Reliability and temperature constrained task scheduling for makespan minimization on heterogeneous multi-core platforms

We study the problem of scheduling tasks onto a heterogeneous multi-core processor platform for makespan minimization, where each cluster on the platform has a probability of failure governed by an exponential law and the processor platform has a thermal constraint specified by a peak temperature threshold. The goal of our work is to design algorithms that optimize makespan under the constraints of reliability and temperature. We first provide a mixed-integer linear programming (MILP) formulation for assigning and scheduling independent tasks with reliability and temperature constraints on the heterogeneous platform to minimize the makespan. However, MILP takes exponential time to finish. We then propose a two-stage heuristic that determines the assignment, replication, operating frequency, and execution order of tasks to minimize the makespan while satisfying the real-time, reliability, and temperature constraints based on the analysis of the effects of task assignment on makespan, reliability, and temperature. We finally carry out extensive simulation experiments to validate our proposed MILP formulation and two-stage heuristic. Simulation results demonstrate that the proposed MILP formulation can achieve the best performance in reducing makespan among all the methods used in the comparison. The results also show that the proposed two-stage heuristic has a close performance as the representative existing approach ESTS and a better performance when compared to the representative existing approach RBSA, in terms of reducing makespan. In addition, the proposed two-stage heuristic has the highest feasibility as compared to RBSA and ESTS.