A generalization of the matrix M/G/l paradigm for Markov chains with a tree structure
A generalization of the matrix M/G/l paradigm for Markov chains with a tree structure
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具有树结构的马尔可夫链矩阵 M/G/l 范式的推广
DOI：
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发表时间：
1995
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通讯作者：
R. Yeung
中科院分区：
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作者：
T. Takine;B. Sengupta;R. Yeung
我们将 M/G/1 范式的理论推广到树状结构。马尔可夫链中有两个变量，其中一个变量取一棵 d 叉树节点上的值。另一个是辅助变量，它采用 m 个可能值之一。对于该结构，稳态概率取决于 d 矩阵，G 1 ,..., G d ，它们是非线性矩阵方程组的解。我们还将该理论应用于不允许抢占的多类后到先服务队列。
We generalize the theory of the M/G/1 paradigm to tree-like structures. There are two variables in the Markov chain, one of which takes values on the nodes of a d-ary tree. The other is an auxiliary variable, which takes one of m possible values. For this structure, the steady state probability depends on d matrices, G 1 ,..., G d which are solutions of a system of non-linear matrix equations. We also apply the theory to a multiple class last-come-first-served queue in which no preemption is allowed.