Reliability and availability analysis of self-stabilizing systems

Self-stabilizing systems are often only evaluated in terms of worst-case time and space complexities for the recovery from arbitrary state disruptions. In this paper, we interpret and formalize well-known fault tolerance measures for masking fault-tolerant systems, namely reliabilty, instantaneous availability, and limiting availability in the context of self-stabilizing systems. This allows to additionally evaluate self-stabilizing systems by these well-accepted measures. The calculation is challenging due to a large (and possibly infinite) state space. We present an analysis procedure that comprises a suitable state abstraction thereby making the calculation tractable. Exemplarily, we apply the procedure to a system that constructs a depth-first search spanning tree showing that our approach is feasible and yields meaningful results.