MILP formulations for spatio-temporal thermal-aware scheduling in Cloud and HPC datacenters

Abstract

This paper focuses on scheduling problems related to the execution of computational jobs in datacenters with thermal constraints. Mixed integer linear programming (MILP) formulations are proposed that encompass both spatial and temporal aspects of the temperature evolution under a unified model. This model takes into account the dynamics of heat production and dissipation in order to schedule jobs at appropriate times on appropriate machines. The proposed MILP formulations are applicable to both high-performance computing (HPC) and Cloud settings, and can target several objectives including energy and makespan minimization, while incorporating the cooling costs and dynamic voltage and frequency scaling capabilities of servers. The applicability and usefulness of our formulations are demonstrated via several HPC and Cloud case-studies.