57,389 research outputs found
A Matrix-Analytic Solution for Randomized Load Balancing Models with Phase-Type Service Times
In this paper, we provide a matrix-analytic solution for randomized load
balancing models (also known as \emph{supermarket models}) with phase-type (PH)
service times. Generalizing the service times to the phase-type distribution
makes the analysis of the supermarket models more difficult and challenging
than that of the exponential service time case which has been extensively
discussed in the literature. We first describe the supermarket model as a
system of differential vector equations, and provide a doubly exponential
solution to the fixed point of the system of differential vector equations.
Then we analyze the exponential convergence of the current location of the
supermarket model to its fixed point. Finally, we present numerical examples to
illustrate our approach and show its effectiveness in analyzing the randomized
load balancing schemes with non-exponential service requirements.Comment: 24 page
Doubly Exponential Solution for Randomized Load Balancing Models with General Service Times
In this paper, we provide a novel and simple approach to study the
supermarket model with general service times. This approach is based on the
supplementary variable method used in analyzing stochastic models extensively.
We organize an infinite-size system of integral-differential equations by means
of the density dependent jump Markov process, and obtain a close-form solution:
doubly exponential structure, for the fixed point satisfying the system of
nonlinear equations, which is always a key in the study of supermarket models.
The fixed point is decomposited into two groups of information under a product
form: the arrival information and the service information. based on this, we
indicate two important observations: the fixed point for the supermarket model
is different from the tail of stationary queue length distribution for the
ordinary M/G/1 queue, and the doubly exponential solution to the fixed point
can extensively exist even if the service time distribution is heavy-tailed.
Furthermore, we analyze the exponential convergence of the current location of
the supermarket model to its fixed point, and study the Lipschitz condition in
the Kurtz Theorem under general service times. Based on these analysis, one can
gain a new understanding how workload probing can help in load balancing jobs
with general service times such as heavy-tailed service.Comment: 40 pages, 4 figure
Prochlo: Strong Privacy for Analytics in the Crowd
The large-scale monitoring of computer users' software activities has become
commonplace, e.g., for application telemetry, error reporting, or demographic
profiling. This paper describes a principled systems architecture---Encode,
Shuffle, Analyze (ESA)---for performing such monitoring with high utility while
also protecting user privacy. The ESA design, and its Prochlo implementation,
are informed by our practical experiences with an existing, large deployment of
privacy-preserving software monitoring.
(cont.; see the paper
Privacy Preserving Multi-Server k-means Computation over Horizontally Partitioned Data
The k-means clustering is one of the most popular clustering algorithms in
data mining. Recently a lot of research has been concentrated on the algorithm
when the dataset is divided into multiple parties or when the dataset is too
large to be handled by the data owner. In the latter case, usually some servers
are hired to perform the task of clustering. The dataset is divided by the data
owner among the servers who together perform the k-means and return the cluster
labels to the owner. The major challenge in this method is to prevent the
servers from gaining substantial information about the actual data of the
owner. Several algorithms have been designed in the past that provide
cryptographic solutions to perform privacy preserving k-means. We provide a new
method to perform k-means over a large set using multiple servers. Our
technique avoids heavy cryptographic computations and instead we use a simple
randomization technique to preserve the privacy of the data. The k-means
computed has exactly the same efficiency and accuracy as the k-means computed
over the original dataset without any randomization. We argue that our
algorithm is secure against honest but curious and passive adversary.Comment: 19 pages, 4 tables. International Conference on Information Systems
Security. Springer, Cham, 201
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