A Compositional Framework for End-to-End Path Delay Calculation of Automotive Systems under Different Path Semantics

While the real-time systems community has developed very valuable approaches to timing and scheduling analysis for processors and buses over the last four decades, another very relevant issue has received only limited attention: end-to-end timing. Most of the known work poses restrictions on specific task activation and communication mechanisms, e.g. unbounded FIFO queues along event-triggered paths. In automotive systems, however, register buffers and periodic sampling are far more common. In this paper, we present a formal framework for the calculation of end-to-end latencies in multi-rate, register-based systems. We show that in systems with sampling, analysis must distinguish between different "meanings" of end-to-end timing. For instance, control engineers are mostly concerned with the "maximum age of data", i.e. the worst-case timing of the latest possible signal. In body electronics, the "first reaction" is key, i.e. worst-case timing of the earliest possible signal. Because the analysis of either case can be different, a clear distinction is mandatory. This paper gives examples and introduces the notion of such end-to-end timing semantics, thereby considering the specific mechanisms and effects typically found in automotive execution platforms such as over- and under-sampling and jitter.