Energy-performance tradeoffs in server farms with batch services and setup times

Data centers consume a large amount of energy, much of which is wasted due to idle servers. Turning off idle servers might be an effective power-saving solution; however, there is a trade-off between energy savings and system performance. Hence, we propose a setup queueing model with a batching policy that allows servers to process a set of jobs simultaneously to minimize power consumption while maintaining acceptable performance. We consider an M/M/$c/$SET–BATCH queue, a multi-server batch service queue with a fixed batch size and setup times, and some variants, including systems in which idle servers delay before turning off or systems in which the batch size is dynamic. We analyze the steady-state probabilities and system performance of the M/M/$c/$SET–BATCH system and its variants. Our analysis of the M/M/$c/$SET–BATCH system with lower computational complexity is made possible by utilizing the special structure of the model. In addition, we use simulations to compare the M/M/$c/$SET–BATCH model with some other variants with different setup time distributions. The results suggest that the model performs better when the setup time has a larger coefficient of variation. Our results indicate that the batching policy enhances the system performance, especially when we allow servers to be idle before turning them off.