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The N-policy for an unreliable server with delaying repair and two phases of service

机译：延迟维修和两个服务阶段的不可靠服务器的N策略

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摘要

This paper deals with an M-X/G/1 with an additional second phase of optional service and unreliable server, which consist of a breakdown period and a delay period under N-policy. While the server is working with any phase of service, it may break down at any instant and the service channel will fail for a short interval of time. Further concept of the delay time is also introduced. If no customer arrives during the breakdown period, the server becomes idle in the system until the queue size builds up to a threshold value N (>= 1). As soon as the queue size becomes at least N, the server immediately begins to serve the first phase of regular service to all the waiting customers. After the completion of which, only some of them receive the second phase of the optional service. We derive the queue size distribution at a random epoch and departure epoch as well as various system performance measures. Finally we derive a simple procedure to obtain optimal stationary policy under a suitable linear cost structure.
机译：本文讨论的是M-X / G / 1，它具有可选服务和不可靠服务器的附加第二阶段，其中包括故障时间和N策略下的延迟时间。当服务器使用任何阶段的服务时，它可能随时崩溃，并且服务通道将在短时间内失败。还介绍了延迟时间的其他概念。如果在故障期间没有客户到达，则服务器将在系统中处于空闲状态，直到队列大小达到阈值N（> = 1）为止。一旦队列大小至少达到N，服务器将立即开始为所有等待的客户提供常规服务的第一阶段。完成后，只有其中一些获得了可选服务的第二阶段。我们得出随机时间和离开时间以及各种系统性能指标的队列大小分布。最后，我们推导了一个简单的过程，可以在合适的线性成本结构下获得最优固定策略。

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