A comprehensive model for energy-efficient and SLA-aware task scheduling in the cloud–edge computing continuum

Federated cloud–edge computing supports latency sensitive applications but complicates sustainable and SLA aware resource management. Existing schedulers usually treat energy, carbon emissions, renewable energy, battery storage, and SLA compliance separately and therefore miss the interactions among them. This paper presents a unified mixed-integer linear programming (MILP) formulation for task scheduling in federated cloud–edge systems. The formulation jointly models tier specific power profiles, renewable generation, battery charging and discharging, task migration, grid carbon emissions, and contention-aware SLA penalties. We evaluate it on workloads derived from Google Cluster Traces v3 and compare exact MILP optimization with the NSGA-II evolutionary algorithm and two greedy baselines. In the main setting, MILP produces 2.7 times fewer SLA violations than NSGA-II while using less energy, and on-site renewable supply reduces grid carbon emissions by 44.6% relative to grid-only operation. A scalability study shows that MILP suits offline planning for moderate instance sizes, whereas NSGA-II offers more predictable runtime for larger online instances.