ABSTRACT This paper presents a steady-state analysis of an M/M/1 retrial queue with working vacations, in which the server is subject to starting failures. The proposed queueing model is described in terms of the quasi-birth-death (QBD) process. We first derive the system stability condition. We then use the matrix-geometric method to compute the stationary probability distribution of the orbit size. Some performance measures for the system are developed. We construct a cost model, and our objective is to determine the optimal service rates during normal and vacation periods that minimize the expected cost per unit time. The canonical particle swarm optimization (CPSO) algorithm is employed to deal with the cost optimization problem. Numerical results are provided to illustrate the effects of system parameters on the performance measures and the optimal service rates. These results depict the system behaviour and show how the CPSO algorithm can be used to find numerical solutions for optimal service rates.

中文翻译：

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带工作假期和启动失败的重试队列性能分析与优化

摘要 本文提出了一个有工作假期的 M/M/1 重试队列的稳态分析，其中服务器容易启动失败。提出的排队模型是根据准生死 (QBD) 过程来描述的。我们首先推导出系统稳定条件。然后我们使用矩阵几何方法来计算轨道大小的平稳概率分布。为系统开发了一些性能度量。我们构建了一个成本模型，我们的目标是确定在正常和假期期间使单位时间的预期成本最小化的最优服务费率。典型粒子群优化（CPSO）算法用于处理成本优化问题。提供了数值结果来说明系统参数对性能测量和最佳服务率的影响。这些结果描述了系统行为并展示了如何使用 CPSO 算法找到最优服务率的数值解。