Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A functional central limit theorem for the M/GI/$\infty$ queue   In this paper, we present a functional fluid limit theorem and a functional
central limit theorem for a queue with an infinity of servers M/GI/$\infty$.
The system is represented by a point-measure valued process keeping track of
the remaining processing times of the customers in service. The convergence in
law of a sequence of such processes after rescaling is proved by
compactness-uniqueness methods, and the deterministic fluid limit is the
solution of an integrated equation in the space $\mathcal{S}^{\prime}$ of
tempered distributions. We then establish the corresponding central limit
theorem, that is, the approximation of the normalized error process by a
$\mathcal{S}^{\prime}$-valued diffusion. We apply these results to provide
fluid limits and diffusion approximations for some performance processes.

16
The categories of this paper are: stat
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph