Energy-Efficient Real-Time Scheduling for Two-Type Heterogeneous   Multiprocessors
  We propose three novel mathematical optimization formulations that solve the same two-type heterogeneous multiprocessor scheduling problem for a real-time taskset with hard constraints. Our formulations are based on a global scheduling scheme and a fluid model. The first formulation is a mixed-integer nonlinear program, since the scheduling problem is intuitively considered as an assignment problem. However, by changing the scheduling problem to first determine a task workload partition and then to find the execution order of all tasks, the computation time can be significantly reduced. Specifically, the workload partitioning problem can be formulated as a continuous nonlinear program for a system with continuous operating frequency, and as a continuous linear program for a practical system with a discrete speed level set. The task ordering problem can be solved by an algorithm with a complexity that is linear in the total number of tasks. The work is evaluated against existing global energy/feasibility optimal workload allocation formulations. The results illustrate that our algorithms are both feasibility optimal and energy optimal for both implicit and constrained deadline tasksets. Specifically, our algorithm can achieve up to 40% energy saving for some simulated tasksets with constrained deadlines. The benefit of our formulation compared with existing work is that our algorithms can solve a more general class of scheduling problems due to incorporating a scheduling dynamic model in the formulations and allowing for a time-varying speed profile. Moreover, our algorithms can be applied to both online and offline scheduling schemes. 
Mason Thammawichai and Eric C. Kerrigan
cs.DC cs.OS cs.SY math.OC