Embedded systems with real-time constraints depend on a priori knowledge of worst-case execution times (WCETs) to determine if tasks meet deadlines. Static timing analysis derives bounds on WCETs but requires statically known loop bounds. This work removes the constraint on known loop bounds through parametric analysis expressing WCETs as functions. Tighter WCETs are dynamically discovered to exploit slack by dynamic voltage scaling (DVS) saving 60% to 82% energy over DVS-oblivious techniques and showing savings close to more costly dynamic-priority DVS algorithms. Overall, parametric analysis expands the class of real-time applications to programs with loop-invariant dynamic loop bounds while retaining tight WCET bounds.

Static timing analysis safely bounds worst-case execution times to determine if tasks can meet their deadlines in hard real-time systems. However, conventional timing analysis requires that the upper bound of loops be known statically, which limits its applicability. Parametric timing analysis methods remove this constraint by providing the WCET as a formula parameterized on loop bounds. This paper contributes a novel technique to allow parametric timing analysis to interact with dynamic real-time schedulers. By dynamically detecting actual loop bounds, a lower WCET bound can be calculated, on-the-fly, for the remaining execution of a task. We analyze the benefits from parametric analysis in terms of dynamically discovered slack in a schedule. We then assess the potential for dynamic power conservation by exploiting parametric loop bounds for ParaScale, our intra-task dynamic voltage scaling (DVS) approach. Our results demonstrate that the parametric approach to timing analysis provides 66%-80% additional savings in power consumption. We further show that using this approach combined with online intra-task DVS to exploit parametric execution times results in much lower power consumption. Hence, even in the absence of dynamic scheduling, significant savings in power can be obtained, e.g., in the case of cyclic executives.