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.

中文翻译：

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HeRTA：Heaviside 实时分析

我们研究了事件绑定函数的数学特性，因为它们用于最坏情况的响应时间分析和利用率测试。我们找出两种方法之间的差异和相似之处。基于此分析，我们推导出更一般的形式来描述事件和事件边界。这种新的统一方法为实时系统的研究提供了清晰的新见解，简化了模型，并将支持未来工作中的代数证明。最后，我们提出了一个统一的分析，它允许对任何调度程序进行代数定义。将此类功能引入实时调度理论将引导两种更系统的方式将新概念和应用程序集成到该理论中。最后但同样重要的是，我们展示了如何改进动态调度中的响应时间分析。