Computing the conditional stationary distribution in Markov chains of level-dependent M/G/1-type
Computing the conditional stationary distribution in Markov chains of level-dependent M/G/1-type
复制标题
计算水平相关 M/G/1 型马尔可夫链中的条件平稳分布
DOI：
10.1080/15326349.2018.1451753
复制
发表时间：
2018
影响因子：
0.7
通讯作者：
Masatoshi Kimura and Tetsuya Takine
中科院分区：
文献类型：
--
作者：
室田一雄;池上敦子;土谷隆;山下浩;蒲地 政文;畔上秀幸;斉藤努;枇々木規雄;滝根哲哉;金森敬文;Masatoshi Kimura and Tetsuya Takine
This paper considers the computation of the conditional stationary distribution in Markov chains of level-dependent M/G/1-type, given that the level is not greater than a predefined threshold. This problem has been studied recently and a computational algorithm is proposed under the assumption that matrices representing downward jumps are nonsingular. We first show that this assumption can be eliminated in a general setting of Markov chains of level-dependent G/G/1-type. Next we develop a computational algorithm for the conditional stationary distribution in Markov chains of level-dependent M/G/1-type, by modifying the above-mentioned algorithm slightly. In principle, our algorithm is applicable to any Markov chain of level-dependent M/G/1-type, if the Markov chain is irreducible and positive-recurrent. Furthermore, as an input to the algorithm, we can set an error bound for the computed conditional distribution, which is a notable feature of our algorithm. Some numerical examples are also provided.
