Analysis of a M/M/k system with exponential setup times and reserves servers

A critical issue in modern server farm system architecture is to know how to efficiently allocate the number of servers to manage unpredictable demand patterns, in order to get the best performance without wasting energy. Although it is demanded to shut down servers when they become inactive to save energy, the high configuration cost (in terms of setup time and energy consumption) required to restart the server can affect performance. The problem is even more complicated since today's servers offer several states of sleep or standby that allow the setup cost to be balanced by the power consumed while the server is "in sleep". In this paper, we will consider the M/M/k queuing system with setup costs: M/M/k/Setup. Servers are obviously shut down when there is no work to be done, but turning on a server that has been shut down will incur setup costs. The setup cost takes the shape of a delay and a power penalty, event that idle servers are shut down to save on running expenses. Since servers in setup mode consume a lot of energy, the number of servers that can be in setup at any given time is often limited. In the configuration model, a maximum of one server can be setup at any time. The proposed mechanism and its performance parameters are described by a a mathematical model. In addition, the effect of the proposed mechanism on energy consumption behaviour is assessed. The discussion on the results shows the role of the consideration of reserves in the system.