Efficient exact Boolean schedulability tests for fixed priority preemption threshold scheduling

We propose (1) a new sufficient test, (2) new initial values for the start/finish times, (3) pre-calculation of the interference time within the start time, (4) incremental start/finish time calculation, and (5) early exits in start/finish time calculations. These are based on some previous work for FPS. The new initial start time, pre-calculation, and the incremental calculations also can be used for the exact response time analysis for PTS. Our empirical results show that the overall proposed methods reduce the iteration count/run time of the conventional test by about 60%/40%, regardless of the number of tasks and the total utilization.