Bounding the effectiveness of temporal redundancy in fault-tolerant real-time scheduling under error bursts

Reliability is a key requirement in many distributed real-time systems deployed in safety and mission critical applications, and temporal redundancy is a widely employed strategy towards guaranteeing it. The temporal redundancy approach is typically based on task re-executions in form of entire tasks, task alternates or, check-pointing blocks, and each of the re-execution strategies have different impacts on the Fault Tolerance feasibility (FT-feasibility) of the system, which is traditionally defined as the existence of a schedule that guarantees timeliness of all tasks under a specified fault hypothesis. In this paper, we propose the use of resource augmentation to quantify the FT-feasibility of real-time task sets and use it to derive limits on the effectiveness of temporal redundancy in fault-tolerant real-time scheduling under error bursts of bounded lengths. We derive the limits for the general case, and then show that for the specific case when the error burst length is no longer than half the shortest deadline, the lower limit on the effectiveness of temporal redundancy is given by the resource augmentation bound 2, while, the corresponding upper-limit is 6. Our proposed approach empowers a system designer to quantify the effectiveness of a particular implementation of temporal redundancy.