N-控制策略且温储备失效M/G/1可修排队

M/G/1 repairable queue with N-control policy and warm standby failure

把“N-门限值进入控制策略”引入到具有温储备失效和延迟修理的M／G／1可修排队系统，其中在系统处于温储备失效的状态下最多容许N（≥1）个顾客进入系统．利用全概率分解技术和Laplace变换工具，讨论了系统在任意时刻t队长的瞬态和稳态分布，得到了稳态队长分布的递推表达式．同时分别讨论了当N=1与N-00时的特殊情况．最后，建立了系统单位时间总成本费用函数，通过数值计算例子讨论了最优门限值N．

This paper considers an M/G/1 repairable queuing system with warm standby and delayed repair, in which the ＂N-threshold entering-control policy＂ is introduced. In such a policy, at most N（≥ 1） customers are allowed to enter into the system during the warm standby failure period. By the total probability decomposition technique and the Laplace transform, this paper discusses the transient queue length distribution and the steady state queue length distribution at any time t, and obtain the recursion expression of the steady state queue length distribution. Moreover, This paper also considers some special cases when N = I and N -. Finally, the total long run expected average cost per unit time for the system is developed, and the optimal threshold N＊ is determined by numerically examples.