Performance–energy trade-off in controllable servers with set-up delays

Abstract

We develop queueing models for a single node in a server farm and analytically study the impact of set-up delay on the performance–energy trade-off. The objective is to compare how an optimized static speed scaling scheme performs against two (gated and linear) optimized dynamic speed scaling schemes, where the processor can be switched off when it is idle but the penalty is the set-up delay (time to wake up the processor from the off state and the energy consumed during the set-up delay). In the gated scheme, the processor speed is zero when the server is idle and constant otherwise, and in the linear scheme the processing speed scales linearly with the number of jobs. In our analysis, the set-up delay and the job sizes can have general distributions, except in the linear scheme. Our results demonstrate that the set-up delay has a considerable impact on the optimal trade-off. The linear scheme is always better than the gated scheme and, when the set-up delays are long, even the static scheme can be better. Also, we observe that greater variability in the job size distribution leads to higher gains. In practice, however, the trade-off is affected highly by the parameters.

Keywords:

• Performance–energy trade-off
• speed scaling
• M/G/1
• set-up delay

Notes

No potential conflict of interest was reported by the author(s).

1 Dividing (1(1) ) by gives us a weighted combination of the mean delay and the mean energy per job.

Additional information

Funding

This work was partially supported by the TOP-Energy project [grant number 268992] funded by the Academy of Finland.