Decomposition results for an m/m/k with staggered setup

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 propert...

• Type: Journal
• Year: 2010
• Where: SIGMETRICS
• Authors: Anshul Gandhi, Mor Harchol-Balter, Ivo Adan
• Keywords: Hardware, Response Time, Setup Costs, SIGMETRICS 2010, Staggered Setup