Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The heavy traffic limit of an unbalanced generalized processor sharing
  model   This work considers a server that processes $J$ classes using the generalized
processor sharing discipline with base weight vector $\alpha=(\alpha
_1,...,\alpha_J)$ and redistribution weight vector
$\beta=(\beta_1,...,\beta_J)$. The invariant manifold $\mathcal{M}$ of the
so-called fluid limit associated with this model is shown to have the form
$\mathcal{M}=\{x\in\mathbb{R}_+^J:x_j=0 for j\in\mathcal{S}\}$, where
$\mathcal{S}$ is the set of strictly subcritical classes, which is identified
explicitly in terms of the vectors $\alpha$ and $\beta$ and the long-run
average work arrival rates $\gamma_j$ of each class $j$. In addition, under
general assumptions, it is shown that when the heavy traffic condition
$\sum_{j=1}^J\gamma_j=\sum_{j=1}^J\alpha_j$ holds, the functional central limit
of the scaled unfinished work process is a reflected diffusion process that
lies in $\mathcal{M}$. The reflected diffusion limit is characterized by the
so-called extended Skorokhod map and may fail to be a semimartingale. This
generalizes earlier results obtained for the simpler, balanced case where
$\gamma_j=\alpha_j$ for $j=1,...,J$, in which case $\mathcal{M}=\mathbb{R}_+^J$
and there is no state-space collapse. Standard techniques for obtaining
diffusion approximations cannot be applied in the unbalanced case due to the
particular structure of the GPS model. Along the way, this work also
establishes a comparison principle for solutions to the extended Skorokhod map
associated with this model, which may be of independent interest.

16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex