A Note on the Exact Schedulability Analysis for Segmented Self-Suspending Systems

This report considers a sporadic real-time task system with n sporadic tasks on a uniprocessor platform, in which the lowest-priority task is a segmented self-suspension task and the other higher-priority tasks are ordinary sporadic realtime tasks. Under fixed-priority preemptive scheduling, Nelissen et al. in ECRTS 2015 provided a mixed-integer linear programming (MILP) formulation to test whether the lowest-priority self-suspending task can meet its deadline or not, with only a sketched proof. This report provides a comprehensive support and proof to explain several hidden properties that were not proved in their paper.