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We propose three novel mathematical optimization formulations that solve thesame two-type heterogeneous multiprocessor scheduling problem for a real-timetaskset with hard constraints. Our formulations are based on a globalscheduling scheme and a fluid model. The first formulation is a mixed-integernonlinear program, since the scheduling problem is intuitively considered as anassignment problem. However, by changing the scheduling problem to firstdetermine a task workload partition and then to find the execution order of alltasks, the computation time can be significantly reduced. Specifically, theworkload partitioning problem can be formulated as a continuous nonlinearprogram for a system with continuous operating frequency, and as a continuouslinear program for a practical system with a discrete speed level set. The taskordering problem can be solved by an algorithm with a complexity that is linearin the total number of tasks. The work is evaluated against existing globalenergy/feasibility optimal workload allocation formulations. The resultsillustrate that our algorithms are both feasibility optimal and energy optimalfor both implicit and constrained deadline tasksets. Specifically, ouralgorithm can achieve up to 40% energy saving for some simulated tasksets withconstrained deadlines. The benefit of our formulation compared with existingwork is that our algorithms can solve a more general class of schedulingproblems due to incorporating a scheduling dynamic model in the formulationsand allowing for a time-varying speed profile. Moreover, our algorithms can beapplied to both online and offline scheduling schemes.

Energy-Efficient Real-Time Scheduling for Two-Type Heterogeneous Multiprocessors