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Algorithms 2018, 11(5), 58; https://doi.org/10.3390/a11050058

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

Institute of Telematics, Hamburg University of Technology, 21073 Hamburg, Germany
An extended abstract of this work appeared at the 19th International Symposium on Stabilization, Safety, and Security of Distributed Systems 2017 in Boston, USA.
Received: 10 February 2018 / Revised: 28 March 2018 / Accepted: 2 May 2018 / Published: 3 May 2018
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Abstract

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. View Full-Text
Keywords: distributed algorithms; fault-tolerance; self-stabilization; Markov chain; lumping distributed algorithms; fault-tolerance; self-stabilization; Markov chain; lumping
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Turau, V. Computing Fault-Containment Times of Self-Stabilizing Algorithms Using Lumped Markov Chains. Algorithms 2018, 11, 58.

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