Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Interacting multi-class transmissions in large stochastic networks   The mean-field limit of a Markovian model describing the interaction of
several classes of permanent connections in a network is analyzed. Each of the
connections has a self-adaptive behavior in that its transmission rate along
its route depends on the level of congestion of the nodes of the route. Since
several classes of connections going through the nodes of the network are
considered, an original mean-field result in a multi-class context is
established. It is shown that, as the number of connections goes to infinity,
the behavior of the different classes of connections can be represented by the
solution of an unusual nonlinear stochastic differential equation depending not
only on the sample paths of the process, but also on its distribution.
Existence and uniqueness results for the solutions of these equations are
derived. Properties of their invariant distributions are investigated and it is
shown that, under some natural assumptions, they are determined by the
solutions of a fixed-point equation in a finite-dimensional space.

13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
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The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga