On Sustainability for Offset Based Response-Time Analysis

It is known that offsets in general are not sustainable, i.e., if offsets in a system are modified it is not trivial to determine if this affects schedulability or not. In this paper we investigate if there are situations where offsets can be deemed sustainable, i.e., situations where one can safely modify an offset without impairing schedulability. We introduce, for the approximate Response-Time Analysis, a concept of a subsumes relation between demand bound functions and show that if offsets are modified in such a way that the modified demand bound function is subsumed by the original demand bound function, then the modification is sustainable. We show an example of how this information can be used in an engineering context where all system parameters are fixed but offsets. We generate all transaction that are subsumed by a schedulable transaction and merge this information in a presentable form for the engineer. This information can be used to safely modify the transaction or to investigate the robustness of the schedulability.