This paper analyses a server farm with a simple management operation, which is desirable to reduce power consumption. A block of servers is named as ‘reserves’. Depending on the number of jobs staying in the system, power-up and power-down thresholds are employed to control the state of the reserves. In addition, the process of power-up is not immediately. During the period, the servers cannot serve jobs but still consuming power. The server may be subject to be breakdown. This system was modelled by an infinite capacity queueing system and analysed by matrix-geometric technique. The matrix-geometric method is applied to compute the rate matrix and the stationary probabilities. A cost model is formulated to search the optimum number of permanent server and the optimum power-down threshold. The optimization tasks are carried out by the direct search method. Both analytic processes and numerical results provide very useful and helpful information for decision-makers.

本文分析了具有简单管理操作的服务器场，这对于降低功耗非常有用。服务器块称为“储备”。根据系统中剩余的作业数量，可以使用加电和断电阈值来控制备用状态。此外，加电过程不会立即进行。在此期间，服务器无法执行任务，但仍在消耗功率。服务器可能会发生故障。该系统由无限容量排队系统建模，并通过矩阵几何技术进行分析。应用矩阵几何方法来计算速率矩阵和平稳概率。制定成本模型以搜索最佳的永久服务器数量和最佳的关机阈值。优化任务通过直接搜索方法执行。分析过程和数值结果都为决策者提供了非常有用和有用的信息。