可修排队系统可靠性指标的分解特性

The Decomposition Properties of Reliability Indices in Repairable Queueing Systems

本文提出了分析可修排队系统的另一途径-分解法,剖析了一些典型可修排队系统的结构,即是经典排队系统模型与经典可靠性系统模型的一种卷积关系.应用提出的分解分析法,我们不仅可推导出在交通强度ρ<1时的有关结果,而且可得到在交通强度ρ≥1时的有关结果和一些重要的分解关系式.它使得我们把对可修排队系统的研究,转化为分别对经典排队系统与经典可靠性系统的研究,降低了对可修排队系统研究的难度.

In this paper the decomposition method - a new approach of analyzing the repairable queueing system is provided. A kind of convolution relation between the standard queueing system and the standard reliability system is found by studying the structures of typical repairable queueing systems. And by using this decomposition method the results under the conditionρ<1 are derived. Furthermore, another results under the condition ρ ≥ 1 and some important relations are also obtained. It makes studying the repairable queueing system into studying the standard queueing system and studying the standard reliability system respectively, which greatly reduce the difficulty to study some repairable queueing systems.