Tree Structured QBD Markov Chains and Tree‐Like QBD Processes
Tree Structured QBD Markov Chains and Tree‐Like QBD Processes
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树结构 QBD 马尔可夫链和树状 QBD 过程
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
C. Blondia
中科院分区：
文献类型：
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作者：
B. V. Houdt;C. Blondia
摘要本文证明了任意树结构的拟生灭（QBD）马尔可夫链可以嵌入具有特殊结构的树状QBD过程。此外，我们还提出了一个代数证明，证明将自然不动点迭代（FPI）应用于非线性矩阵方程V = B + ∑ s=1 d U s（I-V）-1 D s来求解树状QBD过程，相当于Yeung和Alfa（1996）提出的更复杂的迭代算法。
Abstract In this paper, we show that an arbitrary tree structured quasi‐birth–death (QBD) Markov chain can be embedded in a tree‐like QBD process with a special structure. Moreover, we present an algebraic proof that applying the natural fixed point iteration (FPI) to the nonlinear matrix equation V = B + ∑ s=1 d U s (I − V)−1 D s that solves the tree‐like QBD process, is equivalent to the more complicated iterative algorithm presented by Yeung and Alfa (1996).