Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of multidimensional skip-free Markov modulated reflecting
  random walks: Revisit to Malyshev and Menshikov's results and application to
  queueing networks   Let $\{\boldsymbol{X}_n\}$ be a discrete-time $d$-dimensional process on
$\mathbb{Z}_+^d$ with a supplemental (background) process $\{J_n\}$ on a finite
set and assume the joint process
$\{\boldsymbol{Y}_n\}=\{(\boldsymbol{X}_n,J_n)\}$ to be Markovian. Then, the
process $\{\boldsymbol{X}_n\}$ can be regarded as a kind of reflecting random
walk (RRW for short) in which the transition probabilities of the RRW are
modulated according to the state of the background process $\{J_n\}$; we assume
this modulation is space-homogeneous inside $\mathbb{Z}_+^d$ and on each
boundary face of $\mathbb{Z}_+^d$. Further we assume the process
$\{\boldsymbol{X}_n\}$ is skip free in all coordinates and call the joint
process $\{\boldsymbol{Y}_n\}$ a $d$-dimensional skip-free Markov modulated
reflecting random walk (MMRRW for short). The MMRRW is an extension of an
ordinary RRW and stability of ordinary RRWs have been studied by Malyshev and
Menshikov. Following their results, we obtain stability and instability
conditions for MMRRWs and apply our results to stability analysis of a
two-station network.

20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th