A central issue for verifying the schedulability of hard real-time systems is the correct evaluation of task execution times. These values are significantly influenced by the preemption overhead, which mainly includes the cache related delays and the context switch times introduced by each preemption. Since such an overhead significantly depends on the particular point in the code where preemption takes place, this paper proposes a method for placing suitable preemption points in each task in order to maximize the chances of finding a schedulable solution. In a previous work, we presented a method for the optimal selection of preemption points under the restrictive assumption of a fixed preemption cost, identical for each preemption point. In this paper, we remove such an assumption, exploring a more realistic and complex scenario where the preemption cost varies throughout the task code. Instead of modeling the problem with an integer programming formulation, with exponential worst-case complexity, we derive an optimal algorithm that has a linear time and space complexity. This somewhat surprising result allows selecting the best preemption points even in complex scenarios with a large number of potential preemption locations. Experimental results are also presented to show the effectiveness of the proposed approach in increasing the system schedulability.
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