Computing Fault-Containment Times of Self-Stabilizing Algorithms Using Lumped Markov Chains

The analysis of self-stabilizing algorithms is often limited to the worst case stabilization time starting from an arbitrary state, i.e., a state resulting from a sequence of faults. Considering the fact that these algorithms are intended to provide fault tolerance in the long run, this is not the m...

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Bibliographic Details
Published inAlgorithms Vol. 11; no. 5; p. 58
Main Author Turau, Volker
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.05.2018
Subjects
Algorithms
Coloring
Containment
distributed algorithms
Fault tolerance
Faults
Lumping
Markov analysis
Markov chain
Markov chains
Recovery time
self-stabilization
Upper bounds
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Summary:The analysis of self-stabilizing algorithms is often limited to the worst case stabilization time starting from an arbitrary state, i.e., a state resulting from a sequence of faults. Considering the fact that these algorithms are intended to provide fault tolerance in the long run, this is not the most relevant metric. A common situation is that a running system is an a legitimate state when hit by a single fault. This event has a much higher probability than multiple concurrent faults. Therefore, the worst case time to recover from a single fault is more relevant than the recovery time from a large number of faults. This paper presents techniques to derive upper bounds for the mean time to recover from a single fault for self-stabilizing algorithms based on Markov chains in combination with lumping. To illustrate the applicability of the techniques they are applied to a new self-stabilizing coloring algorithm.
ISSN:1999-4893
1999-4893
DOI:10.3390/a11050058