Energy optimization for periodic applications running on safety/time-critical time-triggered multiprocessor systems has been studied recently. An interesting feature of the applications on the systems is that some tasks are strictly periodic while others are non-strictly periodic, i.e., the start time interval between any two successive instances of the same task is not fixed as long as task deadlines can be met. Energy-efficient scheduling of such applications on the systems has, however, been rarely investigated. In this paper, we focus on the problem of static scheduling multiple periodic applications consisting of both strictly and non-strictly periodic tasks on safety/time-critical time-triggered multiprocessor systems for energy minimization. The challenge of the problem is that both strictly and non-strictly periodic tasks must be intelligently addressed in scheduling to optimize energy consumption. We introduce a new practical task model to characterize the unique feature of specific tasks, and formulate the energy-efficient scheduling problem based on the model. Then, an improved Mixed Integer Linear Programming (MILP) method is proposed to obtain the optimal scheduling solution by considering strict and non-strict periodicity of the specific tasks. To decrease the high complexity of MILP, we also develop a heuristic algorithm to efficiently find a high-quality solution in reasonable time. Extensive evaluation results demonstrate the proposed MILP and heuristic methods can on average achieve about 14.21% and 13.76% energy-savings respectively compared with existing work.
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