Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subexponential tail equivalence of the queue length distributions of
  BMAP/GI/1 queues with and without retrials   The main contribution of this paper is to prove the subexponential tail
equivalence of the stationary queue length distributions in the BMAP/GI/1
queues with and without retrials. We first present a
stochastic-decomposition-like result of the stationary queue length in the
BMAP/GI/1 retrial queue, which is an extension of the stochastic decomposition
of the stationary queue length in the M${}^X$/GI/1 retrial queue. The
stochastic-decomposition-like result shows that the stationary queue length
distribution in the BMAP/GI/1 retrial queue is decomposed into two parts: the
stationary conditional queue length distribution given that the server is idle;
and a certain matrix sequence associated with the stationary queue length
distribution in the corresponding standard BMAP/GI/1 queue (without retrials).
Using the stochastic-decomposition-like result and matrix analytic methods, we
prove the subexponential tail equivalence of the stationary queue length
distributions in the BMAP/GI/1 queues with and without retrials. This tail
equivalence result does not necessarily require that the size of an arriving
batch is light-tailed, unlike Yamamuro's result for the M${}^X$/GI/1 retrial
queue (Queueing Syst. 70:187--205, 2012). As a by-product, the key lemma to the
roof of the main theorem presents a subexponential asymptotic formula for the
stationary distribution of a level-dependent M/G/1-type Markov chain, which is
the first reported result on the subexponential asymptotics of level-dependent
block-structured Markov chains.

26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con