具有温储备失效的M/G/1可修排队系统

本文把“服务台在系统闲期中可能温储备失效”引入到M/G/1可修排队系统中，考虑了具有温储备失效特征的M/G/1可修排队系统.使用全概率分解技术和利用拉普拉斯变换工具，导出了在任意时刻t队长的瞬态分布的拉普拉斯变换的表达式，进一步获得了队长的稳态分布的递推式，同时，给出了稳态队长和稳态等待时间的随机分解结果. 最后通过数值计算实例讨论了平均附加队长随温储备失效参数和修复参数的变化情况.

M/G/1 repairable queueing system with warm standby failure

This paper considered the M/G/1 repairable queueing system with warm standby failure in which the "service station may fail in warm standby during idle period". By using the total probability decomposition technique and Laplace transform, we give the recursion expressions of the Laplace transform of the transient queue length distribution at any time t. And the recursion expressions of the steady state queue length distribution are also obtained. Meanwhile, we demonstrate stochastic decomposition structures of the steady state queue length distribution and the steady state waiting time. Finally, numerical examples are given to illustrate the effect of the warm standby failure parameter and repairable parameter on the expected additional queue length.