Offset-based response time analysis techniques obtain tight worst-case response time (WCRT) bounds by accounting release time dependencies between tasks. The maximum response time variation of a task or a message (i.e., the difference between the worst-case and best-case response time) is used to compute the end-to-end delays of distributed systems (Palencia and Harbour, 1998), (Tindell and Clark, 1994). Hence, the WCRT evaluation plays an important role in determining tight end-to-end delays of distributed systems. In real-time theory, there exist two approaches for computing the WCRT of a task: the classical response time analysis (RTA) approach and the modular performance analysis with the Real-Time Calculus (MPA-RTC). MPA-RTC has its roots in Network Calculus (NC). MPA-RTC offers more powerful abstraction than RTA based techniques and allows composition in terms of tasks, event streams, and resource sharing which makes it a strong candidate to analyze distributed systems (Wandeler, 2006), (Perathoner, 2011). However, one of the key limitations of the MPA-RTC is its inability to handle offset dependencies between tasks, whereas the classical RTA techniques can handle them. In this paper, we propose a method to consider offset dependencies between tasks using an MPA-RTC framework for a fixed priority scheduler in a uniprocessor system. Hence, our approach leverages the advantages of the expressive MPA-RTC framework model. We propose novel heuristics and approximation to reduce the inherent complexity of an offset-based RTA. We quantitatively evaluate the effectiveness of our approach to the state-of-the-art classical offset-based RTA techniques.

基于偏移的响应时间分析技术通过考虑任务之间的释放时间依赖性来获得严格的最坏情况响应时间（WCRT）界限。任务或消息的最大响应时间变化（即最坏情况和最佳情况响应时间之间的差）用于计算分布式系统的端到端延迟（Palencia和Harbour，1998年）， （Tindell和Clark，1994年）。因此，WCRT评估在确定分布式系统的端到端紧密延迟方面起着重要作用。在实时理论中，存在两种计算任务的WCRT的方法：经典响应时间分析（RTA）方法和使用实时演算的模块化性能分析（MPA-RTC）。MPA-RTC起源于网络演算（NC）。与基于RTA的技术相比，MPA-RTC提供了更强大的抽象，并允许在任务，事件流和资源共享方面进行组合，这使其成为分析分布式系统的强大候选者（Wandeler，2006年）（Perathoner，2011年）。但是，MPA-RTC的主要限制之一是它无法处理任务之间的偏移量依赖性，而传统的RTA技术可以处理它们。在本文中，我们提出了一种使用MPA-RTC框架为单处理器系统中的固定优先级调度程序考虑任务之间的偏移依赖关系的方法。因此，我们的方法利用了富有表现力的MPA-RTC框架模型的优势。我们提出新颖的启发式方法和近似方法，以减少基于偏移的RTA的固有复杂性。