Carbon-aware optimization for Internet Data Centers with renewable generation: Robust workload allocation and carbon procurement via multi-class mean field game

With the increasing integration of renewable energy into regional power grids, significant spatial differences in carbon intensity have emerged. These differences highlight the need for carbon-aware workload allocation in geographically distributed Internet Data Centers, where aligning computational loads with low-carbon regions can enhance both environmental and economic outcomes. In this paper, we propose a two-stage optimization framework that integrates renewable-aware workload allocation and strategic carbon allowance procurement. In the first stage, a robust optimization model based on column-and-constraint generation is developed to manage uncertainties in workload demand and carbon prices, enabling stable and cost-effective workload distribution across regions with varying renewable energy penetration. In the second stage, a multi-class mean field game model is constructed to capture strategic interactions and behavioral heterogeneity among Internet Data Centers in carbon markets. We apply a Deep Galerkin Method to solve the resulting high-dimensional partial differential equations, yielding a robust and convergent procurement strategy. Simulation results demonstrate that the proposed framework achieves over 28% cost savings while ensuring carbon compliance and workload satisfaction. This study offers theoretical and practical insights for carbon-regulated Internet Data Center operations, and supports the broader integration of renewable energy in large-scale digital infrastructure.