Optimal Task Phasing for End-To-End Latency in Harmonic and Semi-Harmonic Automotive Systems

In the context of automotive systems, the end-toend latency of a sequence of tasks (a so-called cause-effect chain) is a common metric to ensure correct timing behavior. To control the end-to-end latency, proper task configuration is crucial. While the literature considers the configuration of task periods, optimization of task phases to minimize the end-to-end latency is only sparsely discussed. In this work, we examine the configuration of task phases to optimize the end-to-end latency of a cause-effect chain that communicates under the Logical Execution Time (LET) paradigm. To that end, we develop a strategy for cause-effect chains with harmonic or semi-harmonic periods, which are very common in industrial applications. We prove that our strategy is optimal in the sense that it minimizes the end-to-end latency. Furthermore, our evaluation based on a real-world use-case and on synthetic automotive benchmarks shows that optimizing task phases can reduce end-to-end latencies significantly. Our approach takes at most <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$49 \mu ~\mathrm{s}$</tex> to find the optimal phasing and compute the end-toend latency for cause-effect chains with 50 tasks, reducing the end-to-end latency by 28 % in median.