The Degree of Masking Fault Tolerance vs. Temporal Redundancy

Self-stabilizing systems, intended to run for a long time, commonly have to cope with transient faults during their mission. We model the behavior of a distributed self-stabilizing system under such a fault model as a Markov chain. Adding fault detection to a self-correcting non-masking fault tolerant system is required to progress from non-masking systems towards their masking fault tolerant functional equivalents. We introduce a novel measure, called limiting window availability (LWA) and apply it on self-stabilizing systems in order to quantify the probability of (masked) stabilization against the time that is needed for stabilization. We show how to calculate LWA based on Markov chains: first, by a straightforward Markov chain modeling and second, by using a suitable abstraction resulting in a space-reduced Markov chain. The proposed abstraction can in particular be applied to spot fault tolerance bottlenecks in the system design.