This article deals with single server queue with modified vacation policy. The modified vacation policy captures the operation of a close down period, type 1 vacation period, type 2 vacation period, a start-up period and a dormant period. Here, type 1 vacations takes a short period of random duration and type 2 vacation take a long period of random duration. Explicit expressions have been obtained for steady state queue size distribution at service completion point and steady state system size probabilities. The Laplace-Stieltjes transform of waiting time and its corresponding mean value have been obtained for the system. Finally, some numerical examples have been provided and use the parabolic method to search the optimum value of the control parameter p.

中文翻译：

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修改后休假策略的单服务器队列分析

本文处理具有修改后的休假策略的单服务器队列。修改后的休假策略捕获关闭时间段，类型1休假时间段，类型2休假时间段，启动时间段和休眠时间段的操作。在这里，类型1的休假需要很短的随机持续时间，类型2的休假需要很长的随机持续时间。对于服务完成点处的稳态队列大小分布和稳态系统大小概率，已经获得了明确的表达式。已经为系统获得了等待时间的Laplace-Stieltjes变换及其相应的平均值。最后，提供了一些数值示例，并使用抛物线法搜索控制参数p的最佳值。