Period sensitivity analysis and D-P domain feasibility region in dynamic priority systems

In the design of a real-time application it is fundamental to know how a change in the task parameters would affect the feasibility of the system. Relaxing the classical assumptions on static task sets with fixed periods and deadlines can give higher resource utilisation and better performance. But the changes on task parameters have to be done always maintaining feasibility. In practice, period and deadline modifications are only necessary on single tasks. Our work focuses on finding the feasibility region of deadlines and periods (called D-P feasibility region) for a single task in the context of dynamic, uniprocessor scheduling of hard real-time systems. This way, designers can choose the optimal deadline and period pairs that best fit application requirements. We provide an exact and an approximated algorithm to calculate this region. We will show that the approximated solution is very close to the exact one and it takes considerably less time.