Parametric Polynomial-Time Algorithms for Computing Response-Time Bounds for Static-Priority Tasks with Release Jitters

Abstract

Feasibility analysis algorithms are based on particular metrics such as processor utilization, load factor, processor demand, response-times, etc. The design of efficient algorithms for computing these metrics is a major issue in real-time scheduling theory. In this paper we propose two FPTASs (fully-polynomial time approximation schemes) for checking feasibility of static-priority tasks subjected to release jitters executed upon a uniprocessor platform. We then use these FPTASs for computing two upper bounds of worst-case response-times. Lastly, we show that these bounds do not achieve constant error bounds in comparison with values computed by an exact worst-case responsetime analysis (performed in pseudo-polynomial time), and we present numerical experiments.

Approximation techniques for response-time analysis of static-priority tasks

“…In other words, they perform a compromise between computational effort to decide the feasibility of task systems and the quality of taken decisions. Such approaches have been developed for EDF scheduling (Chakraborty et al 2002;Slomka 2004, 2005;Masrur et al 2008) and for static-priority scheduling (Fisher and Baruah 2005a;Richard and Goossens 2006;Fisher et al 2007;Richard et al 2007) which allow to verify the feasibility and to derive the response-time bound of a task at the same time:…”

“…Section 3 presents an improvement of the approximate test presented in Fisher et al (2007) and two new methods for computing upper bounds of task worst-case response times. Section 4 presents results on worstcase error bounds of these approximate values of worst-case response times.…”

“…Using the framework of the approximate feasibility analysis presented by Fisher and Baruah (2005b), we have shown how to compute approximate (upper bounds) worst-case response times by proposing the first deduction method in Richard and Goossens (2006), Fisher et al (2007). In the next section we will present a new approximation scheme that improves best known results (e.g., Fisher and Baruah 2005b;Fisher et al 2007) for feasibility analysis and extends the approximation scheme to incorporate the factors of release jitters.…”

“…In the next section we will present a new approximation scheme that improves best known results (e.g., Fisher and Baruah 2005b;Fisher et al 2007) for feasibility analysis and extends the approximation scheme to incorporate the factors of release jitters. Then, we present two new methods for computing wrct upper bounds that improve the results presented in Richard and Goossens (2006), Richard et al (2007), Fisher et al (2007). …”

“…In Fisher et al (2007), under the assumption that all the task parameters are integers, the following approximate request bound function was defined:…”