Network arrivals are often modeled as Poisson processes for analytic simplicity, even though a number of traffic studies have shown that packet interarrivals are not exponentially distributed. We evaluate 24 wide-area traces, investigating a number of wide-area TCP arrival processes (session and connection arrivals, FTP data connection arrivals within FTP sessions, and TELNET packet arrivals) to determine the error introduced by modeling them using Poisson processes. We find that user-initiated TCP session arrivals, such as remotelogin and file-transfer, are well-modeled as Poisson processes with fixed hourly rates, but that other connection arrivals deviate considerably from Poisson; that modeling TELNET packet interarrivals as exponential grievously underestimates the burstiness of TELNET traffic, but using the empirical Tcplib [Danzig et al, 1992] interarrivals preserves burstiness over many time scales; and that FTP data connection arrivals within FTP sessions come bunched into “connection bursts,” the largest of which are so large that they completely dominate FTP data traffic. Finally, we offer some results regarding how our findings relate to the possible self-similarity of widearea traffic.

Recently the notion of self-similarity has been shown to apply to wide-area and local-area network traffic. In this paper we examine the mechanisms that give rise to the self-similarity of network traffic. We present a hypothesized explanation for the possible self-similarity of traffic by using a particular subset of wide area traffic: traffic due to the World Wide Web (WWW). Using an extensive set of traces of actual user executions of NCSA Mosaic, reflecting over half a million requests for WWW documents, we examine the dependence structure of WWW traffic. While our measurements are not conclusive, we show evidence that WWW traffic exhibits behavior that is consistent with self-similar traffic models. Then we show that the self-similarity insuch traffic can be explained based on the underlying distributions of WWW document sizes, the effects of caching and user preference in le transfer, the effect of user "think time", and the superimposition of many such transfers in a local area network. To do this we rely on empirically measured distributions both from our traces and from data independently collected at over thirty WWW sites.

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real

A number of recent empirical studies of traffic measurements from a variety of working packet networks have convincingly demonstrated that actual network traffic is self-similar or long-range 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 self-similarity 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 real-time 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...

We present a detailed statistical analysis of a 2-hour long empirical sample of VBR video. The sample was obtained by applying a simple intraframe video compression code to an action movie. The main findings of our analysis are (1) the tail behavior of the marginal bandwidth distribution can be accurately described using "heavy-tailed" distributions (e.g., Pareto); (2) the autocorrelation of the VBR video sequence decays hyperbolically (equivalent to long-range dependence) and can be modeled using self-similar processes. We combine our findings in a new (non-Markovian) source model for VBR video and present an algorithm for generating synthetic traffic. Trace-driven simulations show that statistical multiplexing results in significant bandwidth efficiency even when long-range dependence is present. Simulations of our source model show long-range dependence and heavy-tailed marginals to be important components which are not accounted for in currently used VBR video traffic models. 1 I...

We propose an indexing method for time sequences for processing similarity queries. We use the Discrete Fourier Transform (DFT) to map time sequences to the frequency domain, the crucial observation being that, for most sequences of practical interest, only the first few frequencies are strong. Another important observation is Parseval's theorem, which specifies that the Fourier transform preserves the Euclidean distance in the time or frequency domain. Having thus mapped sequences to a lower-dimensionality space by using only the first few Fourier coe cients, we use R-trees to index the sequences and e ciently answer similarity queries. We provide experimental results which show that our method is superior to search based on sequential scanning. Our experiments show that a few coefficients (1-3) are adequate to provide good performance. The performance gain of our method increases with the number and length of sequences.

Most of a signal information is often found in irregular structures and transient phenomena. We review the mathematical characterization of singularities with Lipschitz exponents. The main theorems that estimate local Lipschitz exponents of functions, from the evolution across scales of their wavelet transform are explained. We then prove that the local maxima of a wavelet transform detect the location of irregular structures and provide numerical procedures to compute their Lipschitz exponents. The wavelet transform of singularities with fast oscillations have a different behavior that we study separately. We show that the size of the oscillations can be measured from the wavelet transform local maxima. It has been shown that one and two-dimensional signals can be reconstructed from the local maxima of their wavelet transform [14]. As an application, we develop an algorithm that removes white noises by discriminating the noise and the signal singularities through an analysis of their ...

A long-standing difficulty for connectionist modeling has been how to represent variable-sized recursive data structures, such as trees and lists, in fixed-width patterns. This paper presents a connectionist architecture which automatically develops compact distributed representations for such compositional structures, as well as efficient accessing mechanisms for them. Patterns which stand for the internal nodes of fixed-valence trees are devised through the recursive use of back-propagation on three-layer autoassociative encoder networks. The resulting representations are novel, in that they combine apparently immiscible aspects of features, pointers, and symbol structures. They form a bridge between the data structures necessary for high-level cognitive tasks and the associative, pattern recognition machinery provided by neural networks. 2 J. B. Pollack 1. Introduction One of the major stumbling blocks in the application of Connectionism to higherlevel cognitive tasks, such as Na...

The explosion of WWW traffic necessitates an accurate picture of WWW use, and in particular requires a good understanding of client requests for WWW documents. To address this need, we have collectedtraces of actual executions of NCSA Mosaic, reflecting over half a million user requests for WWW documents. In this paper we describe the methods we used to collect our traces, and the formats of the collected data. Next, we present a descriptive statistical summary of the traces we collected, which identifies a number of trends and reference patterns in WWW use. In particular, we show that many characteristics of WWW use can be modelled using power-law distributions, including the distribution of document sizes, the popularity of documents as a function of size, the distribution of user requests for documents, and the number of references to documents as a function of their overall rank in popularity (Zipf's law). Finally, we show how the power-law distributions derived from our traces can beused to guide system designers interested in caching WWW documents.

. Unlabeled document collections are becoming increasingly common and available; mining such data sets represents a major contemporary challenge. Using words as features, text documents are often represented as high-dimensional and sparse vectors--a few thousand dimensions and a sparsity of 95 to 99% is typical. In this paper, we study a certain spherical k-means algorithm for clustering such document vectors. The algorithm outputs k disjoint clusters each with a concept vector that is the centroid of the cluster normalized to have unit Euclidean norm. As our first contribution, we empirically demonstrate that, owing to the high-dimensionality and sparsity of the text data, the clusters produced by the algorithm have a certain "fractal-like" and "self-similar" behavior. As our second contribution, we introduce concept decompositions to approximate the matrix of document vectors; these decompositions are obtained by taking the least-squares approximation onto the linear subspace spanned...