Onuttom Narayan

Experimental queueing analysis with long-range dependent packet traffic

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 dependence (LRD), which is marked by the presence of correlations that can extend over many time scales. We demonstrate empirically that, beyond its statistical significance in traffic measurements, long-range dependence has considerable impact on queueing performance, and is a dominant characteristic for a number of packet traffic engineering problems. In addition, we give conditions under which the use of compact and simple traffic models that incorporate long-range dependence in a parsimonious manner (e.g., fractional Brownian motion) is justified and can lead to new insights into the traffic management of high speed networks.

Performance impacts of multi-scaling in wide area TCP/IP traffic

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 queueing simulations, we show that the fine timescale features can affect performance substantially at low and intermediate utilizations, while the coarse timescale self-similarity is important at intermediate and high utilizations. We outline an analytical method for estimating performance for traffic that is self-similar on coarse timescales and multi-fractal on fine timescales, and show that the engineering problem of setting safe operating points for planning or admission control can be significantly affected by fine timescale fluctuations in network traffic.

Large-scale curvature of networks.

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 (IP) layer possess global negative curvature. We show that negative curvature is independent of previously studied network properties, and that it has a major impact on core congestion: the load at the core of a finite negatively curved network with N nodes scales as N(2), as compared to N(1.5) for a generic finite flat network.

Disorder-induced microscopic magnetic memory

Using coherent x-ray speckle metrology, we have measured the influence of disorder on major loop return point memory (RPM) and complementary point memory (CPM) for a series of perpendicular anisotropy Co/Pt multilayer films. In the low disorder limit, the domain structures show no memory with field cycling--no RPM and no CPM. With increasing disorder, we observe the onset and the saturation of both the RPM and the CPM. These results provide the first direct ensemble-sensitive experimental study of the effects of varying disorder on microscopic magnetic memory and are compared against the predictions of existing theories.

Accounting for boundary effects in nearest neighbor searching

Givenn data points ind-dimensional space, nearest-neighbor searching involves determining the nearest of these data points to a given query point. Most averagecase analyses of nearest-neighbor searching algorithms are made under the simplifying assumption thatd is fixed and thatn is so large relative tod thatboundary effects can be ignored. This means that for any query point the statistical distribution of the data points surrounding it is independent of the location of the query point. However, in many applications of nearest-neighbor searching (such as data compression by vector quantization) this assumption is not met, since the number of data pointsn grows roughly as 2 d .Largely for this reason, the actual performances of many nearest-neighbor algorithms tend to be much better than their theoretical analyses would suggest. We present evidence of why this is the case. We provide an accurate analysis of the number of cells visited in nearest-neighbor searching by the bucketing andk-d tree algorithms. We assumem dpoints uniformly distributed in dimensiond, wherem is a fixed integer ≥2. Further, we assume that distances are measured in theL ∞ metric. Our analysis is tight in the limit asd approaches infinity. Empirical evidence is presented showing that the analysis applies even in low dimensions.

Disorder-induced magnetic memory: Experiments and theories

Beautiful theories of magnetic hysteresis based on random microscopic disorder have been developed over the past ten years. Our goal was to directly compare these theories with precise experiments. To do so, we first developed and then applied coherent x-ray speckle metrology to a series of thin multilayer perpendicular magnetic materials. To directly observe the effects of disorder, we deliberately introduced increasing degrees of disorder into our films. We used coherent x rays, produced at the Advanced Light Source at Lawrence Berkeley National Laboratory, to generate highly speckled magnetic scattering patterns. The apparently “random” arrangement of the speckles is due to the exact configuration of the magnetic domains in the sample. In effect, each speckle pattern acts as a unique fingerprint for the magnetic domain configuration. Small changes in the domain structure change the speckles, and comparison of the different speckle patterns provides a quantitative determination of how much the domain structure has changed. Our experiments quickly answered one longstanding question: How is the magnetic domain configuration at one point on the major hysteresis loop related to the configurations at the same point on the loop during subsequent cycles? This is called microscopic return-point memory RPM. We found that the RPM is partial and imperfect in the disordered samples, and completely absent when the disorder is below a threshold level. We also introduced and answered a second important question: How are the magnetic domains at one point on the major loop related to the domains at the complementary point, the inversion symmetric point on the loop, during the same and during subsequent cycles? This is called microscopic complementary-point memory CPM. We found that the CPM is also partial and imperfect in the disordered samples and completely absent when the disorder is not present. In addition, we found that the RPM is always a little larger than the CPM. We also studied the correlations between the domains within a single ascending or descending loop. This is called microscopic half-loop memory and enabled us to measure the degree of change in the domain structure due to changes in the applied field. No existing theory was capable of reproducing our experimental results. So we developed theoretical models that do fit our experiments. Our experimental and theoretical results set benchmarks for future work.

Equilibration and universal heat conduction in fermi-pasta-ulam chains.

It is shown numerically that for Fermi Pasta Ulam (FPU) chains with alternating masses and heat baths at slightly different temperatures at the ends, the local temperature (LT) on small scales behaves paradoxically in steady state. This expands the long established problem of equilibration of FPU chains. A well-behaved LT appears to be achieved for equal mass chains; the thermal conductivity is shown to diverge with chain length N as N^(1/3), relevant for the much debated question of the universality of one dimensional heat conduction. The reason why earlier simulations have obtained systematically higher exponents is explained.

Reexamination of experimental tests of the fluctuation theorem

The fluctuation theorem and the Jarzynski equality are examined in the light of recent experimental tests. For a particle dragged through a solvent, it is shown that Q, the heat exchanged with the reservoir, does not obey the Jarzynski equality due to slowly decaying tails in its distribution. For molecular stretching experiments, substantial corrections to the Jarzynski equality can result from not measuring the force at the end of the molecule that is moved. We also present a proof of the fluctuation theorem for Langevin dynamics that is considerably simpler than the standard proof.

Accounting for Boundary Effects in Nearest-Neighbor Searching

Givenn data points ind-dimensional space, nearest-neighbor searching involves determining the nearest of these data points to a given query point. Most averagecase analyses of nearest-neighbor searching algorithms are made under the simplifying assumption thatd is fixed and thatn is so large relative tod thatboundary effects can be ignored. This means that for any query point the statistical distribution of the data points surrounding it is independent of the location of the query point. However, in many applications of nearest-neighbor searching (such as data compression by vector quantization) this assumption is not met, since the number of data pointsn grows roughly as 2d.Largely for this reason, the actual performances of many nearest-neighbor algorithms tend to be much better than their theoretical analyses would suggest. We present evidence of why this is the case. We provide an accurate analysis of the number of cells visited in nearest-neighbor searching by the bucketing andk-d tree algorithms. We assumemdpoints uniformly distributed in dimensiond, wherem is a fixed integer ≥2. Further, we assume that distances are measured in theL∞ metric. Our analysis is tight in the limit asd approaches infinity. Empirical evidence is presented showing that the analysis applies even in low dimensions.

Self-Similar Barkhausen Noise in Magnetic Domain Wall Motion.

A model for domain wall motion in ferromagnets is analyzed. Long-range magnetic dipolar interactions are shown to give rise to self-similar dynamics when the external magnetic field is increased adiabatically. The power spectrum of the resultant Barkhausen noise is of the form