1,663 research outputs found
Conditional limit theorems for regulated fractional Brownian motion
We consider a stationary fluid queue with fractional Brownian motion input.
Conditional on the workload at time zero being greater than a large value ,
we provide the limiting distribution for the amount of time that the workload
process spends above level over the busy cycle straddling the origin, as
. Our results can be interpreted as showing that long delays occur
in large clumps of size of order . The conditional limit result
involves a finer scaling of the queueing process than fluid analysis, thereby
departing from previous related literature.Comment: Published in at http://dx.doi.org/10.1214/09-AAP605 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Estimation of Scale and Hurst Parameters of Semi-Selfsimilar Processes
The characteristic feature of semi-selfsimilar process is the invariance of
its finite dimensional distributions by certain dilation for specific scaling
factor. Estimating the scale parameter and the Hurst index of such
processes is one of the fundamental problem in the literature. We present some
iterative method for estimation of the scale and Hurst parameters which is
addressed for semi-selfsimilar processes with stationary increments. This
method is based on some flexible sampling scheme and evaluating sample variance
of increments in each scale intervals , . For such iterative method we find the initial estimation for the
scale parameter by evaluating cumulative sum of moving sample variances and
also by evaluating sample variance of preceding and succeeding moving sample
variance of increments. We also present a new efficient method for estimation
of Hurst parameter of selfsimilar processes. As an example we introduce simple
fractional Brownian motion (sfBm) which is semi-selfsimilar with stationary
increments. We present some simulations and numerical evaluation to illustrate
the results and to estimate the scale for sfBm as a semi-selfsimilar process.
We also present another simulation and show the efficiency of our method in
estimation of Hurst parameter by comparing its performance with some previous
methods.Comment: 15 page
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
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
Sample-path large deviations for tandem and priority queues with Gaussian inputs
This paper considers Gaussian flows multiplexed in a queueing network. A
single node being a useful but often incomplete setting, we examine more
advanced models. We focus on a (two-node) tandem queue, fed by a large number
of Gaussian inputs. With service rates and buffer sizes at both nodes scaled
appropriately, Schilder's sample-path large-deviations theorem can be applied
to calculate the asymptotics of the overflow probability of the second queue.
More specifically, we derive a lower bound on the exponential decay rate of
this overflow probability and present an explicit condition for the lower bound
to match the exact decay rate. Examples show that this condition holds for a
broad range of frequently used Gaussian inputs. The last part of the paper
concentrates on a model for a single node, equipped with a priority scheduling
policy. We show that the analysis of the tandem queue directly carries over to
this priority queueing system.Comment: Published at http://dx.doi.org/10.1214/105051605000000133 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Sample path large deviations for multiclass feedforward queueing networks in critical loading
We consider multiclass feedforward queueing networks with first in first out
and priority service disciplines at the nodes, and class dependent
deterministic routing between nodes. The random behavior of the network is
constructed from cumulative arrival and service time processes which are
assumed to satisfy an appropriate sample path large deviation principle. We
establish logarithmic asymptotics of large deviations for waiting time, idle
time, queue length, departure and sojourn-time processes in critical loading.
This transfers similar results from Puhalskii about single class queueing
networks with feedback to multiclass feedforward queueing networks, and
complements diffusion approximation results from Peterson. An example with
renewal inter arrival and service time processes yields the rate function of a
reflected Brownian motion. The model directly captures stationary situations.Comment: Published at http://dx.doi.org/10.1214/105051606000000439 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Characterization of laser propagation through turbulent media by quantifiers based on the wavelet transform: dynamic study
We analyze, within the wavelet theory framework, the wandering over a screen
of the centroid of a laser beam after it has propagated through a time-changing
laboratory-generated turbulence. Following a previous work (Fractals 12 (2004)
223) two quantifiers are used, the Hurst parameter, , and the Normalized
Total Wavelet Entropy, . The temporal evolution of both
quantifiers, obtained from the laser spot data stream is studied and compared.
This allows us to extract information of the stochastic process associated to
the turbulence dynamics.Comment: 11 pages, 3 figures, accepted to be published in Physica
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