A Process Algebraic Framework for Modeling Resource Demand and Supply

As real-time embedded systems become more complex, resource partitioning is increasingly used to guarantee real-time performance. Recently, several compositional frameworks of resource partitioning have been proposed using real-time scheduling theory with various notions of real-time tasks running under restricted resource supply environments. However, these real-time scheduling-based approaches are limited in their expressiveness in that, although capable of describing resource-demand tasks, they are unable to model resource supply. This paper describes a process algebraic framework for reasoning about resource demand and supply inspired by the timed process algebra ACSR. In ACSR, realtime tasks are specified by enunciating their consumption needs for resources. To also accommodate resource-supply processes we define PADS where, given a resource CPU, the complimented resource CPU denotes for availability of CPU for the corresponding demand process. Using PADS, we define a supply-demand relation where a pair (S,T) belongs to the relation if the demand process T can be scheduled under supply S. We develop a theory of compositional schedulability analysis as well as a technique for synthesizing an optimal supply process for a set of tasks. We illustrate our technique via a number of examples.