Server farms with setup costs

In this paper we consider server farms with a setup cost. This model is common in manufacturing systems and data centers, where there is a cost to turn servers on. Setup costs always take the form of a time delay, and sometimes there is additionally a power penalty, as in the case of data centers. Any server can be either on, off, or in setup mode. While prior work has analyzed single servers with setup costs, no analytical results are known for multi-server systems. In this paper, we derive the first closed-form solutions and approximations for the mean response time and mean power consumption in server farms with setup costs. We also analyze variants of server farms with setup, such as server farm models with staggered boot up of servers, where at most one server can be in setup mode at a time, or server farms with an infinite number of servers. For some variants, we find that the distribution of response time can be decomposed into the sum of response time for a server farm without setup and the setup time. Finally, we apply our analysis to data centers, where both response time and power consumption are key metrics. Here we analyze policy design questions such as whether it pays to turn servers off when they are idle, whether staggered boot up helps, how to optimally mix policies, and other questions related to the optimal data center size.