This paper considers an unreliable restorable single-server queueing system with losses in which server failures may occur during operation. The random variables describing the system have general distributions. For increasing the efficiency of this system, it is proposed to carry out preventive maintenance of the server as soon as the accumulated operating time exceeds an upper permissible threshold. A semi-Markov model of the system’s evolution over time is constructed. The explicit-form expressions for the final probabilities and mean sojourn times of the system in different physical states are derived using the stationary distribution of the embedded Markov chain. The frequency of preventive maintenance of the server is optimized via maximizing the average specific profit and minimizing the average specific costs of the system.

本文考虑了一个不可靠的可恢复单服务器排队系统，该系统具有在运行过程中可能发生服务器故障的损失。描述系统的随机变量具有一般分布。为了提高该系统的效率，建议一旦累计运行时间超过允许的上限，就对服务器进行预防性维护。建立了系统随时间演化的半马尔可夫模型。利用嵌入的马尔可夫链的平稳分布，得出了系统在不同物理状态下的最终概率和平均停留时间的显式形式表达式。服务器的预防性维护频率是通过最大化系统的平均特定收益和最小化系统的平均特定成本来优化的。