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—Oscillators are often difficult to analyze or simulate, because they generate waveforms that can span a range of widely separated time scales. We present a general oscillator formulation that separates slow and fast dynamics without approximations, and captures amplitude and frequency modulation in a natural and compact manner. To handle… (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)

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)

- Ashok Erramilli, Onuttom Narayan, Walter Willinger
- 1996

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)

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)

- C H Liu, S R Nagel, D A Schecter, S N Coppersmith, S Majumdar, O Narayan +1 other
- Science
- 1995

Experimental observations and numerical simulations of the large force inhomogeneities present in stationary bead packs are presented. Forces much larger than the mean occurred but were exponentially rare. An exactly soluble model reproduced many aspects of the experiments and simulations. In this model, the fluctuations in the force distribution arise… (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)

— 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)

- Onuttom Narayan
- 1998

For a storage model with a fractional Brownian input process, an exact asymptotic expression for the queue length distribution is obtained, using a few plausible assumptions. The probability that the queue length is greater than x is shown to be asymptotically proportional to a Weibullian function multiplied by x ? : For a fractional Brownian input process… (More)