Improved approximate response time bounds for static-priority tasks

We consider sporadic tasks with static priorities and constrained deadlines to be executed upon a uniprocessor platform. Pseudo-polynomial time algorithms are known for computing worst-case response times for this task model. Some applications require to evaluate efficiently upper bounds of response times. For this purpose, we propose parametric algorithms that allow to make a tradeoff between quality of results and computational effort according to an input accuracy parameter. In this paper, we present a parametric polynomial-time algorithm for computing upper bounds of worst-case response times, that is based on an improved FPTAS (Fully Polynomial Time Approximation Scheme). Then, we show that our bound does not achieve constant error bound in comparison with the exact worstcase response time. However, using the resource augmentation technique, we obtain a performance guarantee that allows to define a compromise between our response-time bound and processor capacity requirements. The algorithm average behavior is then analyzed through numerical experimentations.