle properties via both analysis and simulation. We show with either type of sleep schedule the benefit of added redundancy saturates at some point in that the reduction in duty cycles starts to diminish beyond a certain threshold in deployment redundancy. We also show that at the expense of extra control overhead, a coordinated sleep schedule is more robust and can achieve higher duty cycle reduction with the same amount of redundancy compared to a random sleep schedule.
Optimal Spectrum Sensing Framework for Cognitive Radio Networks
 IEEE TRANS. ON WIRELESS COMM
, 2008
"... Spectrum sensing is the key enabling technology for cognitive radio networks. The main objective of spectrum sensing is to provide more spectrum access opportunities to cognitive radio users without interfering with the operations of the licensed network. Hence, recent research has been focused on ..."
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Cited by 107 (11 self)
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Spectrum sensing is the key enabling technology for cognitive radio networks. The main objective of spectrum sensing is to provide more spectrum access opportunities to cognitive radio users without interfering with the operations of the licensed network. Hence, recent research has been focused on the interference avoidance problem. Moreover, current radio frequency (RF) frontends cannot perform sensing and transmission at the same time, which inevitably decreases their transmission opportunities, leading to the socalled sensing efficiency problem. In this paper, in order to solve both the interference avoidance and the spectrum efficiency problem, an optimal spectrum sensing framework is developed. More specifically, first a theoretical framework is developed to optimize the sensing parameters in such a way as to maximize the sensing efficiency subject to interference avoidance constraints. Second, in order to exploit multiple spectrum bands, spectrum selection and scheduling methods are proposed where the best spectrum bands for sensing are selected to maximize the sensing capacity. Finally, an adaptive and cooperative spectrum sensing method is proposed where the sensing parameters are optimized adaptively to the number of cooperating users. Simulation results show that the proposed sensing framework can achieve maximum sensing efficiency and opportunities in multiuser/multispectrum environments, satisfying interference constraints.