In sprite the state-of-the-art, significantly reducing carbon footprint (CF) in communications systems remains urgent. We address this challenge in the context of edge computing. The carbon intensity of electricity supply largely varies spatially as well as temporally. This, together with energy sharing via a battery management system (BMS), justifies the potential of CF-oriented task offloading, by redistributing the computational tasks in time and space. In this paper, we consider optimal task scheduling and offloading, as well as battery charging to minimize the total CF. We formulate this CF minimization problem as an integer linear programming model. However, we demonstrate that, via a graph-based reformulation, the problem can be cast as a minimum-cost flow problem. This finding reveals that global optimum can be admitted in polynomial time. Numerical results using real-world data show that optimization can reduce up to 83.3% of the total CF.

翻译：尽管现有技术已取得进展，但显著降低通信系统的碳足迹（CF）仍是一项紧迫任务。我们在边缘计算场景下应对这一挑战。电力供应的碳强度在时空上存在显著差异，结合电池管理系统（BMS）的能量共享机制，通过任务在时间与空间上的再分配，使以碳足迹为导向的任务卸载具有可行性。本文研究最优任务调度、卸载与电池充电策略，以实现总碳足迹最小化。我们将碳足迹最小化问题建模为整数线性规划模型，但通过基于图的重构，该问题可转化为最小费用流问题。这一发现表明，全局最优解可在多项式时间内求得。基于真实数据的数值实验显示，优化可降低高达83.3%的总碳足迹。