2,056 research outputs found
Large Deviations Analysis for Distributed Algorithms in an Ergodic Markovian Environment
We provide a large deviations analysis of deadlock phenomena occurring in
distributed systems sharing common resources. In our model transition
probabilities of resource allocation and deallocation are time and space
dependent. The process is driven by an ergodic Markov chain and is reflected on
the boundary of the d-dimensional cube. In the large resource limit, we prove
Freidlin-Wentzell estimates, we study the asymptotic of the deadlock time and
we show that the quasi-potential is a viscosity solution of a Hamilton-Jacobi
equation with a Neumann boundary condition. We give a complete analysis of the
colliding 2-stacks problem and show an example where the system has a stable
attractor which is a limit cycle
Agent Behavior Prediction and Its Generalization Analysis
Machine learning algorithms have been applied to predict agent behaviors in
real-world dynamic systems, such as advertiser behaviors in sponsored search
and worker behaviors in crowdsourcing. The behavior data in these systems are
generated by live agents: once the systems change due to the adoption of the
prediction models learnt from the behavior data, agents will observe and
respond to these changes by changing their own behaviors accordingly. As a
result, the behavior data will evolve and will not be identically and
independently distributed, posing great challenges to the theoretical analysis
on the machine learning algorithms for behavior prediction. To tackle this
challenge, in this paper, we propose to use Markov Chain in Random Environments
(MCRE) to describe the behavior data, and perform generalization analysis of
the machine learning algorithms on its basis. Since the one-step transition
probability matrix of MCRE depends on both previous states and the random
environment, conventional techniques for generalization analysis cannot be
directly applied. To address this issue, we propose a novel technique that
transforms the original MCRE into a higher-dimensional time-homogeneous Markov
chain. The new Markov chain involves more variables but is more regular, and
thus easier to deal with. We prove the convergence of the new Markov chain when
time approaches infinity. Then we prove a generalization bound for the machine
learning algorithms on the behavior data generated by the new Markov chain,
which depends on both the Markovian parameters and the covering number of the
function class compounded by the loss function for behavior prediction and the
behavior prediction model. To the best of our knowledge, this is the first work
that performs the generalization analysis on data generated by complex
processes in real-world dynamic systems
Integration of streaming services and TCP data transmission in the Internet
We study in this paper the integration of elastic and streaming traffic on a
same link in an IP network. We are specifically interested in the computation
of the mean bit rate obtained by a data transfer. For this purpose, we consider
that the bit rate offered by streaming traffic is low, of the order of
magnitude of a small parameter \eps \ll 1 and related to an auxiliary
stationary Markovian process (X(t)). Under the assumption that data transfers
are exponentially distributed, arrive according to a Poisson process, and share
the available bandwidth according to the ideal processor sharing discipline, we
derive the mean bit rate of a data transfer as a power series expansion in
\eps. Since the system can be described by means of an M/M/1 queue with a
time-varying server rate, which depends upon the parameter \eps and process
(X(t)), the key issue is to compute an expansion of the area swept under the
occupation process of this queue in a busy period. We obtain closed formulas
for the power series expansion in \eps of the mean bit rate, which allow us to
verify the validity of the so-called reduced service rate at the first order.
The second order term yields more insight into the negative impact of the
variability of streaming flows
Queueing analysis of opportunistic scheduling with spatially correlated channels
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