NUMERICAL IMPLEMENTATION OF THE AUGMENTED TRUNCATION APPROXIMATION TO SINGLE-SERVER QUEUES WITH LEVEL-DEPENDENT ARRIVALS AND DISASTERS
NUMERICAL IMPLEMENTATION OF THE AUGMENTED TRUNCATION APPROXIMATION TO SINGLE-SERVER QUEUES WITH LEVEL-DEPENDENT ARRIVALS AND DISASTERS
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DOI：
10.15807/jorsj.64.61
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发表时间：
2021-04
影响因子：
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通讯作者：
Masatoshi Kimura;T. Takine
中科院分区：
文献类型：
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作者：
Masatoshi Kimura;T. Takine
本文研究了到达与到达水平相关且有灾难的单服务器排队系统中稳态队长分布的计算问题。我们假设服务时间服从一般分布，因此，我们考虑通过嵌入马尔可夫链的平稳队长分布。由于这种嵌入马尔可夫链具有无穷多个状态、水平依赖性和水平的双向跳跃性，很难精确计算全局平衡方程的解。因此，我们考虑增广截断近似。特别是，我们专注于嵌入马尔可夫链的截断状态转移概率矩阵的计算，假设潜在的连续时间吸收马尔可夫链在服务时间是不一致的。在一定的稳定性条件下，我们发展了一种截断转移概率矩阵的计算方法，其中截断误差的上界可以预先设定。我们还提供了一些数值例子，并证明我们的程序工作得很好。
This paper considers the computation of the stationary queue length distribution in singleserver queues with level-dependent arrivals and disasters. We assume that service times follow a general distribution and therefore, we consider the stationary queue length distribution via an imbedded Markov chain. Because this imbedded Markov chain has infinitely many states, level dependence, and bidirectional jumps of levels, it is hard to compute the solution of the global balance equation exactly. We thus consider the augmented truncation approximation. In particular, we focus on the computation of the truncated state transition probability matrix of the imbedded Markov chain, assuming that the underlying continuous-time absorbing Markov chain during a service time is not uniformizable. Under some stability conditions, we develop a computational procedure for the truncated transition probability matrix, where the upper bound of errors owing to truncation can be set in advance. We also provide some numerical examples and demonstrate that our procedure works well.