On the Interaction Between Load Balancing and Speed Scaling

Speed scaling has been widely adopted in computer and communication systems, in particular, to reduce energy consumption. An important question is how speed scaling interacts with other resource allocation mechanisms such as scheduling and routing. In this paper, we study the interaction of speed scaling with load balancing. We characterize the equilibrium resulting from the load balancing and speed scaling interaction, and introduce two optimal load-balancing designs, in terms of traditional performance metric and cost-aware (in particular, energy-aware) performance metric, respectively. Especially, we characterize the load-balancing-speed-scaling equilibrium with respect to the optimal load-balancing schemes in processor-sharing systems. Our results show that the degree of inefficiency at the equilibrium is mostly bounded by the heterogeneity of the system, but independent of the number of servers. These results provide insights in understanding the interaction of load balancing with speed scaling and guiding new designs.