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Abstruct-Recent traffic measurement studies from a wide range of working packet networks have convincingly established the presence of significant statistical features that are characteristic of fractal traffic processes, in the sense that these features span many time scales. Of particular interest in packet traffic modeling is a property called long-range(More)
Understanding key structural properties of large-scale networks is crucial for analyzing and optimizing their performance and improving their reliability and security. Here, through an analysis of a collection of data networks across the globe as measured and documented by previous researchers, we show that communications networks at the Internet protocol(More)
— Recent measurement and simulation studies have revealed that wide area network traffic has complex statistical—possibly multifractal—characteristics on short timescales, and is self-similar on long timescales. In this paper, using measured TCP traces and queue-ing simulations, we show that the fine timescale features can affect performance substantially(More)
Given n data points in d-dimensional space, nearest-neighbor searching involves determining the nearest of these data points to a given query point. Most average-case analyses of nearest-neighbor searching algorithms are made under the simplifying assumption that d is fixed and that n is so large relative to d that boundary effects can be ignored. This(More)
Recent measurement and simulation studies have revealed that wide area network traac displays complex statistical characteristics-possibly multifractal scaling-on ne timescales, in addition to the well-known property of self-similar scaling on coarser timescales. In this paper we investigate the performance and network engineering sig-niicance of these ne(More)
We show that the load at each node in a preferential attachment network scales as a power of the degree of the node. For a network whose degree distribution is p(k)∼k{-γ} , we show that the load is l(k)∼k{η} with η=γ-1 , implying that the probability distribution for the load is p(l)∼1/l{2} independent of γ . The results are obtained through scaling(More)
Through detailed analysis of scores of publicly available data sets corresponding to a wide range of large-scale networks, from communication and road networks to various forms of social networks, we explore a little-studied geometric characteristic of real-life networks, namely their hyperbolicity. In smooth geometry, hyperbolicity captures the notion of(More)
We present a novel formulation, called the WaMPDE, for solving systems with forced autonomous components. An important feature of the WaMPDE is its ability to capture frequency modulation (FM) in a natural and compact manner. This is made possible by a key new concept: that of warped time, related to normal time through separate time scales. Using warped(More)
—We show that the normalized Laplacian of the giant component of the Erdös-Renyi random graph G(n, pn) in the regime pn = d n for d a constant greater than 1 (sparse regime) has zero spectral gap as n ! 1. This is in contrast to earlier results showing the existence of a spectral gap when npn = O(log 2 (n)). We also prove that in the regime pn = d n , for(More)