Computing the fault-containment time of self-stabilizing algorithms using Markov chains and lumping

Abstract

The analysis of self-stabilizing algorithms is in the vast majority of all cases limited to the worst case stabilization time starting from an arbitrary configuration. Considering the fact that these algorithms are intended to provide fault tolerance in the long run this is not the most relevant metric. From a practical point of view the worst case time to recover in case of a single fault is much more crucial. This paper presents techniques to derive upper bounds for the mean time to recover from a single fault for self-stabilizing algorithms Markov chains in combination with lumping. To illustrate the applicability of the techniques they are applied to a self-stabilizing coloring algorithm.