Decomposition results for an m/m/k with staggered setup
Decomposition results for an m/m/k with staggered setup
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交错设置的 m/m/k 的分解结果
DOI：
10.1145/1870178.1870195
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
I. Adan
中科院分区：
文献类型：
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作者：
Anshul Gandhi;Mor Harchol;I. Adan
本文考虑了一类带安装费用的M/M/k排队系统。当没有工作要做时，服务器会关闭，但打开关闭的服务器会产生设置成本。设置成本采取时间延迟和功率惩罚的形式。安装成本在制造系统、数据中心和磁盘场中很常见，这些地方的闲置服务器被关闭以节省运营成本。由于处于设置模式的服务器消耗大量电力，因此随时可以设置的服务器数量通常是有限的。在交错安装模式中，任何时候最多只能安装一台服务器。虽然最近的文献分析了M/M/k系统交错设置和指数分布的设置时间，没有得到封闭形式的解决方案。我们提供了第一个分析封闭形式的表达式的限制分布的系统状态，响应时间的分布，以及上述系统的平均功耗。特别地，我们证明了以下分解性质：交错设置的M/M/k系统的响应时间在分布上等于没有设置的M/M/k系统的响应时间与设置时间之和。
In this paper, we consider an M/M/k queueing system with setup costs. Servers are turned off when there is no work to do, but turning on an off server incurs a setup cost. The setup cost takes the form of a time delay and a power penalty. Setup costs are common in manufacturing systems, data centers and disk farms, where idle servers are turned off to save on operating costs. Since servers in setup mode consume a lot of power, the number of servers that can be in setup at any time is often limited. In the staggered setup model, at most one server can be in setup at any time. While recent literature has analyzed an M/M/k system with staggered setup and exponentially distributed setup times, no closed-form solutions were obtained. We provide the first analytical closed-form expressions for the limiting distribution of the system states, the distribution of response times, and the mean power consumption for the above system. In particular, we prove the following decomposition property: the response time for an M/M/k system with staggered setup is equal, in distribution, to the sum of response time for an M/M/k system without setup, and the setup time.