相位的清晰分析：无跳单向拟生灭过程的精确极限概率
Clearing Analysis on Phases: Exact Limiting Probabilities for Skip-free, Unidirectional, Quasi-birth-death Processes
摘要：
计算、服务和制造系统中的许多问题都可以通过具有无限个层次和有限个阶段的无限重复马尔可夫链来建模。许多这样的链是准生灭过程（QBD），其过渡在级别上是无跳跃的，因为人们只能在连续的级别之间过渡，并且在相位上是单向的，因为人们只能从较低编号的相位过渡到较高编号的相位。我们提出了一个程序，我们称之为清除分析阶段（CAP），以确定这种马尔可夫链的极限概率准确。CAP方法产生链的重复部分中的每个状态的极限概率，作为提升到对应于状态水平的幂的标量基的线性组合。这些线性组合中的权重可以通过求解有限的线性方程组线性方程组来确定。
英文摘要：
Many problems in computing, service, and manufacturing systems can be modeled via infinite repeating Markov chains with an infinite number of levels and a finite number of phases. Many such chains are quasi-birth-death processes (QBDs) with transitions that are skip-free in level, in that one can only transition between consecutive levels, and unidirectional in phase, in that one can only transition from lower-numbered phases to higher-numbered phases. We present a procedure, which we call Clearing Analysis on Phases (CAP), for determining the limiting probabilities of such Markov chains exactly. The CAP method yields the limiting probability of each state in the repeating portion of the chain as a linear combination of scalar bases raised to a power corresponding to the level of the state. The weights in these linear combinations can be determined by solving a finite system of linear equations.
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