Abstract—Recent results have shown that the feasibility problem of scheduling periodic tasks with self-suspensions is NPhard in the strong sense. We observe that a variation of the problem statement that includes sporadic tasks instead of periodic tasks results in a simple characterization of the critical scheduling instant. This in turn leads to an exact characterization of the critical instant for self-suspending tasks with respect to the interference (preemption) from higher-priority sporadic tasks. Using this characterization, we provide pseudo-polynomial response-time tests for analyzing the schedulability of such self-suspending tasks. Self-suspending tasks can also result in more worst-case interference to lower-priority tasks than their equivalent non-suspending counterparts with zero suspension intervals. Hence, we develop a dynamic slack enforcement scheme, which guarantees that the worst-case interference caused by suspending sporadic tasks is no more than the worst-case i...