Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of Large Unreliable Stochastic Networks   In this paper a stochastic model of a large distributed system where users'
files are duplicated on unreliable data servers is investigated. Due to a
server breakdown, a copy of a file can be lost, it can be retrieved if another
copy of the same file is stored on other servers. In the case where no other
copy of a given file is present in the network, it is definitively lost. In
order to have multiple copies of a given file, it is assumed that each server
can devote a fraction of its processing capacity to duplicate files on other
servers to enhance the durability of the system.
  A simplified stochastic model of this network is analyzed. It is assumed that
a copy of a given file is lost at some fixed rate and that the initial state is
optimal: each file has the maximum number $d$ of copies located on the servers
of the network. Due to random losses, the state of the network is transient and
all files will be eventually lost. As a consequence, a transient
$d$-dimensional Markov process $(X(t))$ with a unique absorbing state describes
the evolution this network. By taking a scaling parameter $N$ related to the
number of nodes of the network. a scaling analysis of this process is
developed. The asymptotic behavior of $(X(t))$ is analyzed on time scales of
the type $t\mapsto N^p t$ for $0\leq p\leq d{-}1$. The paper derives asymptotic
results on the decay of the network: Under a stability assumption, the main
results state that the critical time scale for the decay of the system is given
by $t\mapsto N^{d-1}t$. When the stability condition is not satisfied, it is
shown that the state of the network converges to an interesting local
equilibrium which is investigated. As a consequence it sheds some light on the
role of the key parameters $\lambda$, the duplication rate and $d$, the maximal
number of copies, in the design of these systems.

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The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
1
The categories of this paper are: cs
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The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio