7 papers · 1 filter
Asymptotics of the occupation measure defined on a nonnegative matrix of two-dimensional quasi-birth-and-death type
Toshihisa Ozawa
We consider a nonnegative matrix having the same block structure as that of the transition probability matrix of a two-dimensional quasi-birth-and-death process (2d-QBD process for…
Tail Asymptotics in any direction of the stationary distribution in a two-dimensional discrete-time QBD process
Toshihisa Ozawa
We consider a discrete-time two-dimensional quasi-birth-and-death process (2d-QBD process for short) on , where $\boldsymbol{…
Asymptotic property of the occupation measures in a multi-dimensional skip-free Markov modulated random walk
Toshihisa Ozawa
We consider a discrete-time -dimensional process on with a background process on a countable se…
Asymptotic property of the occupation measures in a two-dimensional skip-free Markov modulated random walk
Toshihisa Ozawa
We consider a discrete-time two-dimensional process on with a background process on a finite set , where individual processes…
Stability condition of a two-dimensional QBD process and its application to estimation of efficiency for two-queue models
Toshihisa Ozawa
In order to analyze stability of a two-queue model, we consider a two-dimensional quasi-birth-and-death process (2d-QBD process), denoted by $\{\boldsymbol{Y}(t)\}=\{((L_1(t),L_2(t…
Exact asymptotic formulae of the stationary distribution of a discrete-time 2d-QBD process: an example and additional proofs
Toshihisa Ozawa, Masahiro Kobayashi
A discrete-time two-dimensional quasi-birth-and-death process (2d-QBD process), , is a two-dimensional skip-free random walk $\{(X_{…