Integrating State-Dependent M/M/c Queue Analysis into Optimization Models for Energy-Aware Multi-Server Data Centers

This paper investigates optimal server and computational operations under state-dependent MIMIc queuing rules for energy-aware data center management. Specifically, our model integrates demand response with server operations, focusing on optimizing static server count and dynamic server availability to enhance both energy and operational efficiency. Our model also considers renewable energy adoption rates, which are crucial for data center sustain ability. We derive steady-state results for state-dependent MIMIc queues tailored to dynamic server operations in data centers. Our optimization model incorporates these steady-state results and accounts for energy-related costs and processing efficiency. Through numerical experiments using both synthetic and real-world data, our analysis demonstrates that integrating demand response with server operations can effectively enhance energy and operational efficiency. We also found that incentives for renewable energy usage in server operations can significantly increase the utilization of renewable energy without markedly affecting data center expenses or processing times. Furthermore, our research reveals the impact of variations in energy and time cost weights on server operations, providing insights into balancing energy efficiency with renewable energy integration in data centers.