HeRTA: Heaviside Real-Time Analysis

TL;DR

This paper introduces a unified mathematical framework for analyzing event bound functions in real-time systems, simplifying models, enabling algebraic proofs, and improving response time analysis in dynamic scheduling.

Contribution

It develops a general form for event bounds, unifies response time and utilization analyses, and enhances the algebraic approach to real-time scheduling theory.

Findings

Unified analysis of event bounds and response time functions.

Simplified models for real-time system analysis.

Improved response time analysis in dynamic scheduling.

Abstract

We investigate the mathematical properties of event bound functions as they are used in the worst-case response time analysis and utilization tests. We figure out the differences and similarities between the two approaches. Based on this analysis, we derive a more general form do describe events and event bounds. This new unified approach gives clear new insights in the investigation of real-time systems, simplifies the models and will support algebraic proofs in future work. In the end, we present a unified analysis which allows the algebraic definition of any scheduler. Introducing such functions to the real-time scheduling theory will lead two a more systematic way to integrate new concepts and applications to the theory. Last but not least, we show how the response time analysis in dynamic scheduling can be improved.