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.
Highlights
If we have a careful review of existing work in real-time scheduling theory, mainly two different approaches to satisfy the real-time capability of an embedded system exist: the bound test or, in more general, the utilization based approach1 and the response time analysis
As we will later see in this paper, the concept of a unified event bound allows the integration of different task models developed during the past decades to only one analysis approach
Because we defined a compact unified event, request- and demand bound by using an integral and we model its limits by a Heaviside function, we can combine the result of the network respective the real-time calculus with the work done in established scheduling theory
Summary
If we have a careful review of existing work in real-time scheduling theory, mainly two different approaches to satisfy the real-time capability of an embedded system exist: the bound test or, in more general, the utilization based approach and the response time analysis. Looking at related work, the two approaches are different in a tiny detail: while the utilization based computations built on the floor operator, the response time analysis uses the ceiling operator. Looking closer to previous work leads to problems in formulating a utilization-based test for static scheduling and a response time analysis for dynamic scheduling. The work of [12] and [43] show the limitations on floor and ceil operators in the context of the real-time scheduling theory Both papers postulate new analysis techniques if an event count with more mathematical expressiveness is known. The idea of this paper is to adapt mathematical models used in physics, signal- and control theory to the problem of real-time scheduling analysis. – we adopt assumptions of the analysis of arbitrary deadlines to the analysis of response times in dynamic scheduled systems and found a deterministic and tighter analysis as in previous work
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