arXiv:2508.19760v3 Announce Type: replace Abstract: Phased execution models are a well-known solution to tackle the unpredictability of today's complex COTS multi-core platforms. The semantics of these models dedicate phases for a task's execution and shared memory accesses. Memory phases are solely dedicated to load all necessary instructions and data to private local memory, and to write back the results of the computation. During execution phases, only the private local memory is accessed. While non-preemptive execution phases utilize the local memory well, schedulability is reduced due to blocking. On the other hand, fully preemptive execution phases allow for better schedulability, but require local memory to be large enough to hold all tasks involved in preemption simultaneously. Limited preemption is a promising approach that provides moderation between non-preemptive and fully preemptive scheduling. In this paper, we propose using preemption thresholds to limit the number of preemptions to minimize local memory usage while maintaining schedulability. We propose worst-case response-time and worst-case memory-requirement analyses for sporadic 3-phase tasks under partitioned fixed-priority scheduling with preemption thresholds. We consider two distinct arbitration schemes for memory-phase scheduling between cores: task-priority-based and core-priority-based. We further show how the state-of-the-art algorithm to assign preemption thresholds can be applied to the considered task model. Evaluations demonstrate that preemption thresholds can significantly reduce the memory usage compared to fully preemptive scheduling, while maintaining high schedulability ratios compared to non-preemptive scheduling.