Departmental Papers (CIS)

Date of this Version


Document Type

Journal Article


Manuscript Number: TCS-D-10-00731R2


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 PADS for reasoning about resource demand and resource supply inspired by the timed process algebra ACSR. In ACSR, real-time tasks are specified by enunciating their consumption needs for resources. To also accommodate resource-supply processes in PADS, given a resource cpu we write c̅p̅u̅ to denote the availability of cpu for a requesting task process. Using PADS, we define a supply-demand relation where a pair (T , S) 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. Furthermore, we define ordering relations between supplies which describe when a supply offers more resource capacity than another. With this notion it is possible to formally represent hierarchical scheduling approaches that assign more “generous” resource allocations to tasks in exchange for a simple representation. We illustrate our techniques via a number of examples.

Subject Area

CPS Real-Time

Publication Source

Theoretical Computer Science





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Copyright/Permission Statement

NOTICE: This is the author’s version of a work that was accepted for publication in Theoretical Computer Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Theoretical Computer Science, Volume 413, Issue 1, January 2012, DOI: 10.1016/j.tcs.2011.08.025



Date Posted: 09 March 2012

This document has been peer reviewed.