A Formal Framework for Precise Parametric WCET Formulas

Parametric worst-case execution time (WCET) formulas are a valuable tool to estimate the impact of input data properties on the WCET at design time, or to guide scheduling decisions at runtime. Previous approaches to parametric WCET analysis either provide only informal ad-hoc solutions or tend to be rather pessimistic, as they do not take flow constraints other than simple loop bounds into account. We develop a formal framework around path- and frequency expressions, which allow us to reason about execution frequencies of program parts. Starting from a reducible control flow graph and a set of (parametric) constraints, we show how to obtain frequency expressions and refine them by means of sound approximations, which account for more sophisticated flow constraints. Finally, we obtain closed-form parametric WCET formulas by means of partial evaluation. We developed a prototype, implementing our solution to parametric WCET analysis, and compared existing approaches within our setting. As our framework supports fine-grained transformations to improve the precision of parametric formulas, it allows to focus on important flow relations in order to avoid intractably large formulas

Computing Maximum Blocking Times with Explicit Path Analysis under Non-local Flow Bounds *

ABSTRACT Worst-case time (WCET) analyses for single tasks are well established and their results ultimately serve the purpose of providing execution time parameters for schedulability analyses. Besides WCET analysis, an important problem is maximum blocking time (MBT) analysis which is essential in deferred preemption schedules for the selection of preemption points. Among the most pressing problems in this context is the need for good path analyses, which are a fundamental bottleneck for selecting these points. Current state of the art relies on ILP-based or severely constrained explicit path analyses, both of which are unsatisfactory in general. In this paper, we propose a general explicit path analysis to compute maximum blocking times, specifically for scheduling policies with deferred preemption. The proposal improves the current state of the art significantly for both WCET and MBT analysis, as it is efficient, accurate, easily extensible and computes path lengths between all program points, without imposing any artificial constraints, and under a general flow bound model, unmatched by other existing explicit path analyses, while significantly outperforming the ILP-based approach. To the best of the authors' knowledge, no explicit path analysis for MBT has been proposed yet