FAST: Frequency-Aware Static Timing Analysis

Abstract

Energy is a valuable resource in embedded systems as the lifetime of many such systems is constrained by their battery capacity. Recent advances in processor design have added support for dynamic frequency/voltage scaling (DVS) for saving energy. Recent work on real-time scheduling focuses on saving energy in static as well as dynamic scheduling environments by exploiting idle time and slack because of early task completion for DVS of subsequent tasks. These scheduling algorithms rely on <i>a priori</i> knowledge of worst-case execution times (WCET) for each task. They assume that DVS has no effect on the worst-case execution cycles (WCEC) of a task and scale the WCET according to the processor frequency. However, for systems with memory hierarchies, the WCEC typically <i>does</i> change under DVS because of requency modulation. Hence, current assumptions used by DVS schemes result in a highly exaggerated WCET. This paper contributes novel techniques for tight and flexible static timing analysis, particularly well-suited for dynamic scheduling schemes. The technical contributions are as follows: (1) We assess the problem of changing execution cycles owing to scaling techniques. (2) We propose a parametric approach toward bounding the WCET statically with respect to the frequency. Using a parametric model, we can capture the effect of changes in frequency on the WCEC and, thus, accurately model the WCET over any frequency range. (3) We discuss design and implementation of the frequency-aware static timing analysis (FAST) tool based on our prior experience with static timing analysis. (4) We demonstrate in experiments that our FAST tool provides safe upper bounds on the WCET, which are tight. The FAST tool allows us to capture the WCET of six benchmarks using equations that overestimate the WCET by less than 1%. FAST equations can also be used to improve existing DVS scheduling schemes to ensure that the effect of frequency scaling on WCET is considered and that the WCET used is <i>not</i> exaggerated. (5) We leverage three DVS scheduling schemes by incorporating FAST into them and by showing that the energy consumption further decreases. (6) We compare experimental results using two different energy models to demonstrate or verify the validity of simulation methods. To the best of our knowledge, this study of DVS effects on timing analysis is unprecedented.

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