A Partial Supply Simulation Relation and its Proof System in PADS

Abstract

PADS (Process Algebra for Demand and Supply) is a formal framework to analyze hierarchical scheduling in real-time embedded systems. Inspired by the supply simulation relation in PADS, we introduce a partial supply simulation relation in order to describe the fact that an unschedulable task may finish on time. It is more general than the supply simulation relation. Then, we explore some properties of partial supply simulation relation. Furthermore, we establish a proof system for the partial supply simulation relation in a decomposingcomposing way, which helps to infer tasks' partial schedulabilities. Finally, it is proved that the proof system is sound and complete with respect to the semantic definition of partial supply simulation relation.