有限QBD过程的不定常期望报酬和偏差矩阵
The time-dependent expected reward and deviation matrix of a finite QBD process
摘要：
推导与连续时间马尔可夫链相关的不定常期望报酬函数涉及到其瞬态偏差矩阵的计算。在本文中，我们专注于一个有限的拟生灭（QBD）过程的特殊情况下，出于希望计算的期望收益损失的MAP/PH/1/C队列。我们在这方面使用两种不同的方法。第一个是基于矩阵差分方程的有限系统的解决方案，它提供了一个表达式的块的预期回报向量，偏差矩阵，和平均首次通过时间矩阵。第二种方法基于马尔可夫链的扰动理论中的一些结果，给出了计算有限QBD过程的全偏差矩阵的递归方法。我们比较了这两种方法使用一些数值例子。
英文摘要：
Deriving the time-dependent expected reward function associated with a continuous-time Markov chain involves the computation of its transient deviation matrix. In this paper we focus on the special case of a finite quasi-birth-and-death (QBD) process, motivated by the desire to compute the expected revenue lost in a MAP/PH/1/C queue. We use two different approaches in this context. The first is based on the solution of a finite system of matrix difference equations; it provides an expression for the blocks of the expected reward vector, the deviation matrix, and the mean first passage time matrix. The second approach, based on some results in the perturbation theory of Markov chains, leads to a recursive method to compute the full deviation matrix of a finite QBD process. We compare the two approaches using some numerical examples.
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