This paper investigates the transient behavior of a $ M/M/1 $ queueing model with N-policy, system disaster, repair, preventive maintenance, balking, re-service, closedown and setup times. The server stays dormant (off state) until N customers accumulate in the queue and then starts an exhaustive service (on state). After the service, each customer may either leave the system or get immediate re-service. When the system becomes empty, the server resumes closedown work and then undergoes preventive maintenance. After that, it comes to the idle state and waits N accumulate for service. When the $ N^{th} $ one enters the queue, the server commences the setup work and then starts the service. Meanwhile, the system suffers disastrous breakdown during busy period. It forced the system to the failure state and all the customers get eliminated. After that, the server gets repaired and moves to the idle state. The customers may either join the queue or balk when the size of the system is less than N. The probabilities of the proposed model are derived by the method of generating function for the transient case. Some system performance indices and numerical simulations are also presented.

中文翻译：

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N策略队列的瞬态分析，包括系统灾难修复，预防性维护，再服务停止和建立时间

本文研究了具有N策略，系统灾难，维修，预防性维护，禁止，重新服务，关闭和建立时间的$ M / M / 1 $排队模型的瞬时行为。服务器保持休眠状态（关闭状态），直到N个客户在队列中累积，然后启动详尽的服务（打开状态）。服务之后，每个客户都可以离开系统或立即获得重新服务。当系统变空时，服务器将恢复关闭工作，然后进行预防性维护。此后，它进入空闲状态并等待N累积服务。当$ N ^ {th} $ one进入队列时，服务器开始设置工作，然后启动服务。同时，系统在繁忙时段遭受灾难性故障。它迫使系统进入故障状态，所有客户都被淘汰。之后，服务器得到修复，并进入空闲状态。当系统的大小小于N时，客户可以加入队列，也可以不参加。通过瞬态情况下生成函数的方法，可以得出所提出模型的概率。还介绍了一些系统性能指标和数值模拟。