In a precedent work we saw that finding efficient scheduling algorithms for fixed-priority energy-harvesting systems is one of the challenges of this research area. We presented PFPasap which is an optimal scheduling algorithm. Moreover, the optimality of this algorithm relies on two main assumptions: the considered task sets are energy-non-concrete, and all the tasks consume more energy than it is replenished. Unfortunately, removing one of these two assumptions leads PFPasap to lose its optimality. This is due to the fact that without these assumptions, the worst-case scenario of PFPasap is no longer the synchronous activation with the minimum battery capacity. Moreover, without these assumptions, the worst-case scenario is unknown up to now. There exist some counter examples that prove the non-optimality of PFPasap.The challenge now is to understand why does PFPasap lose its optimality and we try to study deeply the fixed-priority scheduling for energy-harvesting systems by trying to build an optimal algorithm or otherwise to prove the nonexistence of such an algorithm.In this work, we explore different intuitive ideas of scheduling algorithms and we explain why they are not optimal through counter examples. Then, we show the difficulty of finding an optimal algorithm or proving the nonexistence of such an algorithm with a reasonable complexity.
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