Necessary and Sufficient Conditions for Non-preemptive Robustness

A real-time scheduler is robust (sustainable) for a certain task set if its schedulability is preserved under lighter system load by the scheduler. The first part of this paper shows that NPr (non-preemptive) robustness of a zero-concrete periodic task set against increase in period is sufficient to guarantee NPr robustness for all variants of the task set. This proof includes the corresponding concrete or non-concrete periodic and sporadic task sets against any kind of reduction in system load. Based on this result, the second part of this paper gives the necessary and sufficient conditions for robustness for both NPr fixed-priority (NPFP) and NPr earliest-deadline first (NPEDF) schedulers under both discrete time and dense time assumption separately.