Efficient response-time analysis for tasks with offsets

We present a method that enables an efficient implementation of the approximative response-time analysis (RTA) for tasks with offsets presented by Tindell [(1992)] and Palencia Gutierrez et al. [(1998)]. The method allows for significantly faster implementations of schedulability tools using RTA. Furthermore, reducing computation time, from tens of milliseconds to just a fraction of a millisecond, as we show, is a step towards online RTA in for example admission control systems. We formally prove that our reformulation of earlier presented equations is correct and allow us to statically represent parts of the equation, reducing the calculations during fix-point iteration. We show by simulations that the speedup when using our method is substantial. When task sets grow beyond a trivial number of tasks and/or transactions a speed-up of more than 100 times (10 transactions and 10 tasks/transaction) compared to the original analysis can be obtained.