Abstract
Consider a system composed of n sensors operating in synchronous rounds. In each round an input vector of sensor readings x is produced, where the r-th entry of x is a value, selected in a finite set of potential values, produced by the r-th sensor. The sequence of input vectors is assumed to be smooth: exactly one entry of the vector changes from one round to the next one. The system implements a fault-tolerant averaging consensus function f. This function returns, in each round, a representative output value v of the sensor readings x. Assuming there are a + 1 equal entries of the vector, f is required to return a value that appears at least a + 1 times in x.
We study strategies that minimize the instability of a fault-tolerant consensus system. More precisely, we find the strategy that minimizes, in average, the frequency of output changes over a random walk sequence on input vectors (where each component of the vector corresponds to a particular sensor reading).
This work is partially supported by Programs Ecos C09E04 and IXXI (Complex System Institute, Lyon).
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Rémila, E. (2011). The Optimal Strategy for the Average Long-Lived Consensus. In: Kulikov, A., Vereshchagin, N. (eds) Computer Science – Theory and Applications. CSR 2011. Lecture Notes in Computer Science, vol 6651. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20712-9_33
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DOI: https://doi.org/10.1007/978-3-642-20712-9_33
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