Sensitivity Analysis for Fixed-Priority Real-Time Systems

At early stages in the design of real-time embedded applications, the timing attributes of the computational activities are often incompletely specified or subject to changes. Later in the development cycle, schedulability analysis can be used to check the feasibility of the task set. However, the knowledge of the worst-case response times of tasks is often not sufficient to precisely determine the actions that would correct a non-schedulable design. In these situations, sensitivity analysis provides useful information for changing the implementation, by giving a measure of those computation times that must be reduced to achieve feasibility, or those that can be increased in case of a product extension, or providing the range of feasible periods for selecting the proper task activation rates. In this work, we exploit the concept of feasibility region to propose a faster and more concise solution to the sensitivity analysis problem with respect to existing techniques based on binary search. Furthermore, we show how the formalization of other problems in the feasibility domain, such as managing overloads through elastic scheduling, can be extended to the exact analysis.