On flexible and robust parameter assignment for periodic real-time components

Abstract

In order to increase the flexibility of design process, we consider a component-based system in which some components may be changed, repaired, or upgraded. We assume that the worst-case execution time (WCET) of each task that is implemented by a component is known. Our first goal is to find the smallest set of periods that make the task set schedulable by EDF or by RM. We call these periods safe periods because then any period assignment which is larger than the safe periods will be schedulable. Having safe periods, system designer will be able to use any optimization criteria of his choice to assign periods of the tasks without a need to incorporate the response time analysis techniques, which are usually NP-Hard problems, into his optimization constraints. Instead, the schedulability constraint will be reduced to verifying that the assigned periods are larger than the safe periods. Our solution for safe periods for the RM, is based on finding the smallest set of harmonic periods with utilization 1. Here we use our recently developed polynomial-time approximation algorithm with bounded error of 2 for finding these safe periods for RM. As the second part of our contribution, we consider the robustness property. First we explain how to find safe periods such that a certain level of robustness (based on potential changes of each component) is guaranteed. Doing this, if one of the components changes in the future, other components can still run using their previous periods, and hence, we isolate the effect of future changes from parameters of the other components. Finally, we obtain the robustness factor as a function of the available spare capacity of the system, i.e., the unused utilization. We determine to what extend the WCET of any of the components can be increased without violating the safe periods.