37,162 research outputs found
Resource dimensioning through buffer sampling
Link dimensioning, i.e., selecting a (minimal) link capacity such that the users’ performance requirements are met, is a crucial component of network design. It requires insight into the interrelationship among the traffic offered (in terms of the mean offered load , but also its fluctuation around the mean, i.e., ‘burstiness’), the envisioned performance level, and the capacity needed. We first derive, for different performance criteria, theoretical dimensioning formulas that estimate the required capacity as a function of the input traffic and the performance target. For the special case of Gaussian input traffic, these formulas reduce to , where directly relates to the performance requirement (as agreed upon in a service level agreement) and reflects the burstiness (at the timescale of interest). We also observe that Gaussianity applies for virtually all realistic scenarios; notably, already for a relatively low aggregation level, the Gaussianity assumption is justified.\ud
As estimating is relatively straightforward, the remaining open issue concerns the estimation of . We argue that particularly if corresponds to small time-scales, it may be inaccurate to estimate it directly from the traffic traces. Therefore, we propose an indirect method that samples the buffer content, estimates the buffer content distribution, and ‘inverts’ this to the variance. We validate the inversion through extensive numerical experiments (using a sizeable collection of traffic traces from various representative locations); the resulting estimate of is then inserted in the dimensioning formula. These experiments show that both the inversion and the dimensioning formula are remarkably accurate
Classes of behavior of small-world networks
Small-world networks are the focus of recent interest because they appear to
circumvent many of the limitations of either random networks or regular
lattices as frameworks for the study of interaction networks of complex
systems. Here, we report an empirical study of the statistical properties of a
variety of diverse real-world networks. We present evidence of the occurrence
of three classes of small-world networks: (a) scale-free networks,
characterized by a vertex connectivity distribution that decays as a power law;
(b) broad-scale networks, characterized by a connectivity distribution that has
a power-law regime followed by a sharp cut-off; (c) single-scale networks,
characterized by a connectivity distribution with a fast decaying tail.
Moreover, we note for the classes of broad-scale and single-scale networks that
there are constraints limiting the addition of new links. Our results suggest
that the nature of such constraints may be the controlling factor for the
emergence of different classes of networks
Global Modeling and Prediction of Computer Network Traffic
We develop a probabilistic framework for global modeling of the traffic over
a computer network. This model integrates existing single-link (-flow) traffic
models with the routing over the network to capture the global traffic
behavior. It arises from a limit approximation of the traffic fluctuations as
the time--scale and the number of users sharing the network grow. The resulting
probability model is comprised of a Gaussian and/or a stable, infinite variance
components. They can be succinctly described and handled by certain
'space-time' random fields. The model is validated against simulated and real
data. It is then applied to predict traffic fluctuations over unobserved links
from a limited set of observed links. Further, applications to anomaly
detection and network management are briefly discussed
Resource dimensioning through buffer sampling
Link dimensioning, i.e., selecting a (minimal) link capacity such that the users’ performance requirements are met, is a crucial component of network design. It requires insight into the interrelationship between the traffic offered (in terms of the mean offered load M, but also its fluctuation around the mean, i.e., ‘burstiness’), the envisioned performance level, and the capacity needed. We first derive, for different performance criteria, theoretical dimensioning formulae that estimate the required capacity C as a function of the input traffic and the performance target. For the special case of Gaussian input traffic these formulae reduce to C = M+V , where directly relates to the performance requirement (as agreed upon in a service level agreement) and V reflects the burstiness (at the timescale of interest). We also observe that Gaussianity applies for virtually all realistic scenarios; notably, already for a relatively low aggregation level the Gaussianity assumption is justified.\ud
As estimating M is relatively straightforward, the remaining open issue concerns the estimation of V . We argue that, particularly if V corresponds to small time-scales, it may be inaccurate to estimate it directly from the traffic traces. Therefore, we propose an indirect method that samples the buffer content, estimates the buffer content distribution, and ‘inverts’ this to the variance. We validate the inversion through extensive numerical experiments (using a sizeable collection of traffic traces from various representative locations); the resulting estimate of V is then inserted in the dimensioning formula. These experiments show that both the inversion and the dimensioning formula are remarkably accurate
On the multiresolution structure of Internet traffic traces
Internet traffic on a network link can be modeled as a stochastic process.
After detecting and quantifying the properties of this process, using
statistical tools, a series of mathematical models is developed, culminating in
one that is able to generate ``traffic'' that exhibits --as a key feature-- the
same difference in behavior for different time scales, as observed in real
traffic, and is moreover indistinguishable from real traffic by other
statistical tests as well. Tools inspired from the models are then used to
determine and calibrate the type of activity taking place in each of the time
scales. Surprisingly, the above procedure does not require any detailed
information originating from either the network dynamics, or the decomposition
of the total traffic into its constituent user connections, but rather only the
compliance of these connections to very weak conditions.Comment: 57 pages, color figures. Figures are of low quality due to space
consideration
Structural Analysis of Network Traffic Matrix via Relaxed Principal Component Pursuit
The network traffic matrix is widely used in network operation and
management. It is therefore of crucial importance to analyze the components and
the structure of the network traffic matrix, for which several mathematical
approaches such as Principal Component Analysis (PCA) were proposed. In this
paper, we first argue that PCA performs poorly for analyzing traffic matrix
that is polluted by large volume anomalies, and then propose a new
decomposition model for the network traffic matrix. According to this model, we
carry out the structural analysis by decomposing the network traffic matrix
into three sub-matrices, namely, the deterministic traffic, the anomaly traffic
and the noise traffic matrix, which is similar to the Robust Principal
Component Analysis (RPCA) problem previously studied in [13]. Based on the
Relaxed Principal Component Pursuit (Relaxed PCP) method and the Accelerated
Proximal Gradient (APG) algorithm, we present an iterative approach for
decomposing a traffic matrix, and demonstrate its efficiency and flexibility by
experimental results. Finally, we further discuss several features of the
deterministic and noise traffic. Our study develops a novel method for the
problem of structural analysis of the traffic matrix, which is robust against
pollution of large volume anomalies.Comment: Accepted to Elsevier Computer Network
More "normal" than normal: scaling distributions and complex systems
One feature of many naturally occurring or engineered complex systems is tremendous variability in event sizes. To account for it, the behavior of these systems is often described using power law relationships or scaling distributions, which tend to be viewed as "exotic" because of their unusual properties (e.g., infinite moments). An alternate view is based on mathematical, statistical, and data-analytic arguments and suggests that scaling distributions should be viewed as "more normal than normal". In support of this latter view that has been advocated by Mandelbrot for the last 40 years, we review in this paper some relevant results from probability theory and illustrate a powerful statistical approach for deciding whether the variability associated with observed event sizes is consistent with an underlying Gaussian-type (finite variance) or scaling-type (infinite variance) distribution. We contrast this approach with traditional model fitting techniques and discuss its implications for future modeling of complex systems
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