Distributionally Robust Games for Data Center Demand Response Coordination based on CPU utilization and Quality of Service

Abstract

In light of the soaring energy demand of data centers (DC), cloud providers seek effective solutions to reduce power consumption and ease grid stress. Dynamic voltage and frequency scaling (DVFS) could reduce CPU power consumption and provide demand responses. However, its real-time performance depends on uncertain and volatile CPU utilization rates, which highly undermine demand response service quality. This paper first presents a scalable distributionally robust game framework for the aggregator to coordinate DC for the DVFS demand responses. Each DC’s strategy is formulated as a two-stage Wasserstein-metrics distributionally robust optimization (DRO) formulation. To enhance the game scalability, we compare two game formulations, a complementarity model and an equivalent optimization model based on variational inequalities (VI). Using millions of CPU readings from Microsoft virtual machines, games are performed with varying numbers of players. When the game solutions exist, both models achieve the required demand reduction with quality of service (QoS) considerations for each DC. The equivalent optimization model could significantly reduce computation times and allow a 100-player game to be solved on a laptop in one minute.

In light of the soaring energy demand of data centers (DC), cloud providers seek effective solutions to reduce power consumption and ease grid stress. Dynamic voltage and frequency scaling (DVFS) could reduce CPU power consumption and provide demand responses. However, its real-time performance depends on uncertain and volatile CPU utilization rates, which highly undermine demand response service quality. This paper first presents a scalable distributionally robust game framework for the aggregator to coordinate DC for the DVFS demand responses. Each DC’s strategy is formulated as a two-stage Wasserstein-metrics distributionally robust optimization (DRO) formulation. To enhance the game scalability, we compare two game formulations, a complementarity model and an equivalent optimization model based on variational inequalities (VI). Using millions of CPU readings from Microsoft virtual machines, games are performed with varying numbers of players. When the game solutions exist, both models achieve the required demand reduction with quality of service (QoS) considerations for each DC. The equivalent optimization model could significantly reduce computation times and allow a 100-player game to be solved on a laptop in one minute.