Fixed-priority sensitivity analysis for linear compute time models

Several formal results exist that allow an analytic determination of whether a particular scheduling discipline can feasibly schedule a given set of hard real-time periodic tasks. In most cases, these results provide little more than a `yes´ or `no´ answer. In practice, it is also useful to know how sensitive scheduling feasibility is to changes in the characteristics of the task set. This paper presents algorithms that allow a system developer to determine, for fixed-priority preemptive scheduling of hard real-time periodic tasks on a uniprocessor, how sensitive schedule feasibility is to changes in the computation times of various software components. The algorithms allow a system developer to determine what changes in task computation times can be made while preserving schedule feasibility (or what changes are needed to achieve feasibility). Both changes to the computation time of a single task and changes to the computation times of a specified subset of the tasks are analyzable. The algorithms also allow a decomposition of tasks into modules, where a module may be a component of multiple tasks