Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heavy Traffic Queue Length Behaviour in a Switch under Markovian
  Arrivals   The paper studies the input queued switch that is a good model for data
center networks, operating under the MaxWeight algorithm. The heavy-traffic
scaled mean queue length was characterized in \citet{maguluri2018optimal,
maguluri2016heavy} when the arrivals are i.i.d.. This paper characterizes the
heavy-traffic scaled mean sum queue length under Markov modulated arrivals in
the heavy-traffic limit, and shows that it is within a factor of less than $2$
from a universal lower bound. Moreover, the paper obtains lower and upper
bounds, that are applicable in all traffic regimes, and they become tight in
heavy-traffic regime.
  The paper obtains these results by generalizing the drift method that was
developed in \citet{eryilmaz2012asymptotically, maguluri2016heavy} to the case
of Markovian arrivals. The paper illustrates this generalization by first
obtaining the heavy-traffic mean queue length in a single server queue under
Markovian arrivals. The paper also illustrates the generalization of the
transform method \citet{hurtado2018transform} to obtain the queue length
distribution in a single server queue under Markovian arrivals. The key ideas
are the use of geometric mixing of finite-state Markov chains, and studying the
drift of a test function over a time window that depends on the heavy-traffic
parameter.

26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex