Stability of multidimensional skip-free Markov modulated reflecting random walks: Revisit to Malyshev and Menshikov's results and application to queueing networks

Toshihisa Ozawa

Let $\{{\mathbf{X}}_n\}$ 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 pr…